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 |
|---|---|---|---|---|---|---|
106,642 | Is turing completeness related to recursive enumerable languages? | <p>I recently came across this term "Turing complete" in my study of morphogenesis models. When I looked up, it said that a turing complete machine can simulate a universal turing machine. </p>

<p>When I looked up for its relationship with recursive enumerable languages, I couldn't find anything substantial. <... | turing machines turing completeness church turing thesis | 1 | Is turing completeness related to recursive enumerable languages? -- (turing machines turing completeness church turing thesis)
<p>I recently came across this term "Turing complete" in my study of morphogenesis models. When I looked up, it said that a turing complete machine can simulate a universal turing machine. </p... | habedi/stack-exchange-dataset |
106,651 | Some basic questions on halt and move in Turing machines | <p>Im trying to learn about and set up Turing Machines (TMs) the simplest ways using the simplest definite rules. I am using my previous knowledge on simple Cellular Automata to do this. I want to write the computer code, but first I have to get some understanding of the restrictions and possibilities of TMs.</p>
&... | turing machines automata | 1 | Some basic questions on halt and move in Turing machines -- (turing machines automata)
<p>Im trying to learn about and set up Turing Machines (TMs) the simplest ways using the simplest definite rules. I am using my previous knowledge on simple Cellular Automata to do this. I want to write the computer code, but first I... | habedi/stack-exchange-dataset |
106,660 | Singleton in a simple SBM | <p>I can't work out the solution to the following exercise:</p>

<p>We have <span class="math-container">$2n$</span> vertices grouped in <span class="math-container">$2$</span> clusters of equal size. The probability of having an edge between <span class="math-container">$i$</span> and <span class="math-contain... | probabilistic algorithms random graphs | 1 | Singleton in a simple SBM -- (probabilistic algorithms random graphs)
<p>I can't work out the solution to the following exercise:</p>

<p>We have <span class="math-container">$2n$</span> vertices grouped in <span class="math-container">$2$</span> clusters of equal size. The probability of having an edge between... | habedi/stack-exchange-dataset |
106,662 | Repeated String Match: need help to understand the maximum number of repeats needed to be looked at | <p>There's this question on LeetCode <a href="https://leetcode.com/problems/repeated-string-match/" rel="nofollow noreferrer">(link)</a>:</p>

<blockquote>
 <p>Given two strings <code>A</code> and <code>B</code>, find the minimum number of times <code>A</code> has to be repeated such that <code>B</code> is... | algorithms search problem substrings string matching | 1 | Repeated String Match: need help to understand the maximum number of repeats needed to be looked at -- (algorithms search problem substrings string matching)
<p>There's this question on LeetCode <a href="https://leetcode.com/problems/repeated-string-match/" rel="nofollow noreferrer">(link)</a>:</p>

<blockquote... | habedi/stack-exchange-dataset |
106,666 | The language $\{ww \mid w \in \{0,1\}^{*} \}$ is not a CFL | <p>We have proved that the language <span class="math-container">$ L = \{\omega\omega \mid \omega \in \{0,1\}^{*} \} $</span> is not a CFL, and we did so by using pumping lemma. And the proof is clear to me. But I thought of the following CFG:</p>

<p><span class="math-container">$ G = (\{S, S_{1} \},\{0,1\},R,... | context free | 1 | The language $\{ww \mid w \in \{0,1\}^{*} \}$ is not a CFL -- (context free)
<p>We have proved that the language <span class="math-container">$ L = \{\omega\omega \mid \omega \in \{0,1\}^{*} \} $</span> is not a CFL, and we did so by using pumping lemma. And the proof is clear to me. But I thought of the following CFG:... | habedi/stack-exchange-dataset |
106,677 | Avoiding "side effects" in recursive functions | <p>I am writing a function to find the intersection between two sets.</p>

<p>The non-functional requirements of the assignment include avoiding <a href="https://en.wikipedia.org/wiki/Side_effect_%28computer_science%29" rel="nofollow noreferrer"><strong>"side effects"</strong></a>.</p>

<pre><code>funct... | recursion functional programming | 1 | Avoiding "side effects" in recursive functions -- (recursion functional programming)
<p>I am writing a function to find the intersection between two sets.</p>

<p>The non-functional requirements of the assignment include avoiding <a href="https://en.wikipedia.org/wiki/Side_effect_%28computer_science%29" rel="no... | habedi/stack-exchange-dataset |
106,680 | How do we prove the time complexity of this simple problem in probabilistic inference on a Bayesian network? | <p>Suppose we have a simple Bayesian network with two rows of nodes: <span class="math-container">$x_1, x_2, \ldots, x_n$</span> and <span class="math-container">$y_1, y_2, \ldots, y_n$</span>. Each node <span class="math-container">$x_k$</span> takes a state of either 0 or 1 with equal probability. Each node <span ... | time complexity proof techniques probability theory bayesian network | 1 | How do we prove the time complexity of this simple problem in probabilistic inference on a Bayesian network? -- (time complexity proof techniques probability theory bayesian network)
<p>Suppose we have a simple Bayesian network with two rows of nodes: <span class="math-container">$x_1, x_2, \ldots, x_n$</span> and <sp... | habedi/stack-exchange-dataset |
106,693 | How to calculate combination from given n,r and rank? | <p>Suppose that <span class="math-container">$S=\{1,2,...,n\}$</span> and we are given an integer <span class="math-container">$r\leq n$</span>.</p>

<p>An <span class="math-container">$r$</span>-combination of <span class="math-container">$S$</span> is obtained by selecting <span class="math-container">$r$</sp... | combinatorics | 1 | How to calculate combination from given n,r and rank? -- (combinatorics)
<p>Suppose that <span class="math-container">$S=\{1,2,...,n\}$</span> and we are given an integer <span class="math-container">$r\leq n$</span>.</p>

<p>An <span class="math-container">$r$</span>-combination of <span class="math-container"... | habedi/stack-exchange-dataset |
106,701 | Constructing a DFA $M$ such that $L(M) = L(A) \bigtriangleup L(B)$ with a kind of log-space TM | <p>Suppose that <span class="math-container">$A$</span> and <span class="math-container">$B$</span> are DFAs. We know that there is some DFA <span class="math-container">$M$</span> such that <span class="math-container">$L(M) = L(A) \bigtriangleup L(B)$</span>, the symmetric difference. Also, we can construct this <spa... | complexity theory regular languages space complexity | 1 | Constructing a DFA $M$ such that $L(M) = L(A) \bigtriangleup L(B)$ with a kind of log-space TM -- (complexity theory regular languages space complexity)
<p>Suppose that <span class="math-container">$A$</span> and <span class="math-container">$B$</span> are DFAs. We know that there is some DFA <span class="math-containe... | habedi/stack-exchange-dataset |
106,720 | What is the intuition behind a Free-Choice Petri Net? | <p>So I've found this definition in a paper called <code>Time and Petri Nets, Popova-Zeugmann, L.</code>, but I am unable to understand the intuition behind it.</p>

<blockquote>
 <p>N is a free-choice net (FC net) if each shared place is the only pre-
 place of its post-transitions, i.e., <span class... | petri nets | 1 | What is the intuition behind a Free-Choice Petri Net? -- (petri nets)
<p>So I've found this definition in a paper called <code>Time and Petri Nets, Popova-Zeugmann, L.</code>, but I am unable to understand the intuition behind it.</p>

<blockquote>
 <p>N is a free-choice net (FC net) if each shared place i... | habedi/stack-exchange-dataset |
106,726 | Is model checking PSpace-hard *in formula size*? | <p>Sistla/Clarke proved [<a href="http://www.cs.cmu.edu/afs/cs/Web/People/emc/papers/Papers%20In%20Refereed%20Journals/The%20complexity%20of%20propositional%20linear%20temporal%20logics85.pdf" rel="nofollow noreferrer">SC82</a>] that the LTL model-checking problem is PSpace-complete.
Sometimes people write that thi... | complexity theory model checking linear temporal logic parameterized complexity | 1 | Is model checking PSpace-hard *in formula size*? -- (complexity theory model checking linear temporal logic parameterized complexity)
<p>Sistla/Clarke proved [<a href="http://www.cs.cmu.edu/afs/cs/Web/People/emc/papers/Papers%20In%20Refereed%20Journals/The%20complexity%20of%20propositional%20linear%20temporal%20logics8... | habedi/stack-exchange-dataset |
106,736 | How to divide a line of numbers into N groups such that the sums of each group are closest to their mean using dynamic programming? | <p>I have M numbers arranged into a line. I need to divide the line into N groups without changing numbers order such that the sums of the numbers of each group are closest to the mean of these sums by absolute differences.</p>

