id int64 1 141k | title stringlengths 15 150 | body stringlengths 45 28.5k | tags stringlengths 1 102 | label int64 1 1 | text stringlengths 128 28.6k | source stringclasses 1
value |
|---|---|---|---|---|---|---|
1,692 | Prove fingerprinting | <p>Let $a \neq b$ be two integers from the interval $[1, 2^n].$ Let $p$ be a random prime with $ 1 \le p \le n^c.$ Prove that
$$\text{Pr}_{p \in \mathsf{Primes}}\{a \equiv b \pmod{p}\} \le c \ln(n)/(n^{c-1}).$$</p>

<p>Hint: As a consequence of the prime number theorem, exactly $n/ \ln(n) \pm o(n/\ln(n))$ ... | probability theory information theory coding theory number theory | 1 | Prove fingerprinting -- (probability theory information theory coding theory number theory)
<p>Let $a \neq b$ be two integers from the interval $[1, 2^n].$ Let $p$ be a random prime with $ 1 \le p \le n^c.$ Prove that
$$\text{Pr}_{p \in \mathsf{Primes}}\{a \equiv b \pmod{p}\} \le c \ln(n)/(n^{c-1}).$$</p>

... | habedi/stack-exchange-dataset |
1,697 | Are there undecidable properties of non-turing-complete automata? | <p>Are there undecidable properties of linear bounded automata (avoiding the empty set language trick)? What about for a deterministic finite automaton? (put aside intractability). </p>

<p>I would like to get an example (if possible) of an undecidable problem that is defined <em>without using Turing machines</... | computability automata undecidability | 1 | Are there undecidable properties of non-turing-complete automata? -- (computability automata undecidability)
<p>Are there undecidable properties of linear bounded automata (avoiding the empty set language trick)? What about for a deterministic finite automaton? (put aside intractability). </p>

<p>I would like ... | habedi/stack-exchange-dataset |
1,700 | What is meant by interrupts in the context of operating systems? | <p>I've decided to read <a href="http://rads.stackoverflow.com/amzn/click/0470128720" rel="noreferrer">Operating Systems Concepts</a> by Silberschatz, Galvin Gagne (8th edition) over the summer. I've gotten to a topic that's confusing me - interrupts and their role as it relates to operating systems. </p>

<p>T... | operating systems computer architecture process scheduling | 1 | What is meant by interrupts in the context of operating systems? -- (operating systems computer architecture process scheduling)
<p>I've decided to read <a href="http://rads.stackoverflow.com/amzn/click/0470128720" rel="noreferrer">Operating Systems Concepts</a> by Silberschatz, Galvin Gagne (8th edition) over the summ... | habedi/stack-exchange-dataset |
1,706 | Why is this example a regular language? | <p>Consider this example (taken from this document: <a href="http://www.cs.nott.ac.uk/~txa/g51mal/notes-3x.pdf" rel="nofollow">Showing that language is not regular</a>):</p>

<p>$$L = \{1^n \mid n\text{ is even}\} $$</p>

<p>According to the Pumping Lemma, a language $L$ is regular if :</p>

<ul... | formal languages regular languages proof techniques | 1 | Why is this example a regular language? -- (formal languages regular languages proof techniques)
<p>Consider this example (taken from this document: <a href="http://www.cs.nott.ac.uk/~txa/g51mal/notes-3x.pdf" rel="nofollow">Showing that language is not regular</a>):</p>

<p>$$L = \{1^n \mid n\text{ is even}\} $... | habedi/stack-exchange-dataset |
1,710 | Organisation and Architecture of Quantum Computers | <p>What are devices and their interconnections used alongwith Quantum Processors? Are they compatible with hardware devices like Cache, RAM, Disks of current computers?</p>
 | computer architecture quantum computing | 1 | Organisation and Architecture of Quantum Computers -- (computer architecture quantum computing)
<p>What are devices and their interconnections used alongwith Quantum Processors? Are they compatible with hardware devices like Cache, RAM, Disks of current computers?</p>
 | habedi/stack-exchange-dataset |
1,712 | Randomized String Searching | <p>I need to detect whether a binary pattern $P$ of length $m$ occurs in a binary text $T$ of length $n$ where $m < n$.</p>

<p>I want to state an algorithm that runs in time $O(n)$ where we assume that arithmetic operations on $O(\log_2 n)$ bit numbers can be executed in constant time. The algorithm should ... | algorithms strings searching probabilistic algorithms | 1 | Randomized String Searching -- (algorithms strings searching probabilistic algorithms)
<p>I need to detect whether a binary pattern $P$ of length $m$ occurs in a binary text $T$ of length $n$ where $m < n$.</p>

<p>I want to state an algorithm that runs in time $O(n)$ where we assume that arithmetic operatio... | habedi/stack-exchange-dataset |
1,726 | how do you prove that SAT is NP-complete? | <p>As it is, how do you prove that SAT is NP-complete?</p>

<p>I know what it means by NP-complete, so I do not need an explanation on that.</p>

<p>What I want to know is how do you know that one problem, such as SAT, is NP-complete without resorting to reduction to other problems such as hamiltonian p... | complexity theory satisfiability | 1 | how do you prove that SAT is NP-complete? -- (complexity theory satisfiability)
<p>As it is, how do you prove that SAT is NP-complete?</p>

<p>I know what it means by NP-complete, so I do not need an explanation on that.</p>

<p>What I want to know is how do you know that one problem, such as SAT, is NP... | habedi/stack-exchange-dataset |
1,731 | Proving that recursively enumerable languages are closed against taking prefixes | <p>Define $\mathrm{Prefix} (L) = \{x\mid \exists y .xy \in L \}$. I'd love your help with proving that $\mathsf{RE}$ languages are closed under $\mathrm{Prefix}$.</p>

<p>I know that recursively enumerable languages are formal languages for which there exists a Turing machine that will halt and accept when pr... | formal languages turing machines closure properties | 1 | Proving that recursively enumerable languages are closed against taking prefixes -- (formal languages turing machines closure properties)
<p>Define $\mathrm{Prefix} (L) = \{x\mid \exists y .xy \in L \}$. I'd love your help with proving that $\mathsf{RE}$ languages are closed under $\mathrm{Prefix}$.</p>

<p>I ... | habedi/stack-exchange-dataset |
1,740 | DFA with limited states | <p>Lets $L_z \ := \{ a^i b^i c^i : 0 \leq i < z \}$</p>

<p>$\{a,b,c\} \in \sum^*$</p>

<p>there is a DFA with $\frac{z(z+1)}{2}+1$ states - How can I prove this?</p>

<p>And I need largest possible number $n_z$, for which i can prove that every NFA, which accepts $L_z$, have $n_z$ states, at... | formal languages regular languages automata finite automata | 1 | DFA with limited states -- (formal languages regular languages automata finite automata)
<p>Lets $L_z \ := \{ a^i b^i c^i : 0 \leq i < z \}$</p>

<p>$\{a,b,c\} \in \sum^*$</p>

<p>there is a DFA with $\frac{z(z+1)}{2}+1$ states - How can I prove this?</p>

<p>And I need largest possible numbe... | habedi/stack-exchange-dataset |
1,745 | Recursion for runtime of divide and conquer algorithms | <p>A divide and conquer algorithm's work at a specific level can be simplified into the equation:</p>

<p>$\qquad \displaystyle O\left(n^d\right) \cdot \left(\frac{a}{b^d}\right)^k$</p>

<p>where $n$ is the size of the problem, $a$ is the number of sub problems, $b$ is the factor the size of the problem... | algorithm analysis asymptotics runtime analysis recursion mathematical analysis | 1 | Recursion for runtime of divide and conquer algorithms -- (algorithm analysis asymptotics runtime analysis recursion mathematical analysis)
<p>A divide and conquer algorithm's work at a specific level can be simplified into the equation:</p>

<p>$\qquad \displaystyle O\left(n^d\right) \cdot \left(\frac{a}{b^d}\... | habedi/stack-exchange-dataset |
1,753 | Non-regular Languages? | <blockquote>
 <p><strong>Possible Duplicate:</strong><br>
 <a href="https://cs.stackexchange.com/questions/1031/how-to-prove-that-a-language-is-not-regular">How to prove that a language is not regular?</a> </p>
</blockquote>



<p>Why $L_a$ and $L_b$ are not reguluar?</p>

<p>$L... | formal languages regular languages finite automata | 1 | Non-regular Languages? -- (formal languages regular languages finite automata)
<blockquote>
 <p><strong>Possible Duplicate:</strong><br>
 <a href="https://cs.stackexchange.com/questions/1031/how-to-prove-that-a-language-is-not-regular">How to prove that a language is not regular?</a> </p>
</blockquote>&#... | habedi/stack-exchange-dataset |
1,754 | Explain $\log_2(n)$ squared asymptotic run-time for naive nested parallel CREW PRAM mergesort | <p>On from Page 1 of <a href="http://www.inf.ed.ac.uk/teaching/courses/dapa/note3.pdf" rel="nofollow">these lecture notes</a> it is stated in the final paragraph of the section titled CREW Mergesort:</p>

<blockquote>
 <p>Each such step (in a sequence of $\Theta(\log_2\ n)$ steps) takes
 time $\Theta(... | algorithms complexity theory parallel computing | 1 | Explain $\log_2(n)$ squared asymptotic run-time for naive nested parallel CREW PRAM mergesort -- (algorithms complexity theory parallel computing)
<p>On from Page 1 of <a href="http://www.inf.ed.ac.uk/teaching/courses/dapa/note3.pdf" rel="nofollow">these lecture notes</a> it is stated in the final paragraph of the sect... | habedi/stack-exchange-dataset |
1,762 | Counting trees (order matters) | <p>As a follow up to this <a href="https://cs.stackexchange.com/questions/368/counting-binary-trees">question</a> (the number of rooted binary trees of size n), how many possible binary trees can you have if the nodes are now labeled, so that abc is different than bac cab etc ? In other words, order matters. Certainly ... | binary trees combinatorics trees | 1 | Counting trees (order matters) -- (binary trees combinatorics trees)
<p>As a follow up to this <a href="https://cs.stackexchange.com/questions/368/counting-binary-trees">question</a> (the number of rooted binary trees of size n), how many possible binary trees can you have if the nodes are now labeled, so that abc is d... | habedi/stack-exchange-dataset |
1,771 | Why is a regular language called 'regular'? | <p>I have just completed the first chapter of the <a href="http://www-math.mit.edu/~sipser/book.html"><em>Introduction to the Theory of Computation</em></a> by <em>Michael Sipser</em> which explains the basics of finite automata. </p>

<p>He defines a regular language as anything that can be described by a fini... | formal languages regular languages terminology finite automata history | 1 | Why is a regular language called 'regular'? -- (formal languages regular languages terminology finite automata history)
<p>I have just completed the first chapter of the <a href="http://www-math.mit.edu/~sipser/book.html"><em>Introduction to the Theory of Computation</em></a> by <em>Michael Sipser</em> which explains t... | habedi/stack-exchange-dataset |
1,774 | How do I classify my emulator input optimization problem, and with which algorithm should I approach it? | <p>Due to the nature of the question, I have to include lots of background information (because my question is: how do I narrow this down?) That said, it can be summarized (to the best of my knowledge) as:</p>

<p><strong>What methods exist to find local optimums on extremely large combinatorial search spaces?<... | reference request machine learning combinatorics optimization search problem | 1 | How do I classify my emulator input optimization problem, and with which algorithm should I approach it? -- (reference request machine learning combinatorics optimization search problem)
<p>Due to the nature of the question, I have to include lots of background information (because my question is: how do I narrow this ... | habedi/stack-exchange-dataset |
1,779 | $L(M) = L$ where $M$ is a $TM$ that moves only to the right side so $L$ is regular | <p>Suppose that $L(M) = L$ where $M$ is a $TM$ that moves only to the right side.</p>

<p>I need to Show that $L$ is regular.</p>

<p>I'd relly like some help, I tried to think of any way to prove it but I didn't reach to any smart conclusion. what is it about the only side right moves and the regularit... | formal languages computability turing machines regular languages computation models | 1 | $L(M) = L$ where $M$ is a $TM$ that moves only to the right side so $L$ is regular -- (formal languages computability turing machines regular languages computation models)
<p>Suppose that $L(M) = L$ where $M$ is a $TM$ that moves only to the right side.</p>

<p>I need to Show that $L$ is regular.</p>

<... | habedi/stack-exchange-dataset |
1,789 | Quicksort to find median? | <p>Why is the worst scenario $\mathcal{O}\left(n^2\right)$ when using quicksort to find the median of a set of numbers?</p>

<ul>
<li><p>If your algorithm continually picks a number larger than or smaller than <em>all</em> numbers in the list wouldn't your algorithm fail? For example if the list of numbers ... | algorithms algorithm analysis search algorithms | 1 | Quicksort to find median? -- (algorithms algorithm analysis search algorithms)
<p>Why is the worst scenario $\mathcal{O}\left(n^2\right)$ when using quicksort to find the median of a set of numbers?</p>

<ul>
<li><p>If your algorithm continually picks a number larger than or smaller than <em>all</em> number... | habedi/stack-exchange-dataset |
1,796 | Fast Poisson quantile computation | <p>I am seeking a fast algorithm to compute the following function, a quantile of the <a href="http://en.wikipedia.org/wiki/Poisson_distribution" rel="nofollow">Poisson distribution</a>:
$$f(n, \lambda) = e^{-\lambda} \sum_{k=0}^{n} \frac{\lambda^k}{k!} $$</p>

<p>I can think of an algorithm in $O(n)$, but ... | algorithms numerical analysis | 1 | Fast Poisson quantile computation -- (algorithms numerical analysis)
<p>I am seeking a fast algorithm to compute the following function, a quantile of the <a href="http://en.wikipedia.org/wiki/Poisson_distribution" rel="nofollow">Poisson distribution</a>:
$$f(n, \lambda) = e^{-\lambda} \sum_{k=0}^{n} \frac{\lambda^... | habedi/stack-exchange-dataset |
1,797 | Key secrecy vs Algorithm secrecy | <p>it's a well known statement that </p>

<p>"<em>Cryptographic security must rely on a secret key instead of a secret algorithm</em>."</p>

<p>I would like to ask about some details about it. <em>And which are their differences?</em></p>

<p>I see the obvious thing that for a multi user system,... | cryptography security encryption | 1 | Key secrecy vs Algorithm secrecy -- (cryptography security encryption)
<p>it's a well known statement that </p>

<p>"<em>Cryptographic security must rely on a secret key instead of a secret algorithm</em>."</p>

<p>I would like to ask about some details about it. <em>And which are their differences?</em... | habedi/stack-exchange-dataset |
1,801 | From FACTOR To KNAPSACK | <ol>
<li><p>If there were an algorithm that factored in polynomial time by means of examining each possible factor of a complex number efficiently, could one not also use this algorithm to solve unbounded knapsack problems since two factors can be viewed as one value, say within the set for the knapsack problem, an... | complexity theory np complete integers knapsack problems | 1 | From FACTOR To KNAPSACK -- (complexity theory np complete integers knapsack problems)
<ol>
<li><p>If there were an algorithm that factored in polynomial time by means of examining each possible factor of a complex number efficiently, could one not also use this algorithm to solve unbounded knapsack problems since t... | habedi/stack-exchange-dataset |
1,803 | Extracting non-duplicate cells in a particular matrix with repeated entries | <p>Consider a board of $n$ x $n$ cells, where $n = 2k, k≥2$. Each of the numbers from $S = \left\{1,...,\frac{n^2}{2}\right\}$ is written to two cells so that each cell contains exactly one number.</p>

<p>How can I show that $n$ cells $c_{i, j}$ can be chosen with one cell per row and one cell per column such ... | combinatorics probability theory | 1 | Extracting non-duplicate cells in a particular matrix with repeated entries -- (combinatorics probability theory)
<p>Consider a board of $n$ x $n$ cells, where $n = 2k, k≥2$. Each of the numbers from $S = \left\{1,...,\frac{n^2}{2}\right\}$ is written to two cells so that each cell contains exactly one number.</p>
... | habedi/stack-exchange-dataset |
1,809 | Probabilistic test of matrix multiplication with one-sided error | <p>Given three matrices $A, B,C \in \mathbb{Z}^{n \times n}$ we want to test whether $AB \neq C$. Assume that the arithmetic operations $+$ and $-$ take constant time when applied to numbers from $\mathbb{Z}$.</p>

<p>How can I state an algorithm with one-sided error that runs in $O(n^2)$ time and prove its co... | algorithms probabilistic algorithms matrices linear algebra | 1 | Probabilistic test of matrix multiplication with one-sided error -- (algorithms probabilistic algorithms matrices linear algebra)
<p>Given three matrices $A, B,C \in \mathbb{Z}^{n \times n}$ we want to test whether $AB \neq C$. Assume that the arithmetic operations $+$ and $-$ take constant time when applied to number... | habedi/stack-exchange-dataset |
1,810 | Are there NP problems, not in P and not NP Complete? | <p>Are there any known problems in $\mathsf{NP}$ (and not in $\mathsf{P}$) that aren't $\mathsf{NP}$ Complete? My understanding is that there are no currently known problems where this is the case, but it hasn't been ruled out as a possibility. </p>

<p>If there is a problem that is $\mathsf{NP}$ (and not $\m... | complexity theory np complete p vs np | 1 | Are there NP problems, not in P and not NP Complete? -- (complexity theory np complete p vs np)
<p>Are there any known problems in $\mathsf{NP}$ (and not in $\mathsf{P}$) that aren't $\mathsf{NP}$ Complete? My understanding is that there are no currently known problems where this is the case, but it hasn't been ruled ... | habedi/stack-exchange-dataset |
1,816 | Is there a typed SKI calculus? | <p>Most of us know the correspondence between <a href="http://en.wikipedia.org/wiki/Combinatory_logic">combinatory logic</a> and <a href="http://en.wikipedia.org/wiki/Lambda_calculus">lambda calculus</a>. But I've never seen (maybe I haven't looked deep enough) the equivalent of "typed combinators", corresponding to th... | reference request logic lambda calculus type theory combinatory logic | 1 | Is there a typed SKI calculus? -- (reference request logic lambda calculus type theory combinatory logic)
<p>Most of us know the correspondence between <a href="http://en.wikipedia.org/wiki/Combinatory_logic">combinatory logic</a> and <a href="http://en.wikipedia.org/wiki/Lambda_calculus">lambda calculus</a>. But I've ... | habedi/stack-exchange-dataset |
1,825 | Maximum Enclosing Circle of a Given Radius | <p>I try to find an approach to the following problem:</p>