<p>Example:</p>

<p>Numbers: 1 2 3 4 5 6 7 8 9 10, need to divide into 3 gr... | algorithms dynamic programming | 1 | How to divide a line of numbers into N groups such that the sums of each group are closest to their mean using dynamic programming? -- (algorithms dynamic programming)
<p>I have M numbers arranged into a line. I need to divide the line into N groups without changing numbers order such that the sums of the numbers of ea... | habedi/stack-exchange-dataset |
106,740 | Implementing a symbol table with a hash table and a stack | <p>I was in class today, in a Language Translations course, thinking about the best way to write a symbol table for a compiler. My professor showed us a hash-table with linked-lists connecting different levels of "blocks", which are usually { } curly brackets in languages such as C.</p>

<p>My thought was, what... | compilers hash tables stacks | 1 | Implementing a symbol table with a hash table and a stack -- (compilers hash tables stacks)
<p>I was in class today, in a Language Translations course, thinking about the best way to write a symbol table for a compiler. My professor showed us a hash-table with linked-lists connecting different levels of "blocks", which... | habedi/stack-exchange-dataset |
106,762 | Construct a decidable set $B$ such that $B \neq A_w$ for any $w \in \Sigma^\star$ | <p>I've been stuck on this problem for a while. Any hints would be appreciated!</p>

<p>Let <span class="math-container">$A \subseteq \Sigma^\star$</span> be decidable. Given <span class="math-container">$w \in \Sigma^\star$</span>, define <span class="math-container">$$A_w = \{x \in \Sigma^\star\:|\: \langle x... | formal languages turing machines computability | 1 | Construct a decidable set $B$ such that $B \neq A_w$ for any $w \in \Sigma^\star$ -- (formal languages turing machines computability)
<p>I've been stuck on this problem for a while. Any hints would be appreciated!</p>

<p>Let <span class="math-container">$A \subseteq \Sigma^\star$</span> be decidable. Given <sp... | habedi/stack-exchange-dataset |
106,764 | Algorithm for identifying correct subset | <p>My raw data is composite, but for simplicity sake let's say they consist of three elements. One might consider a sample set thusly.</p>

<pre><code>[A,a,1]
[A,b,1]
[B,b,1]
[B,b,2]
[C,b,3]
[A,c,3]
</code></pre>

<p>I need to create a subset that satisfy two key criteria.</p>&#x... | algorithms | 1 | Algorithm for identifying correct subset -- (algorithms)
<p>My raw data is composite, but for simplicity sake let's say they consist of three elements. One might consider a sample set thusly.</p>

<pre><code>[A,a,1]
[A,b,1]
[B,b,1]
[B,b,2]
[C,b,3]
[A,c,3]
</code></pre>

<p>I need... | habedi/stack-exchange-dataset |
106,771 | Is the empty problem (or its complement) Karp reducible to any problem in NP? | <p>I'm currently following a course on Complexity Theory, and whilst studying, I came across a rather counterintuitive statement:</p>

<p>If <span class="math-container">$\textbf{P}=\textbf{NP}$</span>, the following holds:</p>

<p>For every <span class="math-container">$A \in \textbf{NP}$</span>, there... | complexity theory reductions | 1 | Is the empty problem (or its complement) Karp reducible to any problem in NP? -- (complexity theory reductions)
<p>I'm currently following a course on Complexity Theory, and whilst studying, I came across a rather counterintuitive statement:</p>

<p>If <span class="math-container">$\textbf{P}=\textbf{NP}$</span... | habedi/stack-exchange-dataset |
106,774 | Can we generate random numbers using irrational numbers like π and e? | <p>Irrational numbers like <span class="math-container">$\pi$</span>, <span class="math-container">$e$</span> and <span class="math-container">$\sqrt{2}$</span> have a unique and non-repeating sequence after the decimal point. If we extract the <span class="math-container">$n$</span>-th digit from such numbers (where <... | randomized algorithms randomness random number generator | 1 | Can we generate random numbers using irrational numbers like π and e? -- (randomized algorithms randomness random number generator)
<p>Irrational numbers like <span class="math-container">$\pi$</span>, <span class="math-container">$e$</span> and <span class="math-container">$\sqrt{2}$</span> have a unique and non-repea... | habedi/stack-exchange-dataset |
106,812 | Does an algorithm have to terminate? | <p>I was reading about the <em>finiteness property of an algorithm</em> where it is mentioned that</p>

<blockquote>
 <p>the algorithm must always terminate after a finite number of steps.</p>
</blockquote>

<p>Does this mean that any pseudo-code cannot contain infinite loops or it should be eq... | algorithms | 1 | Does an algorithm have to terminate? -- (algorithms)
<p>I was reading about the <em>finiteness property of an algorithm</em> where it is mentioned that</p>

<blockquote>
 <p>the algorithm must always terminate after a finite number of steps.</p>
</blockquote>

<p>Does this mean that any pseudo-... | habedi/stack-exchange-dataset |
106,822 | Determine image of hypercube under linear map | <p>Let <span class="math-container">$A$</span> be an <span class="math-container">$3\times N$</span> matrix (where <span class="math-container">$N$</span> is large) with nonnegative real entries. I'd like an algorithm for determining when a vector <span class="math-container">$v\in\Bbb R^3$</span> can be written as <sp... | linear programming linear algebra convex hull matrix | 1 | Determine image of hypercube under linear map -- (linear programming linear algebra convex hull matrix)
<p>Let <span class="math-container">$A$</span> be an <span class="math-container">$3\times N$</span> matrix (where <span class="math-container">$N$</span> is large) with nonnegative real entries. I'd like an algorith... | habedi/stack-exchange-dataset |
106,827 | Understanding the Linear speedup theorem and how strong it is | <p>Let <span class="math-container">$k \in \mathbb{N} $</span> and define the language <span class="math-container">$L = \{ n,m | n^k = m \}$</span></p>

<p>Consider a (deterministic) TM deciding <span class="math-container">$L$</span> then it has to compute <span class="math-container">$k$</span>'th power whic... | algorithms turing machines time complexity | 1 | Understanding the Linear speedup theorem and how strong it is -- (algorithms turing machines time complexity)
<p>Let <span class="math-container">$k \in \mathbb{N} $</span> and define the language <span class="math-container">$L = \{ n,m | n^k = m \}$</span></p>

<p>Consider a (deterministic) TM deciding <span ... | habedi/stack-exchange-dataset |
106,831 | Closest k points - performance on large lists | <p>Very similar to <a href="https://cs.stackexchange.com/questions/33392/finding-nearest-of-a-list-of-points-on-euclidian-plane-to-a-given-reference-poin">this</a></p>

<p><strong>Problem formulation:</strong> Given a list <span class="math-container">$L$</span>
of n points with GPS coordinates and a second... | algorithms computational geometry euclidean distance | 1 | Closest k points - performance on large lists -- (algorithms computational geometry euclidean distance)
<p>Very similar to <a href="https://cs.stackexchange.com/questions/33392/finding-nearest-of-a-list-of-points-on-euclidian-plane-to-a-given-reference-poin">this</a></p>

<p><strong>Problem formulation:</strong... | habedi/stack-exchange-dataset |
106,836 | Determine number of values less than mean in one pass through list | <p>The problem statement is as follows:</p>

<blockquote>
 <p>Can we determine precisely the number of elements less than the mean in a list <span class="math-container">$A$</span> of <span class="math-container">$n$</span> numbers in only one pass through the array (starting at <span class="math-container... | algorithms probabilistic algorithms | 1 | Determine number of values less than mean in one pass through list -- (algorithms probabilistic algorithms)
<p>The problem statement is as follows:</p>

<blockquote>
 <p>Can we determine precisely the number of elements less than the mean in a list <span class="math-container">$A$</span> of <span class="ma... | habedi/stack-exchange-dataset |
106,847 | How can I develop a pseudo-polynomial time algorithm for a non-integer problem? | <p>I have an scheduling probelm with a set of jobs <span class="math-container">$J$</span>, with a ''non-integer'' parameter <span class="math-container">$\beta_j$</span>, i.e. the parameter is a real number and <span class="math-container">$\beta_j \leqslant 0.5, \exists j \in J$</span>.</p>

<p>Since the pro... | complexity theory np hard scheduling real numbers pseudo polynomial | 1 | How can I develop a pseudo-polynomial time algorithm for a non-integer problem? -- (complexity theory np hard scheduling real numbers pseudo polynomial)
<p>I have an scheduling probelm with a set of jobs <span class="math-container">$J$</span>, with a ''non-integer'' parameter <span class="math-container">$\beta_j$</sp... | habedi/stack-exchange-dataset |
106,897 | How do I model line comments in a CFG? | <p>Assume we want to define a context free grammar of say a programming language, where on each line everything after the character # until the end of line is considered a comment and should be ignored. How to express that in a context free grammar?</p>
 | context free formal grammars | 1 | How do I model line comments in a CFG? -- (context free formal grammars)
<p>Assume we want to define a context free grammar of say a programming language, where on each line everything after the character # until the end of line is considered a comment and should be ignored. How to express that in a context free gramma... | habedi/stack-exchange-dataset |
106,899 | Modelling regex replacement via a DFA | <p>I wish to model the following common construction in code via a finite state automaton for the purposes of static analysis:</p>

<pre><code>s = <string matching regex R1>
t = s.replace(<regex R2>, <string matching regex R3>)
# What is the set of possible strings of t?
</code></p... | finite automata regular expressions static analysis | 1 | Modelling regex replacement via a DFA -- (finite automata regular expressions static analysis)
<p>I wish to model the following common construction in code via a finite state automaton for the purposes of static analysis:</p>

<pre><code>s = <string matching regex R1>
t = s.replace(<regex R2>, &... | habedi/stack-exchange-dataset |
106,904 | Lower bound on $1^k+2^k+\dots+n^k$ | <p>I calculated the worst case scenario of a time complexity of an algorithm problem using recurrence tree. (The problem cannot be solved by master theorem.) </p>

<p>Now I want to find a lower bound on the expression I got. Specifically, I want to prove that</p>

<p><span class="math-container">$$ 1^k ... | asymptotics | 1 | Lower bound on $1^k+2^k+\dots+n^k$ -- (asymptotics)
<p>I calculated the worst case scenario of a time complexity of an algorithm problem using recurrence tree. (The problem cannot be solved by master theorem.) </p>

<p>Now I want to find a lower bound on the expression I got. Specifically, I want to prove that<... | habedi/stack-exchange-dataset |
106,911 | Proof for Unusual QuickSort Partition Scheme | <p>TL:DR
I wrote code for a QuickSort variant. It seems a bit off from original QuickSort. Can anyone tell me why and how this works? Is it a quicksort?</p>

<hr>

<p>The following is code I wrote for a middle pivot quicksort for a high school class of AP CS.</p>

<p>It works for some reason... | quicksort | 1 | Proof for Unusual QuickSort Partition Scheme -- (quicksort)
<p>TL:DR
I wrote code for a QuickSort variant. It seems a bit off from original QuickSort. Can anyone tell me why and how this works? Is it a quicksort?</p>

<hr>

<p>The following is code I wrote for a middle pivot quicksort for a high sch... | habedi/stack-exchange-dataset |
106,919 | Finding an unambiguous grammar of a language provided by a CFG | <p>I'm working through 'Intro to Automata Theory, Language and Computation' 2nd edition by Hopcroft, Motwani & Ullman.</p>

<p>In section 5.4, exercise 5.4.3 I am tasked with finding an unambiguous grammar for the language of this Context-Free Grammar (where epsilon is the empty string):</p>

<p><sp... | formal languages context free formal grammars ambiguity | 1 | Finding an unambiguous grammar of a language provided by a CFG -- (formal languages context free formal grammars ambiguity)
<p>I'm working through 'Intro to Automata Theory, Language and Computation' 2nd edition by Hopcroft, Motwani & Ullman.</p>

<p>In section 5.4, exercise 5.4.3 I am tasked with finding a... | habedi/stack-exchange-dataset |
106,938 | Search a sorted array that ends with zeros in O(log n) time | <p>I have an array of size <span class="math-container">$m$</span>, <span class="math-container">$[1,1,2,2,3,4,5,...,f,0,0, \cdots,0]$</span>, where the first <span class="math-container">$n$</span> elements <span class="math-container">$1,1,2,2,3,4,5,\cdots, f$</span> are sorted.</p>

<p>If I make a binary sea... | algorithms complexity theory data structures search algorithms | 1 | Search a sorted array that ends with zeros in O(log n) time -- (algorithms complexity theory data structures search algorithms)
<p>I have an array of size <span class="math-container">$m$</span>, <span class="math-container">$[1,1,2,2,3,4,5,...,f,0,0, \cdots,0]$</span>, where the first <span class="math-container">$n$<... | habedi/stack-exchange-dataset |
106,957 | Complexity of many constant time steps with occasional logarithmic steps | <p>I have a data structure that can perform a task <span class="math-container">$T$</span> in constant time, <span class="math-container">$O(1)$</span>. However, every <span class="math-container">$k$</span>th invocation requires <span class="math-container">$O(\log{n})$</span>, where <span class="math-container">$k$</... | algorithm analysis runtime analysis amortized analysis | 1 | Complexity of many constant time steps with occasional logarithmic steps -- (algorithm analysis runtime analysis amortized analysis)
<p>I have a data structure that can perform a task <span class="math-container">$T$</span> in constant time, <span class="math-container">$O(1)$</span>. However, every <span class="math-c... | habedi/stack-exchange-dataset |
106,987 | Random walks on Complete Binary Trees | <p>Let <span class="math-container">$T$</span> be a complete binary tree of height <span class="math-container">$n$</span> and root <span class="math-container">$r$</span>.</p>

<p>A random walk starts at <span class="math-container">$r$</span>, and at each step uniformly at random moves on a neighbor.</p>
... | binary trees random walks | 1 | Random walks on Complete Binary Trees -- (binary trees random walks)
<p>Let <span class="math-container">$T$</span> be a complete binary tree of height <span class="math-container">$n$</span> and root <span class="math-container">$r$</span>.</p>

<p>A random walk starts at <span class="math-container">$r$</span... | habedi/stack-exchange-dataset |
106,991 | State Transition Diagrams for XOR | <p>I have found two different versions for State Transition Diagrams for XOR.</p>

<p>I'm confused as to why one has 2 states and the other has 3. What are the implied states in each please?</p>

<p>Are they both functionally equivalent? Are there situations where one is more appropriate than the other?... | finite automata boolean algebra | 1 | State Transition Diagrams for XOR -- (finite automata boolean algebra)
<p>I have found two different versions for State Transition Diagrams for XOR.</p>

<p>I'm confused as to why one has 2 states and the other has 3. What are the implied states in each please?</p>

<p>Are they both functionally equival... | habedi/stack-exchange-dataset |
106,995 | Can a language with some set of higher-order functions like map, fold and filter but without recursion or iteration be Turing complete? | <p>I was reading this <a href="https://swizec.com/blog/are-map-reduce-and-filter-turing-complete/swizec/6341" rel="nofollow noreferrer">article</a> and was wondering if there is any finite set of higher-order functions like map, fold or filter such that they could empower a language to be Turing complete even without h... | programming languages functional programming turing completeness | 1 | Can a language with some set of higher-order functions like map, fold and filter but without recursion or iteration be Turing complete? -- (programming languages functional programming turing completeness)
<p>I was reading this <a href="https://swizec.com/blog/are-map-reduce-and-filter-turing-complete/swizec/6341" rel=... | habedi/stack-exchange-dataset |
106,998 | Are the two LTL properties $GF(\psi_1 \land F\psi_2 )$ and $GF(\psi_2 \land F\psi_1 )$ equivalent? | <p>Is <span class="math-container">$GF(\psi_1 \land F\psi_2 )$</span> equivalent to the property <span class="math-container">$GF(\psi_2 \land F\psi_1 )$</span>?</p>

<p>Attempt:</p>

<p>In the first property each state must eventually see <span class="math-container">$\psi_1$</span> and <span class="ma... | logic formal methods linear temporal logic | 1 | Are the two LTL properties $GF(\psi_1 \land F\psi_2 )$ and $GF(\psi_2 \land F\psi_1 )$ equivalent? -- (logic formal methods linear temporal logic)
<p>Is <span class="math-container">$GF(\psi_1 \land F\psi_2 )$</span> equivalent to the property <span class="math-container">$GF(\psi_2 \land F\psi_1 )$</span>?</p>
&#x... | habedi/stack-exchange-dataset |
107,003 | What is a Meta algorithm? | <p>I am currently reading a <a href="https://www.cs.princeton.edu/~arora/pubs/MWsurvey.pdf" rel="noreferrer">survey paper</a> on the multiplicative weight update meta-algorithm. I am not quite sure what they mean by "meta-algorithm". Is it simply a general algorithm that can be used for different purposes? </p>
&#x... | algorithms | 1 | What is a Meta algorithm? -- (algorithms)
<p>I am currently reading a <a href="https://www.cs.princeton.edu/~arora/pubs/MWsurvey.pdf" rel="noreferrer">survey paper</a> on the multiplicative weight update meta-algorithm. I am not quite sure what they mean by "meta-algorithm". Is it simply a general algorithm that can be... | habedi/stack-exchange-dataset |
107,019 | How to understand a equation related to speaker recognition? | <p>This question refers to the following paper:</p>

<p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.445.6034&rep=rep1&type=pdf" rel="nofollow noreferrer">Support Vector Machines for Speaker and Language Recognition</a>, W. M. Campbell, J. P. Campbell, D. A. Reynolds, E. Singer, P. ... | algorithms machine learning svm speech recognition | 1 | How to understand a equation related to speaker recognition? -- (algorithms machine learning svm speech recognition)
<p>This question refers to the following paper:</p>