<blockquote>
 <p>Given the set of point $S$ and radius $r$, find the center point of circle, such that the circle contains the maximum number of points from the set. The running time should be $O(n^2)$.</p>
</blockquote>

<p>At first i... | algorithms computational geometry | 1 | Maximum Enclosing Circle of a Given Radius -- (algorithms computational geometry)
<p>I try to find an approach to the following problem:</p>

<blockquote>
 <p>Given the set of point $S$ and radius $r$, find the center point of circle, such that the circle contains the maximum number of points from the set.... | habedi/stack-exchange-dataset |
1,828 | Polytime and polyspace algorithm for determining the leading intersection of n discrete monotonic functions | <p>Some frontmatter: I'm a recreational computer scientist and employed software engineer. So, pardon if this prompt seems somewhat out of left field -- I routinely play with mathematical simulcra and open problems when I have nothing better to do. </p>

<p>While playing with the <a href="http://en.wikipedia.or... | algorithms reference request discrete mathematics | 1 | Polytime and polyspace algorithm for determining the leading intersection of n discrete monotonic functions -- (algorithms reference request discrete mathematics)
<p>Some frontmatter: I'm a recreational computer scientist and employed software engineer. So, pardon if this prompt seems somewhat out of left field -- I ro... | habedi/stack-exchange-dataset |
1,852 | How to prove that a constrained version of 3SAT in which no literal can occur more than once, is solvable in polynomial time? | <p>I'm trying to work out an assignment (taken from the book <a href="http://www.cs.berkeley.edu/~vazirani/algorithms.html">Algorithms - by S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani</a>, Chap 8, problem 8.6a), and I'm paraphrasing what it states:</p>

<blockquote>
 <p>Given that 3SAT remains NP-co... | complexity theory satisfiability 3 sat | 1 | How to prove that a constrained version of 3SAT in which no literal can occur more than once, is solvable in polynomial time? -- (complexity theory satisfiability 3 sat)
<p>I'm trying to work out an assignment (taken from the book <a href="http://www.cs.berkeley.edu/~vazirani/algorithms.html">Algorithms - by S. Dasgupt... | habedi/stack-exchange-dataset |
1,859 | Rule of thumb to know if a problem could be NP-complete | <p>This question was inspired by <a href="https://stackoverflow.com/questions/10589995/algorithm-have-a-set-of-points-g-that-can-see-other-points-c-need-an-al/10590173#comment13716914_10590173">a comment on StackOverflow</a>.</p>

<p>Apart from knowing NP-complete problems of the Garey Johnson book, and many ot... | complexity theory np complete intuition | 1 | Rule of thumb to know if a problem could be NP-complete -- (complexity theory np complete intuition)
<p>This question was inspired by <a href="https://stackoverflow.com/questions/10589995/algorithm-have-a-set-of-points-g-that-can-see-other-points-c-need-an-al/10590173#comment13716914_10590173">a comment on StackOverflo... | habedi/stack-exchange-dataset |
1,864 | Hoare triple for assignment P{x/E} x:=E {P} | <p>I am trying to understand Hoare logic presented at Wikipedia,
<a href="http://en.wikipedia.org/wiki/Hoare_logic" rel="nofollow">Hoare logic at Wikipedia</a>
Apparently, if I understand correctly, a Hoare triple $$\{P\}~ C ~\{Q\}$$ means</p>

<blockquote>
 <p>if P just before C, then Q holds imm... | logic programming languages semantics hoare logic software verification | 1 | Hoare triple for assignment P{x/E} x:=E {P} -- (logic programming languages semantics hoare logic software verification)
<p>I am trying to understand Hoare logic presented at Wikipedia,
<a href="http://en.wikipedia.org/wiki/Hoare_logic" rel="nofollow">Hoare logic at Wikipedia</a>
Apparently, if I understand co... | habedi/stack-exchange-dataset |
1,883 | Reconstructing Graphs from Degree Distribution | <p>Given a degree distribution, how fast can we construct a graph that follows the given degree distribution? A link or algorithm sketch would be good. The algorithm should report a "no" incase no graph can be constructed and any one example if multiple graphs can be constructed.</p>
 | algorithms graphs | 1 | Reconstructing Graphs from Degree Distribution -- (algorithms graphs)
<p>Given a degree distribution, how fast can we construct a graph that follows the given degree distribution? A link or algorithm sketch would be good. The algorithm should report a "no" incase no graph can be constructed and any one example if multi... | habedi/stack-exchange-dataset |
1,887 | Why isn't this undecidable problem in NP? | <p>Clearly there aren't any undecidable problems in NP. However, according to <a href="http://en.wikipedia.org/wiki/NP_%28complexity%29">Wikipedia</a>:</p>

<blockquote>
 <p>NP is the set of all decision problems for which the instances where the answer is "yes" have [.. proofs that are] verifiable in pol... | complexity theory computability undecidability decision problem | 1 | Why isn't this undecidable problem in NP? -- (complexity theory computability undecidability decision problem)
<p>Clearly there aren't any undecidable problems in NP. However, according to <a href="http://en.wikipedia.org/wiki/NP_%28complexity%29">Wikipedia</a>:</p>

<blockquote>
 <p>NP is the set of all ... | habedi/stack-exchange-dataset |
1,901 | Common idea in Karatsuba, Gauss and Strassen multiplication | <p>The identities used in multiplication algorithms by</p>

<ul>
<li><p><a href="http://en.wikipedia.org/wiki/Karatsuba_algorithm#The_basic_step">Karatsuba</a> (integers)</p></li>
<li><p><a href="http://en.wikipedia.org/wiki/Multiplication_algorithm#Gauss.27s_complex_multiplication_algorithm">Gauss</a> ... | algorithms matrices | 1 | Common idea in Karatsuba, Gauss and Strassen multiplication -- (algorithms matrices)
<p>The identities used in multiplication algorithms by</p>

<ul>
<li><p><a href="http://en.wikipedia.org/wiki/Karatsuba_algorithm#The_basic_step">Karatsuba</a> (integers)</p></li>
<li><p><a href="http://en.wikipedia.org... | habedi/stack-exchange-dataset |
1,905 | An oracle to separate NP from coNP | <p>How to prove that $\mathsf{NP}^A \neq \mathsf{coNP}^A$ ? I am just looking for a such oracle TM $M$ and a recursive language $L(M) = L$ for which this holds. </p>

<p>I know the proof where you show that there is an oracle $A$ such that $\mathsf{P}^A \neq \mathsf{NP}^A$ and an oracle $A$ such that $\mathsf{P... | complexity theory relativization | 1 | An oracle to separate NP from coNP -- (complexity theory relativization)
<p>How to prove that $\mathsf{NP}^A \neq \mathsf{coNP}^A$ ? I am just looking for a such oracle TM $M$ and a recursive language $L(M) = L$ for which this holds. </p>

<p>I know the proof where you show that there is an oracle $A$ such that... | habedi/stack-exchange-dataset |
1,913 | Recurrences and Generating Functions in Algorithms | <p>Combinatorics plays an important role in computer science. We frequently utilize combinatorial methods in both analysis as well as design in algorithms. For example one method for finding a $k$-vertex cover set in a graph might just inspect all $\binom{n}{k}$ possible subsets. While the binomial functions grows expo... | algorithms algorithm analysis combinatorics | 1 | Recurrences and Generating Functions in Algorithms -- (algorithms algorithm analysis combinatorics)
<p>Combinatorics plays an important role in computer science. We frequently utilize combinatorial methods in both analysis as well as design in algorithms. For example one method for finding a $k$-vertex cover set in a g... | habedi/stack-exchange-dataset |
1,914 | Find median of unsorted array in $O(n)$ time | <p>To find the median of an unsorted array, we can make a min-heap in $O(n\log n)$ time for $n$ elements, and then we can extract one by one $n/2$ elements to get the median. But this approach would take $O(n \log n)$ time.</p>

<p>Can we do the same by some method in $O(n)$ time? If we can, then how?</p>
 | algorithms time complexity | 1 | Find median of unsorted array in $O(n)$ time -- (algorithms time complexity)
<p>To find the median of an unsorted array, we can make a min-heap in $O(n\log n)$ time for $n$ elements, and then we can extract one by one $n/2$ elements to get the median. But this approach would take $O(n \log n)$ time.</p>

<p>Can... | habedi/stack-exchange-dataset |
1,915 | What is postorder traversal on this simple tree? | <p>Given the following tree: </p>

<p><img src="https://i.stack.imgur.com/GbJzO.png" alt="tree"></p>

<p>Which traversal method would give as result the following output: CDBEA?</p>

<p>The answer in my study guide is <em>Postorder</em>, but I think postorder would output: DEBCA. Am I wrong?</p>... | algorithms trees | 1 | What is postorder traversal on this simple tree? -- (algorithms trees)
<p>Given the following tree: </p>

<p><img src="https://i.stack.imgur.com/GbJzO.png" alt="tree"></p>

<p>Which traversal method would give as result the following output: CDBEA?</p>

<p>The answer in my study guide is <em>Pos... | habedi/stack-exchange-dataset |
1,917 | Vapnik-Chervonenkis Dimension: why cannot four points on a line be shattered by rectangles? | <p>So I'm reading <em>"Introduction to Machine Learning"</em> 2nd edition, by Bishop, et. all. On page 27 they discuss the Vapnik-Chervonenkis Dimension which is,</p>

<blockquote>
 <p><em>"The maximum number of points that can be shattered by H [the hypothesis class] is called the Vapnik-Chervonenkis (VC... | machine learning vc dimension | 1 | Vapnik-Chervonenkis Dimension: why cannot four points on a line be shattered by rectangles? -- (machine learning vc dimension)
<p>So I'm reading <em>"Introduction to Machine Learning"</em> 2nd edition, by Bishop, et. all. On page 27 they discuss the Vapnik-Chervonenkis Dimension which is,</p>

<blockquote>
... | habedi/stack-exchange-dataset |
1,918 | Preprocess an array for counting an element in a slice (reduction to RMQ?) | <p>Given an array $a_1,\ldots,a_n$ of natural numbers $\leq k$, where $k$ is a constant, I want to answer in $O(1)$ queries of the form: "how many times does $m$ appear in the array between indices $i$ and $j$"?</p>

<p>The array should be preprocessed in linear time. In particular I'd like to know if there's a... | algorithms arrays algorithm design | 1 | Preprocess an array for counting an element in a slice (reduction to RMQ?) -- (algorithms arrays algorithm design)
<p>Given an array $a_1,\ldots,a_n$ of natural numbers $\leq k$, where $k$ is a constant, I want to answer in $O(1)$ queries of the form: "how many times does $m$ appear in the array between indices $i$ and... | habedi/stack-exchange-dataset |
1,919 | Equality testing of arrays and integers in a procedural language | <p>In terms of references and their implementation on the heap and the stack, how is
equality testing for arrays different from that for integers? </p>

<p>This is to do with Java programming, if you have a stack and a heap, would equality testing for example <code>j == i</code> be the same for arrays and f... | programming languages arrays semantics equality memory management | 1 | Equality testing of arrays and integers in a procedural language -- (programming languages arrays semantics equality memory management)
<p>In terms of references and their implementation on the heap and the stack, how is
equality testing for arrays different from that for integers? </p>

<p>This is to do wi... | habedi/stack-exchange-dataset |
1,921 | Making random sources uniformly distributed | <p>How do I build a random source that outputs the bits 0 and 1 with $prob(0) = prob(1) = 0.5$. We have access to another random source $S$ that outputs $a$ or $b$ with independent probabilities $prob(a)$ and $prob(b) = 1 - prob(a)$ that are unknown to us.</p>

<p>How do I state an algorithm that does the job a... | algorithms probability theory randomized algorithms randomness | 1 | Making random sources uniformly distributed -- (algorithms probability theory randomized algorithms randomness)
<p>How do I build a random source that outputs the bits 0 and 1 with $prob(0) = prob(1) = 0.5$. We have access to another random source $S$ that outputs $a$ or $b$ with independent probabilities $prob(a)$ and... | habedi/stack-exchange-dataset |
1,922 | Deterministic and randomized communication complexity of set equality | <p>Two processors $A, B$ with inputs $a \in \{0, 1\}^n$ (for $A$) and $b \in \{0, 1\}^n$
(for $B$) want to decide whether $a = b$. $A$ does not know $B$’s input and vice versa.</p>

<p>A can send a message $m(a) \in \{0, 1\}^n$ which $B$ can use to decide $a = b$. The communication and computation rules ... | algorithms probability theory randomized algorithms | 1 | Deterministic and randomized communication complexity of set equality -- (algorithms probability theory randomized algorithms)
<p>Two processors $A, B$ with inputs $a \in \{0, 1\}^n$ (for $A$) and $b \in \{0, 1\}^n$
(for $B$) want to decide whether $a = b$. $A$ does not know $B$’s input and vice versa.</p>
&#... | habedi/stack-exchange-dataset |
1,923 | Online generation of uniform samples | <p>A source provides a stream of items $x_1, x_2,\dots$ . At each step $n$ we want to save a random sample $S_n \subseteq \{ (x_i, i)|1 \le i \le n\}$ of size $k$, i.e. $S_n$ should be a uniformly chosen sample from all $\tbinom{n}{k}$ possible samples consisting of seen items. So at each step $n \ge k$ we must decide ... | algorithms probability theory randomized algorithms randomness online algorithms | 1 | Online generation of uniform samples -- (algorithms probability theory randomized algorithms randomness online algorithms)
<p>A source provides a stream of items $x_1, x_2,\dots$ . At each step $n$ we want to save a random sample $S_n \subseteq \{ (x_i, i)|1 \le i \le n\}$ of size $k$, i.e. $S_n$ should be a uniformly ... | habedi/stack-exchange-dataset |
1,936 | When do structural hazards occur in pipelined architectures? | <p>I'm looking for some relatively simple examples of when <a href="http://en.wikipedia.org/wiki/Hazard_%28computer_architecture%29#Structural_hazards">structural hazards</a> occur in a pipelined architecture.</p>

<p>The only scenario I can think of is when memory needs to be accessed during different stages o... | computer architecture cpu pipelines | 1 | When do structural hazards occur in pipelined architectures? -- (computer architecture cpu pipelines)
<p>I'm looking for some relatively simple examples of when <a href="http://en.wikipedia.org/wiki/Hazard_%28computer_architecture%29#Structural_hazards">structural hazards</a> occur in a pipelined architecture.</p>
... | habedi/stack-exchange-dataset |
1,940 | If a point is a vertex of convex hull | <p>The exercise is </p>

<blockquote>
 <p>Given a set of point $S$ and a point $p$. Decide in $O(n)$ time if $p$ is a vertex of convex polygon formed from points of $S$.</p>
</blockquote>

<p>The problem is I am a little bit confused with time complexity $O(n)$. The more naive solution would b... | algorithms computational geometry | 1 | If a point is a vertex of convex hull -- (algorithms computational geometry)
<p>The exercise is </p>

<blockquote>
 <p>Given a set of point $S$ and a point $p$. Decide in $O(n)$ time if $p$ is a vertex of convex polygon formed from points of $S$.</p>
</blockquote>

<p>The problem is I am a lit... | habedi/stack-exchange-dataset |
1,949 | Use closure properties to transform languages to $L := \{ a^nb^n : n\in \mathbb N \}$ | <p>For the purpose of proving that they are not regular, what closure properties can I use to transform the languages</p>

<ol>
<li>$L_a = \{ a^*cw \mid w \in \{a,b \}^* \land |w|_a = |w|_b \}$ and</li>
<li>$L_b = \{ab^{i_1}ab^{i_2}\ldots ab^{i_n} \mid i_j∈\mathbb N \land \exists j∈[1,n] \ i_j \not=... | formal languages context free closure properties | 1 | Use closure properties to transform languages to $L := \{ a^nb^n : n\in \mathbb N \}$ -- (formal languages context free closure properties)
<p>For the purpose of proving that they are not regular, what closure properties can I use to transform the languages</p>

<ol>
<li>$L_a = \{ a^*cw \mid w \in \{a,b \}... | habedi/stack-exchange-dataset |
1,957 | Master theorem not applicable? | <p>Given the following recursive equation</p>

<p>$$ T(n) = 2T\left(\frac{n}{2}\right)+n\log n$$ we want to apply the Master theorem and note that</p>

<p>$$ n^{\log_2(2)} = n.$$</p>

<p>Now we check the first two cases for $\varepsilon > 0$, that is whether</p>

<ul>
<li>$n\log n... | proof techniques asymptotics recurrence relation master theorem | 1 | Master theorem not applicable? -- (proof techniques asymptotics recurrence relation master theorem)
<p>Given the following recursive equation</p>

<p>$$ T(n) = 2T\left(\frac{n}{2}\right)+n\log n$$ we want to apply the Master theorem and note that</p>

<p>$$ n^{\log_2(2)} = n.$$</p>

<p>Now we ch... | habedi/stack-exchange-dataset |
1,958 | Relation between simple and regular grammars | <p>I am reading "An Introduction to Formal Languages and Automata" written by Peter Linz and after reading the first five chapters I face below problem with
simple and regular (especially right linear) grammars which are very similar to each other.</p>

<p>What relation exists between these? What is the dif... | regular languages automata context free formal grammars | 1 | Relation between simple and regular grammars -- (regular languages automata context free formal grammars)
<p>I am reading "An Introduction to Formal Languages and Automata" written by Peter Linz and after reading the first five chapters I face below problem with
simple and regular (especially right linear) grammars... | habedi/stack-exchange-dataset |
1,959 | How to go from a recurrence relation to a final complexity | <p>I have an algorithm, shown below, that I need to analyze. Because it's recursive in nature I set up a recurrence relation. </p>

<pre><code>//Input: Adjacency matrix A[1..n, 1..n]) of an undirected graph G 
//Output: 1 (true) if G is complete and 0 (false) otherwise 
GraphComplete(A[1..n, 1..n]) {... | algorithms algorithm analysis runtime analysis recursion | 1 | How to go from a recurrence relation to a final complexity -- (algorithms algorithm analysis runtime analysis recursion)
<p>I have an algorithm, shown below, that I need to analyze. Because it's recursive in nature I set up a recurrence relation. </p>

<pre><code>//Input: Adjacency matrix A[1..n, 1..n]) of an ... | habedi/stack-exchange-dataset |
1,970 | Data structure with search, insert and delete in amortised time $O(1)$? | <p>Is there a data structure to maintain an ordered list that supports the following operations in $O(1)$ amortized time? </p>