<p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.445.6034&rep=rep1&type=pdf" rel="nofollow noreferrer">Support Vec... | habedi/stack-exchange-dataset |
107,020 | Proving $L = \{\langle M, w, n \rangle$ : $M$ accepts $w$ within $n$ steps $\}$ is decidable | <blockquote>
 <p>Show the following problem is decidable: Given <span class="math-container">$w\in \Sigma^{*}$</span>, <span class="math-container">$n\in \mathbb{N}$</span>, and a Turing machine <span class="math-container">$M$</span>, does <span class="math-container">$M$</span> on <span class="math-container">$w... | turing machines computability decision problem | 1 | Proving $L = \{\langle M, w, n \rangle$ : $M$ accepts $w$ within $n$ steps $\}$ is decidable -- (turing machines computability decision problem)
<blockquote>
 <p>Show the following problem is decidable: Given <span class="math-container">$w\in \Sigma^{*}$</span>, <span class="math-container">$n\in \mathbb{N}$</spa... | habedi/stack-exchange-dataset |
107,022 | Can CNF with an input string be evaluated in logarithmic space? | <p>I have been trying to solve satisfiability of</p>

<p>{<span class="math-container">$<c, w>$</span> | <span class="math-container">$c$</span> is a CNF and <span class="math-container">$w$</span> is a binary string which satifies the <span class="math-container">$c$</span>}. </p>

<p>As first lo... | complexity theory space complexity complexity classes | 1 | Can CNF with an input string be evaluated in logarithmic space? -- (complexity theory space complexity complexity classes)
<p>I have been trying to solve satisfiability of</p>

<p>{<span class="math-container">$<c, w>$</span> | <span class="math-container">$c$</span> is a CNF and <span class="math-contain... | habedi/stack-exchange-dataset |
107,031 | SVM with a priori information about class probabilities | <p>Given are two 2-d sets, each with its own bivariate normal distribution. I need to build an SVM classifier. The a priori probabilities of each class corresponds to the size of its set (20/50 for the first and 30/50 for the second one). I am quite confused about the way to implement the knowledge about set structure ... | probabilistic algorithms classification svm | 1 | SVM with a priori information about class probabilities -- (probabilistic algorithms classification svm)
<p>Given are two 2-d sets, each with its own bivariate normal distribution. I need to build an SVM classifier. The a priori probabilities of each class corresponds to the size of its set (20/50 for the first and 30/... | habedi/stack-exchange-dataset |
107,037 | defining a programming language grammar for doing arithmetic | <p>I'm studying programming language design, and I've been taught the grammar below which lets you write basic math expressions. </p>

<pre><code>Exp ::= Num | Exp Op Exp
Op ::= + | - | * | Div
Num ::= Digit | Digit Num
Digit ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 
</code></pre>

<p>A... | formal grammars syntax syntax trees | 1 | defining a programming language grammar for doing arithmetic -- (formal grammars syntax syntax trees)
<p>I'm studying programming language design, and I've been taught the grammar below which lets you write basic math expressions. </p>

<pre><code>Exp ::= Num | Exp Op Exp
Op ::= + | - | * | Div
Num ::= ... | habedi/stack-exchange-dataset |
107,038 | Isomorphism problem on bounded degree digraphs | <p>By Babai & Luks (1983), it was proved that graph isomorphism problem is tractable on bounded degree graphs. However, I could not find any result when the graph is edge directed. </p>

<p>Is isomorphism problem tractable (or GI-complete) on edge-directed graphs with bounded degree?</p>
 | reference request graph isomorphism | 1 | Isomorphism problem on bounded degree digraphs -- (reference request graph isomorphism)
<p>By Babai & Luks (1983), it was proved that graph isomorphism problem is tractable on bounded degree graphs. However, I could not find any result when the graph is edge directed. </p>

<p>Is isomorphism problem tractab... | habedi/stack-exchange-dataset |
107,041 | Finding an interval in a binary search tree that contains a point | <p>I have a binary search tree where nodes are non-overlapping intervals. I'm given a point, and I need to determine which interval the point belongs to (if any). This is easy to do because I can compare against the low and high of each interval and descend either left, right, or exit.</p>

<p>Is it possible to... | balanced search trees binary search intervals | 1 | Finding an interval in a binary search tree that contains a point -- (balanced search trees binary search intervals)
<p>I have a binary search tree where nodes are non-overlapping intervals. I'm given a point, and I need to determine which interval the point belongs to (if any). This is easy to do because I can compare... | habedi/stack-exchange-dataset |
107,053 | Time complexity of a problem in probabilistic inference on a Bayesian network | <p>Suppose we have a simple Bayesian network with two rows of nodes: <span class="math-container">$x_1, x_2, \ldots, x_n$</span> and <span class="math-container">$y_1, y_2, \ldots, y_n$</span>. Each node <span class="math-container">$x_k$</span> takes a state of either 0 or 1 with equal probability. Each node <span ... | time complexity factoring bayesian network | 1 | Time complexity of a problem in probabilistic inference on a Bayesian network -- (time complexity factoring bayesian network)
<p>Suppose we have a simple Bayesian network with two rows of nodes: <span class="math-container">$x_1, x_2, \ldots, x_n$</span> and <span class="math-container">$y_1, y_2, \ldots, y_n$</span>.... | habedi/stack-exchange-dataset |
107,075 | How to count the combinations not greater than a given volume in a knapsack problem? | <p>You are given a certain set of items with weight wi and the volume of the bag. </p>

<p>Case:</p>

<pre><code>Input: 

3 (count of items) 10 (volume of the bag)
1 2 4 (weight for each item)

Output

8 (since you can put any item in or not 2 * 2 *2)
</code></pre>
&#... | dynamic programming knapsack problems backtracking | 1 | How to count the combinations not greater than a given volume in a knapsack problem? -- (dynamic programming knapsack problems backtracking)
<p>You are given a certain set of items with weight wi and the volume of the bag. </p>

<p>Case:</p>

<pre><code>Input: 

3 (count of items) 10 (volume of ... | habedi/stack-exchange-dataset |
107,085 | Is "Reachable Object" really an NP-complete problem? | <p>I was reading <a href="https://www.ijcai.org/proceedings/2017/0031.pdf" rel="nofollow noreferrer">this paper</a> where the authors explain Theorem 1, which states "Reachable Object" (as defined in the paper) is NP-complete. However, they prove the reduction only in one direction, i.e. from 2P1N SAT to Reachable Obje... | complexity theory np complete np hard satisfiability | 1 | Is "Reachable Object" really an NP-complete problem? -- (complexity theory np complete np hard satisfiability)
<p>I was reading <a href="https://www.ijcai.org/proceedings/2017/0031.pdf" rel="nofollow noreferrer">this paper</a> where the authors explain Theorem 1, which states "Reachable Object" (as defined in the paper... | habedi/stack-exchange-dataset |
107,092 | Find all subsets with a given sum | <p>How to choose from a set of positive numbers all the subsets that sum to some number x?
For example if the set <span class="math-container">$S=[1,1,2,3,4,5,6,7]$</span> and I'm searching for all the subsets that sum to <span class="math-container">$7$</span> I would have <span class="math-container">$[1,6],[1,6]... | sets subset sum finite sets | 1 | Find all subsets with a given sum -- (sets subset sum finite sets)
<p>How to choose from a set of positive numbers all the subsets that sum to some number x?
For example if the set <span class="math-container">$S=[1,1,2,3,4,5,6,7]$</span> and I'm searching for all the subsets that sum to <span class="math-container... | habedi/stack-exchange-dataset |
107,111 | Indexing Edge Permutations for the Rubik's Cube | <p>I'm working on a Rubik's Cube solver that implements Korf's algorithm, as published in his 1997 paper, <a href="https://www.cs.princeton.edu/courses/archive/fall06/cos402/papers/korfrubik.pdf" rel="nofollow noreferrer">Finding Optimal Solutions to Rubik's Cube Using Pattern Databases</a>. His method involves creati... | algorithms hash permutations | 1 | Indexing Edge Permutations for the Rubik's Cube -- (algorithms hash permutations)
<p>I'm working on a Rubik's Cube solver that implements Korf's algorithm, as published in his 1997 paper, <a href="https://www.cs.princeton.edu/courses/archive/fall06/cos402/papers/korfrubik.pdf" rel="nofollow noreferrer">Finding Optimal ... | habedi/stack-exchange-dataset |
107,116 | Range of values for Kolmogorov complexity | <p>Let <span class="math-container">$n$</span> be a positive integer. Is it true that for all <span class="math-container">$1\leq i \leq n$</span> there exists a length <span class="math-container">$n$</span> binary string <span class="math-container">$w$</span> such that <span class="math-container">$K(w) = i$</span>... | kolmogorov complexity | 1 | Range of values for Kolmogorov complexity -- (kolmogorov complexity)
<p>Let <span class="math-container">$n$</span> be a positive integer. Is it true that for all <span class="math-container">$1\leq i \leq n$</span> there exists a length <span class="math-container">$n$</span> binary string <span class="math-container... | habedi/stack-exchange-dataset |
107,120 | Proving Turing Completeness by creating a compiler to a Turing Complete language | <p>Given a programming language A unknown to be Turing Complete, if one can create a compiler for a TC programming language B using A does this imply that A is itself Turing Complete? If so, what is the formal thinking behind the idea?</p>
 | programming languages turing completeness | 1 | Proving Turing Completeness by creating a compiler to a Turing Complete language -- (programming languages turing completeness)
<p>Given a programming language A unknown to be Turing Complete, if one can create a compiler for a TC programming language B using A does this imply that A is itself Turing Complete? If so, w... | habedi/stack-exchange-dataset |
107,123 | What is the asymptotic bound for $1n + 2(n-1) + 3(n-2) + ... + (n-1)2 + n$? | <p>My best guess is that the series
<span class="math-container">$$ \sum_{i=1}^n i(n-(i-1)) $$</span>
becomes
<span class="math-container">$$ 2 \Bigg[ n + 2(n-1) + ... + \frac{n}{2} \bigg(n-\bigg(\frac{n}{2}-1\bigg)\Bigg)\Bigg] $$</span>
So the highest term is <span class="math-container">$n^2$</span> a... | asymptotics | 1 | What is the asymptotic bound for $1n + 2(n-1) + 3(n-2) + ... + (n-1)2 + n$? -- (asymptotics)
<p>My best guess is that the series
<span class="math-container">$$ \sum_{i=1}^n i(n-(i-1)) $$</span>
becomes
<span class="math-container">$$ 2 \Bigg[ n + 2(n-1) + ... + \frac{n}{2} \bigg(n-\bigg(\frac{n}{2}-1\bigg)... | habedi/stack-exchange-dataset |
107,143 | Do the "virtual memory"s mentioned in the 2 articles refer to different things? | <p>I've read the following 2 articles explaining the difference between <code>virtual memory</code> and <code>physical memory</code>. One thing that I found confusing is that the term <code>virtual memory</code> seems to mean different things in these 2 articles.</p>