<ul>
<li><p><strong>GetElement(k)</strong>: Return the $k$th element of the list.</p></li>
<li><p><strong>InsertAfter(x,y)</strong>: Insert the new element y into the list imme... | data structures time complexity asymptotics amortized analysis | 1 | Data structure with search, insert and delete in amortised time $O(1)$? -- (data structures time complexity asymptotics amortized analysis)
<p>Is there a data structure to maintain an ordered list that supports the following operations in $O(1)$ amortized time? </p>

<ul>
<li><p><strong>GetElement(k)</stron... | habedi/stack-exchange-dataset |
1,972 | Decide whether a context-free languages can be accepted by a deterministic pushdown automaton | <p>Given a context-free grammar G, there exists a Nondeterministic Pushdown Automaton N that accepts exactly the language G accepts. (and visa versa)</p>

<p>There <strong>may</strong> also exist a Deterministic Pushdown Automaton D that accepts exactly the language G accepts too. It depends on the grammar.</p... | automata context free pushdown automata | 1 | Decide whether a context-free languages can be accepted by a deterministic pushdown automaton -- (automata context free pushdown automata)
<p>Given a context-free grammar G, there exists a Nondeterministic Pushdown Automaton N that accepts exactly the language G accepts. (and visa versa)</p>

<p>There <strong>m... | habedi/stack-exchange-dataset |
1,974 | Compare-and-Swap in an RDBMS for custom locks and lock escalation | <p>I'm applying the Compare-and-Swap technique to a SQL database to create custom row-level locking in my dataset, allowing for safe READ UNCOMMITTED isolation at the database level.</p>

<p>The Resource table includes a LockOwner <code>GUID</code> and a IsLocked <code>BIT</code> field. To acquire a lock, a di... | concurrency database theory | 1 | Compare-and-Swap in an RDBMS for custom locks and lock escalation -- (concurrency database theory)
<p>I'm applying the Compare-and-Swap technique to a SQL database to create custom row-level locking in my dataset, allowing for safe READ UNCOMMITTED isolation at the database level.</p>

<p>The Resource table inc... | habedi/stack-exchange-dataset |
1,979 | Proof that $\{⟨M⟩ ∣ L(M) \mbox{ is context-free} \}$ is not (co-)recursively enumerable | <p>I would like to use your help with the following problem:</p>

<p>$L=\{⟨M⟩ ∣ L(M) \mbox{ is context-free} \}$. Show that $L \notin RE \cup CoRE$.</p>

<p>I know that to prove $L\notin RE$, it is enough to find a language $L'$ such that $L'\notin RE$ and show that there is a reduction from $L'$ to $L... | formal languages computability context free turing machines | 1 | Proof that $\{⟨M⟩ ∣ L(M) \mbox{ is context-free} \}$ is not (co-)recursively enumerable -- (formal languages computability context free turing machines)
<p>I would like to use your help with the following problem:</p>

<p>$L=\{⟨M⟩ ∣ L(M) \mbox{ is context-free} \}$. Show that $L \notin RE \cup CoRE$.</p>
&... | habedi/stack-exchange-dataset |
1,986 | Prove that regular languages are closed under the cycle operator | <p>I've got in a few days an exam and have problems to solve this task.</p>

<p>Let $L$ be a regular language over the alphabet $\Sigma$. We have the operation 
$\operatorname{cycle}(L) = \{ xy \mid x,y\in \Sigma^* \text{ and } yx\in L\}$
And now we should show that $\operatorname{cycle}(L)$ is also reg... | formal languages regular languages finite automata closure properties | 1 | Prove that regular languages are closed under the cycle operator -- (formal languages regular languages finite automata closure properties)
<p>I've got in a few days an exam and have problems to solve this task.</p>

<p>Let $L$ be a regular language over the alphabet $\Sigma$. We have the operation 
$\opera... | habedi/stack-exchange-dataset |
1,990 | Is there an undecidable finite language of finite words? | <p>Is there <em>a need</em> for $L\subseteq \Sigma^*$ to be <em>infinite</em> to be undecidable?</p>

<p>I mean what if we choose a language $L'$ be a <em>bounded finite version of</em> $L\subseteq \Sigma^*$, that is $|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$. Is it possible for $L'$ to be an unde... | formal languages computability undecidability | 1 | Is there an undecidable finite language of finite words? -- (formal languages computability undecidability)
<p>Is there <em>a need</em> for $L\subseteq \Sigma^*$ to be <em>infinite</em> to be undecidable?</p>

<p>I mean what if we choose a language $L'$ be a <em>bounded finite version of</em> $L\subseteq \Sigma... | habedi/stack-exchange-dataset |
1,993 | Why absence of surjection with the power set is not enough to prove the existence of an undecidable language? | <p>From this statement </p>

<blockquote>
 <p>As there is no surjection from $\mathbb{N}$ onto $\mathcal{P}(\mathbb{N})$, thus there must exist an undecidable language.</p>
</blockquote>

<p>I would like to understand why similar reasoning does not work with a <em>finite</em> set $B$ which also... | formal languages computability undecidability | 1 | Why absence of surjection with the power set is not enough to prove the existence of an undecidable language? -- (formal languages computability undecidability)
<p>From this statement </p>

<blockquote>
 <p>As there is no surjection from $\mathbb{N}$ onto $\mathcal{P}(\mathbb{N})$, thus there must exist an... | habedi/stack-exchange-dataset |
1,998 | Low-degree nodes in sparse graphs | <p>Let $G = (V,E)$ be a graph having $n$ vertices, none of which are isolated, and $n−1$ edges, where $n \geq 2$. Show that $G$ contains at least two vertices of degree one.</p>

<p>I have tried to solve this problem by using the property $\sum_{v \in V} \operatorname{deg}(v) = 2|E|$. Can this problem be solve... | graphs proof techniques | 1 | Low-degree nodes in sparse graphs -- (graphs proof techniques)
<p>Let $G = (V,E)$ be a graph having $n$ vertices, none of which are isolated, and $n−1$ edges, where $n \geq 2$. Show that $G$ contains at least two vertices of degree one.</p>

<p>I have tried to solve this problem by using the property $\sum_{v \... | habedi/stack-exchange-dataset |
2,002 | Is the set of LL(*) grammars the same as the set of CFG grammars? | <p>Is the set of LL(*) grammars the same as the set of context-free grammars?</p>
 | formal languages formal grammars | 1 | Is the set of LL(*) grammars the same as the set of CFG grammars? -- (formal languages formal grammars)
<p>Is the set of LL(*) grammars the same as the set of context-free grammars?</p>
 | habedi/stack-exchange-dataset |
2,006 | Machine Learning algorithms based on "structural risk minimization"? | <p>Which machine learning algorithms (besides SVM's) use the principle of <a href="https://en.wikipedia.org/wiki/Structural_risk_minimization">structural risk minimization</a>?</p>
 | reference request machine learning | 1 | Machine Learning algorithms based on "structural risk minimization"? -- (reference request machine learning)
<p>Which machine learning algorithms (besides SVM's) use the principle of <a href="https://en.wikipedia.org/wiki/Structural_risk_minimization">structural risk minimization</a>?</p>
 | habedi/stack-exchange-dataset |
2,011 | DLOGTIME complexity class and testing the length of the input string | <p>I read that testing the length of the input string is in DLOGTIME.</p>

<p>The question is how can testing the length of the input string be in DLOGTIME?</p>

<p>$\text{DLOGTIME} = O(\log n)$, so what number would be in $n$? (as it seems that $n$ is definitely not the length of the input string..... ... | complexity theory | 1 | DLOGTIME complexity class and testing the length of the input string -- (complexity theory)
<p>I read that testing the length of the input string is in DLOGTIME.</p>

<p>The question is how can testing the length of the input string be in DLOGTIME?</p>

<p>$\text{DLOGTIME} = O(\log n)$, so what number w... | habedi/stack-exchange-dataset |
2,016 | How to convert finite automata to regular expressions? | <p>Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms, e.g. <a href="http://en.wikipedia.org/wiki/Thompson%27s_construction_algorithm">Thompson's algorithm</a>. The other direction seems to be more tedious, though, and sometimes the resulting expressions are... | algorithms formal languages finite automata regular expressions reference question | 1 | How to convert finite automata to regular expressions? -- (algorithms formal languages finite automata regular expressions reference question)
<p>Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms, e.g. <a href="http://en.wikipedia.org/wiki/Thompson%27s_cons... | habedi/stack-exchange-dataset |
2,028 | Finding small node sets that can not be avoided on paths from source to sink | <p>In a directed graph with a starting node and an ending node, how to find a small (doesn't have to be smallest. <10 for example) set S of nodes such that every possible path from the starting node to the ending node contains at least one member of set S. The graph may have loops. This may be NP hard. Is there an a... | algorithms graphs | 1 | Finding small node sets that can not be avoided on paths from source to sink -- (algorithms graphs)
<p>In a directed graph with a starting node and an ending node, how to find a small (doesn't have to be smallest. <10 for example) set S of nodes such that every possible path from the starting node to the ending node... | habedi/stack-exchange-dataset |
2,031 | Can constraint satisfaction problems be solved with Prolog? | <p>Is <a href="http://iggyfernandez.wordpress.com/2012/05/21/sql-vs-nosql-third-international-nocoug-sql-nosql-challenge-sponsored-by-pythian/">"party attendance"</a> type of problems solvable in Prolog? For example:</p>