<p><a href="https://www.techwalla.com/artic... | memory management virtual memory | 1 | Do the "virtual memory"s mentioned in the 2 articles refer to different things? -- (memory management virtual memory)
<p>I've read the following 2 articles explaining the difference between <code>virtual memory</code> and <code>physical memory</code>. One thing that I found confusing is that the term <code>virtual memo... | habedi/stack-exchange-dataset |
107,149 | What is a fractional matching? | <p>For the maximum matching problem, we can find the fractional matching which I understand involves some sort of weighting for the edges. However, I cannot seem to find an exact and simple explanation of what a fractional matching is. How does it compare to an integral matching? </p>

<p>If this question seems... | graphs matching | 1 | What is a fractional matching? -- (graphs matching)
<p>For the maximum matching problem, we can find the fractional matching which I understand involves some sort of weighting for the edges. However, I cannot seem to find an exact and simple explanation of what a fractional matching is. How does it compare to an integr... | habedi/stack-exchange-dataset |
107,154 | Fixed Points of Factorial Function | <p>(This is taken from the book Semantics with Applications)</p>

<p>I'm trying to determine the fixed points for the following block:</p>

<pre><code>
while (x!=1) { y = y *x; x = x -1; }

</code></pre>

<p>As I understand, a fixed point <code>g</code> has to satisfy the following:... | programming languages fixed point | 1 | Fixed Points of Factorial Function -- (programming languages fixed point)
<p>(This is taken from the book Semantics with Applications)</p>

<p>I'm trying to determine the fixed points for the following block:</p>

<pre><code>
while (x!=1) { y = y *x; x = x -1; }

</code></pre>

<p>A... | habedi/stack-exchange-dataset |
107,158 | How exactly does a CPU do process scheduling? | <p>I know in theory how various scheduling algorithms work, such as round robin, where each process is given small time slices to run a few instructions, before the operating system passes execution onto the next process, and so on.</p>

<p>What I don't understand is how this is possible. The operating system i... | operating systems process scheduling | 1 | How exactly does a CPU do process scheduling? -- (operating systems process scheduling)
<p>I know in theory how various scheduling algorithms work, such as round robin, where each process is given small time slices to run a few instructions, before the operating system passes execution onto the next process, and so on.... | habedi/stack-exchange-dataset |
107,162 | Vertex Cover without covering all edges | <p>What would be the name of the problem of a vertex cover that covers all the vertices without the requirement of covering all the edges?</p>

<p>Vertex cover has to answer whether or not there is a set of <span class="math-container">$k$</span> vertices that covers all the edges of the graph, covering therefo... | graphs terminology | 1 | Vertex Cover without covering all edges -- (graphs terminology)
<p>What would be the name of the problem of a vertex cover that covers all the vertices without the requirement of covering all the edges?</p>

<p>Vertex cover has to answer whether or not there is a set of <span class="math-container">$k$</span> v... | habedi/stack-exchange-dataset |
107,164 | Vertex cover of bipartite graph | <p>A vertex cover is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
A minimum vertex cover is a vertex cover with minimal cardinality.</p>
<p>From <a href="https://codeforces.com/blog/entry/63164" rel="nofollow noreferrer">codeforces</a>,</p>
<blockquote>&#... | algorithms graphs approximation vertex cover | 1 | Vertex cover of bipartite graph -- (algorithms graphs approximation vertex cover)
<p>A vertex cover is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
A minimum vertex cover is a vertex cover with minimal cardinality.</p>
<p>From <a href="https://codeforces.com/... | habedi/stack-exchange-dataset |
107,178 | Big Oh Time Complexity Involving 'for i in range(n)' | <p>Given the code below and the comment analysis:</p>

<pre><code>n = len(L) # O(1)
for i in range(n): # O(n) - I read online that range(n) will take constant time 
 but the 'for i in range(n)' part would make this O(n)?
 if L[i] > 0 : # O(1)
 for j in range(n... | time complexity runtime analysis python | 1 | Big Oh Time Complexity Involving 'for i in range(n)' -- (time complexity runtime analysis python)
<p>Given the code below and the comment analysis:</p>

<pre><code>n = len(L) # O(1)
for i in range(n): # O(n) - I read online that range(n) will take constant time 
 but the 'for i in... | habedi/stack-exchange-dataset |
107,180 | ILP representation of the number of maximal 1 sequences in a row | <p>I am currently using an ILP to model events which occur on some input sequence from <span class="math-container">$1...n$</span>. These events modify the input sequence in order to obtain a desired sequence. Each event can happen on some consecutive range <span class="math-container">$(i,j)$</span> and no two events ... | algorithms linear programming integer programming substrings subsequences | 1 | ILP representation of the number of maximal 1 sequences in a row -- (algorithms linear programming integer programming substrings subsequences)
<p>I am currently using an ILP to model events which occur on some input sequence from <span class="math-container">$1...n$</span>. These events modify the input sequence in or... | habedi/stack-exchange-dataset |
107,183 | Will this algorithm always solve a constrained sudoku puzzle in quadratic time? | <h1>Constrained Puzzle Generation:</h1>

<p>Let us say a sudoku puzzle is generated with the following procedure:</p>

<ol>
<li>Gather a sequence input of 9 unique numbers in the range <span class="math-container">$[1 .. 9]$</span>. Call it <span class="math-container">$S$</span>.</li>
<li>Map <... | algorithms sudoku | 1 | Will this algorithm always solve a constrained sudoku puzzle in quadratic time? -- (algorithms sudoku)
<h1>Constrained Puzzle Generation:</h1>

<p>Let us say a sudoku puzzle is generated with the following procedure:</p>

<ol>
<li>Gather a sequence input of 9 unique numbers in the range <span class=... | habedi/stack-exchange-dataset |
107,194 | Finding the shortest path for synchronized pawns in a maze | <p>I have been trying to wrap my head around this problem, and I just can't get it.</p>

<ul>
<li><p>We have an <span class="math-container">$a \times b$</span> matrix where every cell corresponds to either an empty space, denoted with a dot, or a wall, denoted with <span class="math-container">$X$</span>.<... | algorithms graphs trees matrices board games | 1 | Finding the shortest path for synchronized pawns in a maze -- (algorithms graphs trees matrices board games)
<p>I have been trying to wrap my head around this problem, and I just can't get it.</p>

<ul>
<li><p>We have an <span class="math-container">$a \times b$</span> matrix where every cell corresponds to... | habedi/stack-exchange-dataset |
107,195 | Proof that type does not have decidable equality in Agda | <p>Can one create such function in Agda ?</p>

<pre><code>ℕ→ℕ-undecidable : ¬ ( (f g : ℕ → ℕ ) → Dec (f ≡ g)) 
ℕ→ℕ-undecidable = ?
</code></pre>

<p>I am particularly interested in proof using cubical Agda.</p>
 | homotopy type theory agda cubical type theory | 1 | Proof that type does not have decidable equality in Agda -- (homotopy type theory agda cubical type theory)
<p>Can one create such function in Agda ?</p>

<pre><code>ℕ→ℕ-undecidable : ¬ ( (f g : ℕ → ℕ ) → Dec (f ≡ g)) 
ℕ→ℕ-undecidable = ?
</code></pre>

<p>I am particularly interested in proof ... | habedi/stack-exchange-dataset |
107,197 | Given an array of size n, create a sub array with given conditions using dynamic programming | <p>We are given an array of integers of size n, which is not necessarily sorted, and we want to create a sub array. We are allowed to do one of 3 tasks below in each level:
1. skip the number in original array and go to the next
2. insert the number in the start of the sub array 
3. insert the number in the... | algorithms dynamic programming algorithm design | 1 | Given an array of size n, create a sub array with given conditions using dynamic programming -- (algorithms dynamic programming algorithm design)
<p>We are given an array of integers of size n, which is not necessarily sorted, and we want to create a sub array. We are allowed to do one of 3 tasks below in each level:&#... | habedi/stack-exchange-dataset |
107,204 | How to reduce number of move operations in an array? | <p>Say I have an array of numbers, e.g. <code>[0, 1, 2, 3, 4, 5]</code> and I want to end up with an array, e.g. <code>[2, 1, 4, 0, 5, 3]</code>. At my disposal, I have a single method that I can use:</p>

<pre><code>move(fromIndex, toIndex)
</code></pre>

<p>Thus, to achieve my desired array, I cou... | sorting arrays ordering | 1 | How to reduce number of move operations in an array? -- (sorting arrays ordering)
<p>Say I have an array of numbers, e.g. <code>[0, 1, 2, 3, 4, 5]</code> and I want to end up with an array, e.g. <code>[2, 1, 4, 0, 5, 3]</code>. At my disposal, I have a single method that I can use:</p>

<pre><code>move(fromInde... | habedi/stack-exchange-dataset |
107,209 | Can the notation for polynomial reduction, A ≤p B be reversed in computability theory? | <p>I don't know this is a proper question on this forum but I was reading about computability theory and I saw the reduction concept and its notation like this: <span class="math-container">$A \le_pB$</span>. I just wanted to know is this notation can be reversed? that is, can I write this down like <span class="math-c... | computability notation | 1 | Can the notation for polynomial reduction, A ≤p B be reversed in computability theory? -- (computability notation)
<p>I don't know this is a proper question on this forum but I was reading about computability theory and I saw the reduction concept and its notation like this: <span class="math-container">$A \le_pB$</spa... | habedi/stack-exchange-dataset |
107,219 | Can a NP problem be reduced to another NP problem? | <p>I have three related questions which have been bothering me for a while now...</p>

<ol>
<li><p>Suppose I have a problem <span class="math-container">$A$</span>, which is in <strong>NP</strong>. Suppose there is another
problem <span class="math-container">$B$</span> in <strong>NP... | complexity theory np complete np hard np | 1 | Can a NP problem be reduced to another NP problem? -- (complexity theory np complete np hard np)
<p>I have three related questions which have been bothering me for a while now...</p>

<ol>
<li><p>Suppose I have a problem <span class="math-container">$A$</span>, which is in <strong>NP</strong>. Sup... | habedi/stack-exchange-dataset |
107,232 | Question is about a paper "A Block-sorting Lossless Data Compression Algorithm" by M. Burrows and D.J. Wheeler | <p>In the paper A Block-sorting Lossless Data Compression Algorithm by M. Burrows and D.J. Wheeler <a href="https://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.pdf" rel="nofollow noreferrer">Link</a>.
On page number 5. please describe this line</p>

<blockquote>
 <p>If the original string <span cl... | algorithms data compression research | 1 | Question is about a paper "A Block-sorting Lossless Data Compression Algorithm" by M. Burrows and D.J. Wheeler -- (algorithms data compression research)
<p>In the paper A Block-sorting Lossless Data Compression Algorithm by M. Burrows and D.J. Wheeler <a href="https://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.pd... | habedi/stack-exchange-dataset |
107,245 | Triangulation algorithm for an arbitary amount of points? | <p>I have multiple cameras that records the 2D pixel coordinates of the features each camera sees. After some searching, I came across <a href="http://idav.ucdavis.edu/~mhessf/Papers/WACV_2013.pdf" rel="nofollow noreferrer">this paper</a> with a method to calculate the 3D coordinates of the features.</p>

<p>My... | algorithms computer vision | 1 | Triangulation algorithm for an arbitary amount of points? -- (algorithms computer vision)
<p>I have multiple cameras that records the 2D pixel coordinates of the features each camera sees. After some searching, I came across <a href="http://idav.ucdavis.edu/~mhessf/Papers/WACV_2013.pdf" rel="nofollow noreferrer">this p... | habedi/stack-exchange-dataset |
107,247 | Undecidability of emptiness of LBA | <p>How is the emptiness of Linear Bound Automata (LBA) i.e <span class="math-container">$L = \{B \mid L(B) = \emptyset \}$</span> is undecidable? </p>
 | turing machines linear bounded automata | 1 | Undecidability of emptiness of LBA -- (turing machines linear bounded automata)
<p>How is the emptiness of Linear Bound Automata (LBA) i.e <span class="math-container">$L = \{B \mid L(B) = \emptyset \}$</span> is undecidable? </p>
 | habedi/stack-exchange-dataset |
107,254 | Least common multiple of a list of numbers | <p>I'm trying to learn computer science by doing some challenges. One is the following.</p>
<blockquote>
<p>2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.</p>
<p>What is the smallest positive number that is evenly divisible by all of the numbers fr... | algorithms complexity theory | 1 | Least common multiple of a list of numbers -- (algorithms complexity theory)
<p>I'm trying to learn computer science by doing some challenges. One is the following.</p>
<blockquote>
<p>2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.</p>
<p>What is t... | habedi/stack-exchange-dataset |
107,255 | Asymptotics question | <p>Is <span class="math-container">$\frac {n!} {2!\cdot 4!\cdot 8!\dots (n/2)!}=O(4^n)$</span>?</p>

<p>I am really stuck and I tend to believe it's true, but I don't know how to prove it.</p>

<p>Any help would be appreciated!</p>
 | asymptotics factorial big o notation | 1 | Asymptotics question -- (asymptotics factorial big o notation)
<p>Is <span class="math-container">$\frac {n!} {2!\cdot 4!\cdot 8!\dots (n/2)!}=O(4^n)$</span>?</p>

<p>I am really stuck and I tend to believe it's true, but I don't know how to prove it.</p>

<p>Any help would be appreciated!</p>
 | habedi/stack-exchange-dataset |
107,257 | Finding recurrence relation for running time of an algorithm | <p>I am pretty new to this, consider the following algorithm:</p>

<pre><code>Calc_a(n):
 if n ==1: return 1
 else:
 sum = 0
 for i=1 to n-1:
 sum = sum + calc_a(i)
 return sum
</code></pre>

<p>So after running this algorithm a few times I see it basica... | recurrence relation | 1 | Finding recurrence relation for running time of an algorithm -- (recurrence relation)
<p>I am pretty new to this, consider the following algorithm:</p>

<pre><code>Calc_a(n):
 if n ==1: return 1
 else:
 sum = 0
 for i=1 to n-1:
 sum = sum + calc_a(i)
 return sum
... | habedi/stack-exchange-dataset |
107,277 | Why do we still use a Von Neumann Architecture in modern computers? | <p>The Von Neumann architecture was first created in the mid 40s for use in a computing system known as ENIAC for research into the feasibility of thermonuclear weapons. </p>

<p>To this day the Von Neumann architeture is still primary foundation in the majority of modern computers. I have listened to a few his... | computer architecture memory hardware | 1 | Why do we still use a Von Neumann Architecture in modern computers? -- (computer architecture memory hardware)
<p>The Von Neumann architecture was first created in the mid 40s for use in a computing system known as ENIAC for research into the feasibility of thermonuclear weapons. </p>

<p>To this day the Von Ne... | habedi/stack-exchange-dataset |
107,281 | Simple property of DFAs | <p>Do you know if this simple property of a DFA is stated as a property (or theorem) in some Automata theory book (possibly with a particular name)?</p>