<blockquote>
 <p>Burdock Muldoon and Carlotta Pinkstone both said they would come if ... | logic constraint programming prolog logic programming | 1 | Can constraint satisfaction problems be solved with Prolog? -- (logic constraint programming prolog logic programming)
<p>Is <a href="http://iggyfernandez.wordpress.com/2012/05/21/sql-vs-nosql-third-international-nocoug-sql-nosql-challenge-sponsored-by-pythian/">"party attendance"</a> type of problems solvable in Prolo... | habedi/stack-exchange-dataset |
2,040 | Ternary processing instead of Binary | <p>Most of the computers available today are designed to work with binary system. It comes from the fact that information comes in two natural form, <strong>true</strong> or <strong>false</strong>.</p>

<p>We humans accept another form of information called "maybe" :)</p>

<p>I know there are ternary pr... | computer architecture | 1 | Ternary processing instead of Binary -- (computer architecture)
<p>Most of the computers available today are designed to work with binary system. It comes from the fact that information comes in two natural form, <strong>true</strong> or <strong>false</strong>.</p>

<p>We humans accept another form of informati... | habedi/stack-exchange-dataset |
2,049 | How many layers should a neural network have? | <p>Are there any advantages of having more than 2 hidden layers in a Neural Network?</p>

<p>I've seen some places that recommend it, others prove that there is no advantage.</p>

<p>Which one is right?</p>
 | artificial intelligence neural networks neural computing | 1 | How many layers should a neural network have? -- (artificial intelligence neural networks neural computing)
<p>Are there any advantages of having more than 2 hidden layers in a Neural Network?</p>

<p>I've seen some places that recommend it, others prove that there is no advantage.</p>

<p>Which one is ... | habedi/stack-exchange-dataset |
2,064 | Block detection in repeated stream | <p>I need to recover a data block from a repeated stream of data. I'm looking to see what algorithms may already exist for this as it does not feel like a novel situation.</p>

<p>Here are the specifics:</p>

<ol>
<li>There is an N-length block of data contained in a stream</li>
<li>The block is... | algorithms online algorithms communication protocols | 1 | Block detection in repeated stream -- (algorithms online algorithms communication protocols)
<p>I need to recover a data block from a repeated stream of data. I'm looking to see what algorithms may already exist for this as it does not feel like a novel situation.</p>

<p>Here are the specifics:</p>

<o... | habedi/stack-exchange-dataset |
2,067 | What does this performance formula mean? | <p>I have to make a quick clustering program but the following formula is gibberish to me:</p>

<blockquote>
 <p>$\operatorname{Perf}(X,C) = \sum\limits_{i=1}^n\min\{||X_i-C_l||^2 \mid l = 1,...,K\}$</p>
 
 <p>where $X$ is a set of multi-dimensional data and $C$ is a set of centroids for each d... | algorithms terminology evolutionary computing | 1 | What does this performance formula mean? -- (algorithms terminology evolutionary computing)
<p>I have to make a quick clustering program but the following formula is gibberish to me:</p>

<blockquote>
 <p>$\operatorname{Perf}(X,C) = \sum\limits_{i=1}^n\min\{||X_i-C_l||^2 \mid l = 1,...,K\}$</p>
 &#x... | habedi/stack-exchange-dataset |
2,076 | Could someone suggest me a good introductory book or an article on graph clustering? | <p>For my pet project I need to cluster some data which could be easily represented as graph, so I want to use this as an opportunity to educate myself and play with various algorithms. I'd prefer the book on graph clustering as it often more self contained but articles are fine too. Back in the days I used to work in ... | algorithms graphs reference request books | 1 | Could someone suggest me a good introductory book or an article on graph clustering? -- (algorithms graphs reference request books)
<p>For my pet project I need to cluster some data which could be easily represented as graph, so I want to use this as an opportunity to educate myself and play with various algorithms. I'... | habedi/stack-exchange-dataset |
2,079 | Determine missing number in data stream | <p>We receive a stream of $n-1$ pairwise different numbers from the set $\left\{1,\dots,n\right\}$.</p>

<p>How can I determine the missing number with an algorithm that reads the stream once and uses a memory of only $O(\log_2 n)$ bits?</p>
 | algorithms integers online algorithms | 1 | Determine missing number in data stream -- (algorithms integers online algorithms)
<p>We receive a stream of $n-1$ pairwise different numbers from the set $\left\{1,\dots,n\right\}$.</p>

<p>How can I determine the missing number with an algorithm that reads the stream once and uses a memory of only $O(\log_2 n... | habedi/stack-exchange-dataset |
2,081 | Is there a context free, non-regular language $L$, for which $L^*$ is regular? | <p>I know that there are non-regular languages, so that $L^*$ is regular, but all examples I can find are context-sensitive but not context free.</p>

<p>In case there are none how do you prove it?</p>
 | formal languages context free regular languages | 1 | Is there a context free, non-regular language $L$, for which $L^*$ is regular? -- (formal languages context free regular languages)
<p>I know that there are non-regular languages, so that $L^*$ is regular, but all examples I can find are context-sensitive but not context free.</p>

<p>In case there are none how... | habedi/stack-exchange-dataset |
2,088 | Complete Problems for $DSPACE(\log(n)^k)$ | <p>We know that the $polyL$-hierarchy doesn't have complete problems, as it would conflict with the space hierarchy theorem. But: Are there complete problems for each level of this hierarchy?</p>

<p>To be precise: Does the class $DSPACE(\log(n)^k)$ have complete problems under $L$-reductions for each $k > 0... | complexity theory reductions space complexity | 1 | Complete Problems for $DSPACE(\log(n)^k)$ -- (complexity theory reductions space complexity)
<p>We know that the $polyL$-hierarchy doesn't have complete problems, as it would conflict with the space hierarchy theorem. But: Are there complete problems for each level of this hierarchy?</p>

<p>To be precise: Does... | habedi/stack-exchange-dataset |
2,100 | Need help understanding this optimization problem on graphs | <p>Has anyone seen this problem before? It's suppose to be NP-complete.</p>

<blockquote>
 <p>We are given vertices $V_1,\dots ,V_n$ and possible parent sets for each vertex. Each parent set has an associated cost. Let $O$ be an ordering (a permutation) of the vertices. We say that a parent set of a vertex... | algorithms graphs terminology optimization | 1 | Need help understanding this optimization problem on graphs -- (algorithms graphs terminology optimization)
<p>Has anyone seen this problem before? It's suppose to be NP-complete.</p>

<blockquote>
 <p>We are given vertices $V_1,\dots ,V_n$ and possible parent sets for each vertex. Each parent set has an a... | habedi/stack-exchange-dataset |
2,101 | Finding the point nearest to the x-axis over some segment | <p>I have problem with solving the following exercise</p>

<blockquote>
 <p>Given the set $P$ on $n$ points in two dimensions, build in time $O(n\log n)$ a data structure of $P$ such that given a horizontal segment $s$ find the first point that $s$ touches when moving upwards from the x-axis in time $O(\lo... | algorithms computational geometry | 1 | Finding the point nearest to the x-axis over some segment -- (algorithms computational geometry)
<p>I have problem with solving the following exercise</p>

<blockquote>
 <p>Given the set $P$ on $n$ points in two dimensions, build in time $O(n\log n)$ a data structure of $P$ such that given a horizontal seg... | habedi/stack-exchange-dataset |
2,103 | Depth-2 circuits with OR and MOD gates are not universal? | <p>It is well-known that every boolean function $f:\{0,1\}^n\to \{0,1\}$ can be realized using a boolean circuit of depth 2 (over the variables, their negation and constant values) containing AND gates in the first level and one single OR gate in the upper level; this is simply the <a href="http://en.wikipedia.org/wiki... | complexity theory logic circuits | 1 | Depth-2 circuits with OR and MOD gates are not universal? -- (complexity theory logic circuits)
<p>It is well-known that every boolean function $f:\{0,1\}^n\to \{0,1\}$ can be realized using a boolean circuit of depth 2 (over the variables, their negation and constant values) containing AND gates in the first level and... | habedi/stack-exchange-dataset |
2,110 | Space bounded Turing Machine - clarification on Computational Complexity (book: Arora-Barak ) question 4.1 | <p>I have the following question from <a href="http://www.cs.princeton.edu/theory/complexity/" rel="noreferrer">Computational Complexity - A modern Approach</a> by Sanjeev Arora and Boaz Barak:</p>

<blockquote>
 <p><em>[Q 4.1]</em><br>
 Prove the existence of a universal TM for space bounded computat... | complexity theory terminology turing machines space complexity | 1 | Space bounded Turing Machine - clarification on Computational Complexity (book: Arora-Barak ) question 4.1 -- (complexity theory terminology turing machines space complexity)
<p>I have the following question from <a href="http://www.cs.princeton.edu/theory/complexity/" rel="noreferrer">Computational Complexity - A mode... | habedi/stack-exchange-dataset |
2,118 | Number of clique in random graphs | <p>There is a family of random graphs $G(n, p)$ with $n$ nodes (<a href="https://en.wikipedia.org/wiki/Random_graph">due to Gilbert</a>). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_k$ be the number of cliques of size $k$ in $G(n, p)$.</p>

<p>I know that $\mathbb{E}... | graphs combinatorics probability theory random graphs | 1 | Number of clique in random graphs -- (graphs combinatorics probability theory random graphs)
<p>There is a family of random graphs $G(n, p)$ with $n$ nodes (<a href="https://en.wikipedia.org/wiki/Random_graph">due to Gilbert</a>). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_... | habedi/stack-exchange-dataset |
2,127 | Context-free grammar for $\{ a^n b^m a^{n+m} \}$ | <p>I've got a problem with this task. I should declare a context-free grammar for this language:</p>

<p>$\qquad \displaystyle L := \{\, a^nb^ma^{n+m} : n,m \in \mathbb{N}\,\}$</p>

<p>My idea is: We need a start symbol, for example $S$. I know that I can generate the first $a$ and the last $a$ by $S \t... | formal languages context free formal grammars | 1 | Context-free grammar for $\{ a^n b^m a^{n+m} \}$ -- (formal languages context free formal grammars)
<p>I've got a problem with this task. I should declare a context-free grammar for this language:</p>

<p>$\qquad \displaystyle L := \{\, a^nb^ma^{n+m} : n,m \in \mathbb{N}\,\}$</p>

<p>My idea is: We need... | habedi/stack-exchange-dataset |
2,149 | Any very user friendly resources on the Baum-Welch algorithm? | <p>I'd like to understand the <a href="https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm" rel="nofollow">Baum-Welch algorithm</a>. I liked <a href="http://www.youtube.com/watch?v=7zDARfKVm7s&feature=related" rel="nofollow">this video</a> on the Forward-Backward algorithm so I'd like a similar one for Baum-... | algorithms reference request hidden markov models | 1 | Any very user friendly resources on the Baum-Welch algorithm? -- (algorithms reference request hidden markov models)
<p>I'd like to understand the <a href="https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm" rel="nofollow">Baum-Welch algorithm</a>. I liked <a href="http://www.youtube.com/watch?v=7zDARfKVm7s&... | habedi/stack-exchange-dataset |
2,152 | How to prove correctness of a shuffle algorithm? | <p>I have two ways of producing a list of items in a random order and would like to determine if they are equally fair (unbiased).</p>

<p>The first method I use is to construct the entire list of elements and then do a shuffle on it (say a Fisher-Yates shuffle). The second method is more of an iterative method... | algorithms proof techniques randomized algorithms correctness proof randomness | 1 | How to prove correctness of a shuffle algorithm? -- (algorithms proof techniques randomized algorithms correctness proof randomness)
<p>I have two ways of producing a list of items in a random order and would like to determine if they are equally fair (unbiased).</p>

<p>The first method I use is to construct t... | habedi/stack-exchange-dataset |
2,154 | Swap space management during pure demand paging | <p>The following is a doubt that I came across while doing a OS home assignment - however, it seems more concept-based than a straightforward coding question, so IMHO I don't think the homework tag is appropriate for this.</p>

<p>In a pure demand paging scheme for multiple processes running at the same time, g... | operating systems memory allocation virtual memory paging memory management | 1 | Swap space management during pure demand paging -- (operating systems memory allocation virtual memory paging memory management)
<p>The following is a doubt that I came across while doing a OS home assignment - however, it seems more concept-based than a straightforward coding question, so IMHO I don't think the homewo... | habedi/stack-exchange-dataset |
2,155 | How to read typing rules? | <p>I started reading more and more language research papers. I find it very interesting and a good way to learn more about programming in general. However, there usually comes a section where I always struggle with (take for instance part three of <a href="http://math.andrej.com/wp-content/uploads/2012/03/eff.pdf">this... | logic reference request terminology type theory | 1 | How to read typing rules? -- (logic reference request terminology type theory)
<p>I started reading more and more language research papers. I find it very interesting and a good way to learn more about programming in general. However, there usually comes a section where I always struggle with (take for instance part th... | habedi/stack-exchange-dataset |
2,157 | NP-Completeness of a Graph Coloring Problem | <p><strong>Alternative Formulation</strong></p>

<p>I came up with an alternative formulation to the below problem. The alternative formulation is actually a special case of the problem bellow and uses bipartite graphs to describe the problem. However, I believe that the alternative formulation is still NP-hard... | complexity theory graphs np complete | 1 | NP-Completeness of a Graph Coloring Problem -- (complexity theory graphs np complete)
<p><strong>Alternative Formulation</strong></p>

<p>I came up with an alternative formulation to the below problem. The alternative formulation is actually a special case of the problem bellow and uses bipartite graphs to desc... | habedi/stack-exchange-dataset |
2,164 | Transform in linear grammar | <p>i have the following regular grammar :
$$S \rightarrow aS | cS | bQ_1$$
$$Q_1 \rightarrow bQ_2$$
$$Q_2 \rightarrow aQ_3 | cQ_3 | bQ_1$$
$$Q_3 \rightarrow aQ_4 | cQ_4$$ 
$$Q_4 \rightarrow \varepsilon$$</p>

<p>The question is to transform that into a linear grammar with less nonterminals t... | formal grammars | 1 | Transform in linear grammar -- (formal grammars)
<p>i have the following regular grammar :
$$S \rightarrow aS | cS | bQ_1$$
$$Q_1 \rightarrow bQ_2$$
$$Q_2 \rightarrow aQ_3 | cQ_3 | bQ_1$$
$$Q_3 \rightarrow aQ_4 | cQ_4$$ 
$$Q_4 \rightarrow \varepsilon$$</p>

<p>The question is to transform th... | habedi/stack-exchange-dataset |
2,166 | generation of linear grammar | <p>We have the following linear grammar:
$$E \rightarrow aO | bO | bbE | bb$$
$$O \rightarrow aE | bE | abaE | aba$$
Does the linear grammar generate a regular language, if yes why ?
Our alphabet is $\Sigma$ = {a,b} and our nonterminals are E and O. We begin by E.</p>
 | formal languages formal grammars | 1 | generation of linear grammar -- (formal languages formal grammars)
<p>We have the following linear grammar:
$$E \rightarrow aO | bO | bbE | bb$$
$$O \rightarrow aE | bE | abaE | aba$$
Does the linear grammar generate a regular language, if yes why ?
Our alphabet is $\Sigma$ = {a,b} and our nonterminals ... | habedi/stack-exchange-dataset |
2,175 | Constructing a data structure for a computer algebra system | <p>In thinking about how to approach this problem I think several things will be required, some tivial:</p>

<ol>
<li>An expression tree where non-leaf node is an operation (not sure if that part is redundant), but not every node has just two children.</li>
<li>All nodes for operations have a defined nu... | data structures computer algebra mathematical software | 1 | Constructing a data structure for a computer algebra system -- (data structures computer algebra mathematical software)
<p>In thinking about how to approach this problem I think several things will be required, some tivial:</p>

<ol>
<li>An expression tree where non-leaf node is an operation (not sure if th... | habedi/stack-exchange-dataset |
2,184 | Massalin's Synthesis Quajects equivalent to ASM generating macros used in Game Oriented Assembly LISP? | <p><a href="http://valerieaurora.org/synthesis/SynthesisOS/abs.html" rel="nofollow">Alexia Massalin's Dissertation on Synthesis</a> was a Phd thesis on Operating Systems that contained a concept called 'Quajects' (see <a href="http://valerieaurora.org/synthesis/SynthesisOS/ch4.html" rel="nofollow">Chapter 4</a>). </p>&... | operating systems | 1 | Massalin's Synthesis Quajects equivalent to ASM generating macros used in Game Oriented Assembly LISP? -- (operating systems)
<p><a href="http://valerieaurora.org/synthesis/SynthesisOS/abs.html" rel="nofollow">Alexia Massalin's Dissertation on Synthesis</a> was a Phd thesis on Operating Systems that contained a concept... | habedi/stack-exchange-dataset |
2,188 | How to use a greedy algorithm to find the non-decreasing sequence closest to the given one? | <p>You are given n integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirement that the $b_i$'s form a non-decreasing sequence. Define the deviation of such a sequence to be $\max(|a_1-b_1|, \ldots, |a_n-b_n|)$. Design an algor... | algorithms optimization greedy algorithms subsequences | 1 | How to use a greedy algorithm to find the non-decreasing sequence closest to the given one? -- (algorithms optimization greedy algorithms subsequences)
<p>You are given n integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirem... | habedi/stack-exchange-dataset |
2,192 | Finding lambda of Master Theorem | <p>Suppose I have a recurrence like $T(n)=2T(n/4)+\log(n)$ with $a=2, b=4$ and $f(n)=\log(n)$.</p>

<p>That should be <a href="http://en.wikipedia.org/wiki/Master_theorem#Case_1" rel="nofollow">case 1 of the Master theorem</a> because $n^{1/2}>\log(n)$. There is also a lambda in case 1: $f(n)=O(n^{(1/2)-\lam... | proof techniques asymptotics recurrence relation master theorem | 1 | Finding lambda of Master Theorem -- (proof techniques asymptotics recurrence relation master theorem)
<p>Suppose I have a recurrence like $T(n)=2T(n/4)+\log(n)$ with $a=2, b=4$ and $f(n)=\log(n)$.</p>

<p>That should be <a href="http://en.wikipedia.org/wiki/Master_theorem#Case_1" rel="nofollow">case 1 of the Ma... | habedi/stack-exchange-dataset |
2,193 | How can I prove that a complete binary tree has $\lceil n/2 \rceil$ leaves? | <p>Given a complete binary tree with $n$ nodes. I'm trying to prove that a complete binary tree has exactly $\lceil n/2 \rceil$ leaves.
I think I can do this by induction.</p>

<p>For $h(t)=0$, the tree is empty. So there are no leaves and the claim holds for an empty tree.</p>