<p><strong>Property</strong>: Given a DFA <span class="math-container">$A = \{ Q, \Sigma, \delta, q_0, F \}$</span>, if <span class="math-container">$w = uv$<... | automata finite automata reference request | 1 | Simple property of DFAs -- (automata finite automata reference request)
<p>Do you know if this simple property of a DFA is stated as a property (or theorem) in some Automata theory book (possibly with a particular name)?</p>

<p><strong>Property</strong>: Given a DFA <span class="math-container">$A = \{ Q, \Sig... | habedi/stack-exchange-dataset |
107,286 | How do we know $\neg \neg LEM$ isn't provable in MLTT? | <p>I've been trying (fruitlessly) to prove something which I now know is not provable. Take the following definitions:
<span class="math-container">$$LEM \equiv \prod_{A : Type} \neg A \vee A$$</span>
<span class="math-container">$$DNE \equiv \prod_{A : Type} \neg \neg A \to A$$</span>
<span class="math-con... | logic programming languages lambda calculus type theory | 1 | How do we know $\neg \neg LEM$ isn't provable in MLTT? -- (logic programming languages lambda calculus type theory)
<p>I've been trying (fruitlessly) to prove something which I now know is not provable. Take the following definitions:
<span class="math-container">$$LEM \equiv \prod_{A : Type} \neg A \vee A$$</span>... | habedi/stack-exchange-dataset |
107,292 | Constant factor of an array | <p>In <em>Elements of Programming Interviews in Python</em> by Aziz, Lee and Prakash, they state on page 41:</p>

<blockquote>
 <p>Insertion into a full array can be handled by resizing, i.e.,
 allocating a new array with additional memory and copying over the
 entries from the original array. Th... | algorithm analysis data structures amortized analysis | 1 | Constant factor of an array -- (algorithm analysis data structures amortized analysis)
<p>In <em>Elements of Programming Interviews in Python</em> by Aziz, Lee and Prakash, they state on page 41:</p>

<blockquote>
 <p>Insertion into a full array can be handled by resizing, i.e.,
 allocating a new arra... | habedi/stack-exchange-dataset |
107,297 | Regular Expression: L= {w | every even position of w is '1'} | <p>I am trying to solve a regular expression of binary string where every even position is a '1'</p>

<p>I've solved this for an <strong>odd position</strong>: (1(0+1))*(1+ε)</p>

<p>How would it look like for an even position then? Thanks in advance.</p>
 | automata regular expressions | 1 | Regular Expression: L= {w | every even position of w is '1'} -- (automata regular expressions)
<p>I am trying to solve a regular expression of binary string where every even position is a '1'</p>

<p>I've solved this for an <strong>odd position</strong>: (1(0+1))*(1+ε)</p>

<p>How would it look like for... | habedi/stack-exchange-dataset |
107,301 | Limitations of DFA | <p>In this <a href="https://www.seas.upenn.edu/~cit596/notes/dave/npda1.html" rel="nofollow noreferrer">link</a> it is mentioned: </p>

<blockquote>
 <p>A DFA is not powerful enough to recognize many context-free languages because a DFA can't count. </p>
 
 <p>But counting is not enough -- consid... | automata finite automata counting | 1 | Limitations of DFA -- (automata finite automata counting)
<p>In this <a href="https://www.seas.upenn.edu/~cit596/notes/dave/npda1.html" rel="nofollow noreferrer">link</a> it is mentioned: </p>

<blockquote>
 <p>A DFA is not powerful enough to recognize many context-free languages because a DFA can't count.... | habedi/stack-exchange-dataset |
107,319 | Computability - The language of all strings of even length | <p>Define a language <span class="math-container">$L$</span> as follows:
<span class="math-container">$$L = \{\langle M \rangle \in \{0, 1\}^* | M\text{ is a TM that halts on all strings of even length} \}$$</span></p>

<p>I can prove that <span class="math-container">$L$</span> is not decidable/recursive, ... | turing machines computability | 1 | Computability - The language of all strings of even length -- (turing machines computability)
<p>Define a language <span class="math-container">$L$</span> as follows:
<span class="math-container">$$L = \{\langle M \rangle \in \{0, 1\}^* | M\text{ is a TM that halts on all strings of even length} \}$$</span></p>
... | habedi/stack-exchange-dataset |
107,323 | Understanding paging and internal fragmentation | <p>I am currently studing questions but stuck on this one, I hope someone can help me out to understand.</p>

<p><strong>Question</strong>: Assume that we have a paged virtual memory with a page size of 4Ki byte. Assume that each process has four segments (for example: code, data, stack, extra) and that these c... | virtual memory paging | 1 | Understanding paging and internal fragmentation -- (virtual memory paging)
<p>I am currently studing questions but stuck on this one, I hope someone can help me out to understand.</p>

<p><strong>Question</strong>: Assume that we have a paged virtual memory with a page size of 4Ki byte. Assume that each process... | habedi/stack-exchange-dataset |
107,344 | Sudoku Puzzles in O log n time although inefficient | <p>Suppose, I got a hypothetical fixed list of all possible general Sudoku puzzles. I then create the pseudo-code to demonstrate the algorithm. </p>

<ul>
<li><p>The algorithm does a search to compare the indexes of elements
in the puzzle that are not listed as zero.</p></li>
<li><p>In other words,... | np complete sudoku | 1 | Sudoku Puzzles in O log n time although inefficient -- (np complete sudoku)
<p>Suppose, I got a hypothetical fixed list of all possible general Sudoku puzzles. I then create the pseudo-code to demonstrate the algorithm. </p>

<ul>
<li><p>The algorithm does a search to compare the indexes of elements
in... | habedi/stack-exchange-dataset |
107,355 | Do regular languages belong to Space(1)? | <p>I was wondering, if we take some regular language, will it be in Space(1)?</p>

<p>For a regular language X, for instance, we can construct an equivalent NFA that matches strings in the regular language.</p>

<p>But I cannot see why is X in Space(1).</p>

<p>If it is true, why is X or any oth... | complexity theory turing machines space complexity | 1 | Do regular languages belong to Space(1)? -- (complexity theory turing machines space complexity)
<p>I was wondering, if we take some regular language, will it be in Space(1)?</p>

<p>For a regular language X, for instance, we can construct an equivalent NFA that matches strings in the regular language.</p>
... | habedi/stack-exchange-dataset |
107,365 | What is the relation between syntax and type theory? | <p>Type theory and syntax are similar, in that they are inductive rules that determine whether a particular string of symbols is "correctly specified" in some sense.</p>

<p>There is a difference between syntax and type theory. Syntax in programming languages for example, concerns things that do not concern ty... | type theory syntax | 1 | What is the relation between syntax and type theory? -- (type theory syntax)
<p>Type theory and syntax are similar, in that they are inductive rules that determine whether a particular string of symbols is "correctly specified" in some sense.</p>

<p>There is a difference between syntax and type theory. Syntax... | habedi/stack-exchange-dataset |
107,373 | Minimally extend a tree such that there are no bridges in the new graph | <p>We are given an undirected tree on which we should add the minimum number of edges such that there are no bridges in the new graph.</p>

<p>An edge <span class="math-container">$e$</span> is a bridge if the graph with that edge removed is no longer connected.</p>

<p>For example, here is a tree with ... | graphs trees | 1 | Minimally extend a tree such that there are no bridges in the new graph -- (graphs trees)
<p>We are given an undirected tree on which we should add the minimum number of edges such that there are no bridges in the new graph.</p>

<p>An edge <span class="math-container">$e$</span> is a bridge if the graph with t... | habedi/stack-exchange-dataset |
107,376 | reduction from 3-SAT to Subset Sum problem | <p>How to reduce 3-SAT to <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" rel="nofollow noreferrer">subset sum</a> problem?</p>
 | complexity theory automata reductions | 1 | reduction from 3-SAT to Subset Sum problem -- (complexity theory automata reductions)
<p>How to reduce 3-SAT to <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" rel="nofollow noreferrer">subset sum</a> problem?</p>
 | habedi/stack-exchange-dataset |
107,380 | What Do These Symbols Mean in Repetitive Rule Application and How Are They Applied Practically? | <p>Frequently in cs blogs and books I see this notation, <code>=>*</code> and <code>=>+</code> but I am not sure how it is being applied in a production rule and it's significance. What exactly does it represent, and can you show an example of it being applied.</p>
 | formal grammars | 1 | What Do These Symbols Mean in Repetitive Rule Application and How Are They Applied Practically? -- (formal grammars)
<p>Frequently in cs blogs and books I see this notation, <code>=>*</code> and <code>=>+</code> but I am not sure how it is being applied in a production rule and it's significance. What exactly doe... | habedi/stack-exchange-dataset |
107,397 | Fewest traversals to visit all vertices of DAG | <p>I want to find the fewest traversals to visit all vertices of a DAG. To take a very simple case:</p>

<pre><code>Boston -> New York -> San Francisco or Las Vegas, both to -> LA
 -> Pittsburgh -> San Francisco or Las Vegas, both to -> LA
</code></pre>