<p>For $h(t)=1$, the... | data structures graphs proof techniques combinatorics binary trees | 1 | How can I prove that a complete binary tree has $\lceil n/2 \rceil$ leaves? -- (data structures graphs proof techniques combinatorics binary trees)
<p>Given a complete binary tree with $n$ nodes. I'm trying to prove that a complete binary tree has exactly $\lceil n/2 \rceil$ leaves.
I think I can do this by inducti... | habedi/stack-exchange-dataset |
2,197 | How do I test if a polygon is monotone with respect to an arbitrary line? | <blockquote>
 <p><strong>Definition</strong>: A polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line orthogonal to $L$ intersects $P$ at most twice.</p>
</blockquote>

<p>Given a polygon $P$, is it possible to determine if there exists any line $L$ such that th... | algorithms computational geometry | 1 | How do I test if a polygon is monotone with respect to an arbitrary line? -- (algorithms computational geometry)
<blockquote>
 <p><strong>Definition</strong>: A polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line orthogonal to $L$ intersects $P$ at most twice.</p>
</b... | habedi/stack-exchange-dataset |
2,200 | Weighted subset sum problem | <p>Given an integer sequence $\{ a_1, a_2, \ldots, a_N \}$ that has length $N$ and a fixed integer $M\leq N$, the <a href="http://opc.iarcs.org.in/public/WEIGHTED-SUM.pdf" rel="nofollow noreferrer">problem</a> is to find a subset $A =\{i_1, \dots, i_M\} \subseteq [N]$ with $1 \leq i_1 \lt i_1 \lt \dots \lt i_M \leq N$... | algorithms optimization | 1 | Weighted subset sum problem -- (algorithms optimization)
<p>Given an integer sequence $\{ a_1, a_2, \ldots, a_N \}$ that has length $N$ and a fixed integer $M\leq N$, the <a href="http://opc.iarcs.org.in/public/WEIGHTED-SUM.pdf" rel="nofollow noreferrer">problem</a> is to find a subset $A =\{i_1, \dots, i_M\} \subsete... | habedi/stack-exchange-dataset |
2,201 | Optimal myopic maze solver | <p>I was fooling around with <a href="http://neil.fraser.name/software/blockly/demos/maze/index.html" rel="nofollow noreferrer">Google Blocky's Maze demo</a>, and remembered the old rule that if you want to solve a maze, just keep your left hand to the wall. This works for any simple-connected maze and can be implement... | automata finite automata artificial intelligence | 1 | Optimal myopic maze solver -- (automata finite automata artificial intelligence)
<p>I was fooling around with <a href="http://neil.fraser.name/software/blockly/demos/maze/index.html" rel="nofollow noreferrer">Google Blocky's Maze demo</a>, and remembered the old rule that if you want to solve a maze, just keep your lef... | habedi/stack-exchange-dataset |
2,204 | Do the minimum spanning trees of a weighted graph have the same number of edges with a given weight? | <p>If a weighted graph $G$ has two different minimum spanning trees $T_1 = (V_1, E_1)$ and $T_2 = (V_2, E_2)$, then is it true that for any edge $e$ in $E_1$, the number of edges in $E_1$ with the same weight as $e$ (including $e$ itself) is the same as the number of edges in $E_2$ with the same weight as $e$? If the s... | graphs spanning trees weighted graphs | 1 | Do the minimum spanning trees of a weighted graph have the same number of edges with a given weight? -- (graphs spanning trees weighted graphs)
<p>If a weighted graph $G$ has two different minimum spanning trees $T_1 = (V_1, E_1)$ and $T_2 = (V_2, E_2)$, then is it true that for any edge $e$ in $E_1$, the number of edg... | habedi/stack-exchange-dataset |
2,206 | Advanced placement CS A Exam | <p>What would be the standard topics covered in an 'Advanced Placement Computer Science A' test? Is there any good study reference someone can share? </p>

<p><strong>Edit: Answer</strong></p>

<p>An adjustment for my search term returned a <a href="http://en.wikipedia.org/wiki/Advanced_Placement_Comput... | reference request education | 1 | Advanced placement CS A Exam -- (reference request education)
<p>What would be the standard topics covered in an 'Advanced Placement Computer Science A' test? Is there any good study reference someone can share? </p>

<p><strong>Edit: Answer</strong></p>

<p>An adjustment for my search term returned a <... | habedi/stack-exchange-dataset |
2,212 | Show that the halting problem is decidable for one-pass Turing machines | <p>$L=\{<\!M,x\!>\, \mid M's \text{ transition function can only move right and } M\text{ halts on } x \}$. I need to show that $L$ is recursive/decidable.</p>

<p>I thought of checking the encoding of $M$ first and determine whether its transition function moves only right (Can I do that?). If so then ... | formal languages computability turing machines check my proof | 1 | Show that the halting problem is decidable for one-pass Turing machines -- (formal languages computability turing machines check my proof)
<p>$L=\{<\!M,x\!>\, \mid M's \text{ transition function can only move right and } M\text{ halts on } x \}$. I need to show that $L$ is recursive/decidable.</p>

<p>I... | habedi/stack-exchange-dataset |
2,218 | Turing machine and language decidability | <p>The document I am reading is here: <a href="http://www.cs.odu.edu/~toida/nerzic/390teched/tm/definitions.html" rel="nofollow noreferrer">Turing Machines</a></p>

<p>Before getting into the question, here is the notation used on the picture:</p>

<blockquote>
 <p>Here $\Delta$ denotes the blank a... | computability turing machines | 1 | Turing machine and language decidability -- (computability turing machines)
<p>The document I am reading is here: <a href="http://www.cs.odu.edu/~toida/nerzic/390teched/tm/definitions.html" rel="nofollow noreferrer">Turing Machines</a></p>

<p>Before getting into the question, here is the notation used on the p... | habedi/stack-exchange-dataset |
2,222 | Are there complete problems for P and NP under other kinds of reductions? | <p>I know that the complexity class $\mathsf{P}$ has complete problems w.r.t. $\mathsf{NC}$ and $\mathsf{L}$ reductions.</p>

<p>Are these two classes the only possible classes of reductions under which $\mathsf{P}$ has complete problems? </p>

<p>Also, what classes of reduction can be used for $\maths... | complexity theory reductions | 1 | Are there complete problems for P and NP under other kinds of reductions? -- (complexity theory reductions)
<p>I know that the complexity class $\mathsf{P}$ has complete problems w.r.t. $\mathsf{NC}$ and $\mathsf{L}$ reductions.</p>

<p>Are these two classes the only possible classes of reductions under which $... | habedi/stack-exchange-dataset |
2,225 | Point Location Problem in Polygon in Repetitive Mode for a Simple Polygon | <p>I consider <a href="http://en.wikipedia.org/wiki/Point_in_polygon" rel="nofollow">Point Location Problem in Polygon</a> in repetitive mode in the case of simple polygon.</p>

<p>In computational geometry,Point Location Problem in Polygon problem asks whether a given point in the plane lies inside, outside, o... | algorithms computational geometry | 1 | Point Location Problem in Polygon in Repetitive Mode for a Simple Polygon -- (algorithms computational geometry)
<p>I consider <a href="http://en.wikipedia.org/wiki/Point_in_polygon" rel="nofollow">Point Location Problem in Polygon</a> in repetitive mode in the case of simple polygon.</p>

<p>In computational g... | habedi/stack-exchange-dataset |
2,233 | Automata that recognizes Kleene closure of permutations of three symbols | <p>This is an automata theory homework question.</p>

<p>I need to create DFA that meets the following criteria: </p>

<ul>
<li><p>Alphabet $\Sigma = \{ a, b, c \}$</p></li>
<li><p>Machine accepts empty string and strings of length that is a multiple of three, with every block of three containi... | formal languages automata finite automata | 1 | Automata that recognizes Kleene closure of permutations of three symbols -- (formal languages automata finite automata)
<p>This is an automata theory homework question.</p>

<p>I need to create DFA that meets the following criteria: </p>

<ul>
<li><p>Alphabet $\Sigma = \{ a, b, c \}$</p></li>
<... | habedi/stack-exchange-dataset |
2,235 | Can joins be parallelized? | <p>Suppose we want to join two relations on a predicate. Is this in NC?</p>

<p>I realize that a proof of it not being in NC would amount to a proof that $P\not=NC$, so I'd accept evidence of it being an open problem as an answer.</p>

<p>I'm interested in the general case as well as specific cases (e.g... | complexity theory time complexity parallel computing database theory descriptive complexity | 1 | Can joins be parallelized? -- (complexity theory time complexity parallel computing database theory descriptive complexity)
<p>Suppose we want to join two relations on a predicate. Is this in NC?</p>

<p>I realize that a proof of it not being in NC would amount to a proof that $P\not=NC$, so I'd accept evidence... | habedi/stack-exchange-dataset |
2,238 | Turing Recognisable => enumerable | <p>I get the proof of going from an enumerator to a Turing Machine (keep running enumerator and see if it matches input) but I don't see how the other way works.</p>

<p>According to my notes and the book (Intro to the Theory of Computation - Sipser), to get Turing enumerator from a Turing machine, we basically... | computability turing machines intuition | 1 | Turing Recognisable => enumerable -- (computability turing machines intuition)
<p>I get the proof of going from an enumerator to a Turing Machine (keep running enumerator and see if it matches input) but I don't see how the other way works.</p>

<p>According to my notes and the book (Intro to the Theory of Comp... | habedi/stack-exchange-dataset |
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