<p>There are l... | algorithms graphs graph traversal dag | 1 | Fewest traversals to visit all vertices of DAG -- (algorithms graphs graph traversal dag)
<p>I want to find the fewest traversals to visit all vertices of a DAG. To take a very simple case:</p>

<pre><code>Boston -> New York -> San Francisco or Las Vegas, both to -> LA
 -> Pittsburgh -&... | habedi/stack-exchange-dataset |
107,399 | Operator name in LL(1) computation | <p>I'm working from a definition of the LL(1) property of context-free languages in order to build a LL(1)-computer, i.e., a program capable of determining whether a given context-free language is in LL(1).</p>

<p>The definition requires the disjointness of certain sets; each set is defined as an infinite limi... | formal languages context free terminology formal grammars | 1 | Operator name in LL(1) computation -- (formal languages context free terminology formal grammars)
<p>I'm working from a definition of the LL(1) property of context-free languages in order to build a LL(1)-computer, i.e., a program capable of determining whether a given context-free language is in LL(1).</p>

<p... | habedi/stack-exchange-dataset |
107,401 | Complement of NP-complete can be in NP | <p>Here are a couple of questions I struggle with. (We use <span class="math-container">$A'$</span> to denote the complement of the problem <span class="math-container">$A$</span>.)</p>

<ol>
<li>A problem <span class="math-container">$A$</span> is NP-complete if and only if <span class="math-container">$A... | complexity theory np complete np | 1 | Complement of NP-complete can be in NP -- (complexity theory np complete np)
<p>Here are a couple of questions I struggle with. (We use <span class="math-container">$A'$</span> to denote the complement of the problem <span class="math-container">$A$</span>.)</p>

<ol>
<li>A problem <span class="math-contai... | habedi/stack-exchange-dataset |
107,409 | when can i detect the position of error in hamming code | <p>I have 4-bit data with the hamming code <code>0010011</code>.<br>
the parity parameters are: <code>p1=0 , p2=0 , p3=0</code><br>
and the check codes are: <code>c1 = 0 , c2 = 1 , c3 = 0</code><br>
so I thought that I have an error in position 2 of my data but the solution says that I can not detect the po... | error correcting codes hamming code | 1 | when can i detect the position of error in hamming code -- (error correcting codes hamming code)
<p>I have 4-bit data with the hamming code <code>0010011</code>.<br>
the parity parameters are: <code>p1=0 , p2=0 , p3=0</code><br>
and the check codes are: <code>c1 = 0 , c2 = 1 , c3 = 0</code><br>
so I thought... | habedi/stack-exchange-dataset |
107,412 | Can a transcript change dependent random variables into independent variables? | <p>Let's say <span class="math-container">$X, Y$</span> are <em>dependent</em> random variables. Can I find an example such that for a transcript <span class="math-container">$t$</span> conditioned on a communication protocol <span class="math-container">$\Pi=t$</span>, the variables become independent?</p>
 | communication protocols communication complexity | 1 | Can a transcript change dependent random variables into independent variables? -- (communication protocols communication complexity)
<p>Let's say <span class="math-container">$X, Y$</span> are <em>dependent</em> random variables. Can I find an example such that for a transcript <span class="math-container">$t$</span> c... | habedi/stack-exchange-dataset |
107,414 | Lower bound of disjointness by discrepancy? | <p>I need to show that <span class="math-container">$Disc_\mu(Disj) \geq \frac{1}{2n+1}$</span> for any distribution <span class="math-container">$\mu: \{0,1\}^n \times \{0,1\}^n \to [0,1]$</span>. 
Disjointness is defined as </p>

<p><span class="math-container">$Disj(X,Y)=\left\{ \begin{array}[ll]+1 &... | lower bounds communication complexity | 1 | Lower bound of disjointness by discrepancy? -- (lower bounds communication complexity)
<p>I need to show that <span class="math-container">$Disc_\mu(Disj) \geq \frac{1}{2n+1}$</span> for any distribution <span class="math-container">$\mu: \{0,1\}^n \times \{0,1\}^n \to [0,1]$</span>. 
Disjointness is defined as </p... | habedi/stack-exchange-dataset |
107,418 | Proof that POSITIVE-3-SAT is in the complexity class P | <p>I have the following language: </p>

<p><span class="math-container">$$\text{POSITIVE-3-SAT} = \{\langle\phi\rangle \mid \phi\text{ is a satisfiable boolean formula in conjunctive normal form,}\\ \text{ in which all clauses consist of exactly 3 literals and in which no variable appears negated}\}.$$</span></... | satisfiability 3 sat normal forms | 1 | Proof that POSITIVE-3-SAT is in the complexity class P -- (satisfiability 3 sat normal forms)
<p>I have the following language: </p>

<p><span class="math-container">$$\text{POSITIVE-3-SAT} = \{\langle\phi\rangle \mid \phi\text{ is a satisfiable boolean formula in conjunctive normal form,}\\ \text{ in which all... | habedi/stack-exchange-dataset |
107,421 | Proving that L is not regular using closure properties | <p>I need to show that the following language is not regular. </p>

<p><span class="math-container">$$L = \{\ ab^jc^j\ |\ j \geq 0\ \}\ \cup\ \{\ a^ib^jc^k\ |\ i, j, k \geq 0 \ and\ i \neq 1\ \}$$</span></p>

<p>There is also a hint that it cannot be proven just with using the Pumping Lemma. Closure pro... | regular languages pumping lemma closure properties | 1 | Proving that L is not regular using closure properties -- (regular languages pumping lemma closure properties)
<p>I need to show that the following language is not regular. </p>

<p><span class="math-container">$$L = \{\ ab^jc^j\ |\ j \geq 0\ \}\ \cup\ \{\ a^ib^jc^k\ |\ i, j, k \geq 0 \ and\ i \neq 1\ \}$$</spa... | habedi/stack-exchange-dataset |
107,423 | Basic second-order logic example contains a mistake? | <p>I'm reading the following course on second-order logic, by Péter Mekis :
<a href="http://phil.elte.hu/mekis/sol.pdf" rel="nofollow noreferrer">http://phil.elte.hu/mekis/sol.pdf</a> .
The course seems excellent, but I'm stuck on one of his first examples for showing the power of second-order logic w.r.t first... | logic first order logic | 1 | Basic second-order logic example contains a mistake? -- (logic first order logic)
<p>I'm reading the following course on second-order logic, by Péter Mekis :
<a href="http://phil.elte.hu/mekis/sol.pdf" rel="nofollow noreferrer">http://phil.elte.hu/mekis/sol.pdf</a> .
The course seems excellent, but I'm stuck on... | habedi/stack-exchange-dataset |
107,429 | lambda calculus with church numerals | <p>today I found this term in our exercises: ((^fx.f(f(f x)) ^gy.g(g y )) ^z.z + 1) (0)</p>

<p>I am quit unaware how to solve this type of question.
I know this is the church numeral 3 , 2 , the identity function +1 and zero.
But for my understanding it lacks an operator like +-*/ 
as ex.</p>
&... | lambda calculus functional programming church numerals | 1 | lambda calculus with church numerals -- (lambda calculus functional programming church numerals)
<p>today I found this term in our exercises: ((^fx.f(f(f x)) ^gy.g(g y )) ^z.z + 1) (0)</p>

<p>I am quit unaware how to solve this type of question.
I know this is the church numeral 3 , 2 , the identity functi... | habedi/stack-exchange-dataset |
107,430 | What are the sufficient conditions for a grammar to be unambiguous? | <p><a href="https://cs.stackexchange.com/questions/84475/how-to-check-for-ambiguous-grammar-if-you-dont-know-the-string">There is no algorithm that, given an arbitrary grammar, decides if it's ambiguous or not</a>. However, Are there any sufficient conditions that make it easier to tell that a grammar is unambiguous?</... | context free formal grammars ambiguity | 1 | What are the sufficient conditions for a grammar to be unambiguous? -- (context free formal grammars ambiguity)
<p><a href="https://cs.stackexchange.com/questions/84475/how-to-check-for-ambiguous-grammar-if-you-dont-know-the-string">There is no algorithm that, given an arbitrary grammar, decides if it's ambiguous or no... | habedi/stack-exchange-dataset |
107,431 | How do I determine if this argument is valid? | <p>I'm studying propositional logic the section on "valid arguments".</p>

<p>A self-assessment question reads</p>

<p>"Show whether or not the following argument is valid"</p>

<p><span class="math-container">$\frac{P}{C}$</span></p>

<p>I don't know what function to apply to P to calcu... | propositional logic | 1 | How do I determine if this argument is valid? -- (propositional logic)
<p>I'm studying propositional logic the section on "valid arguments".</p>

<p>A self-assessment question reads</p>

<p>"Show whether or not the following argument is valid"</p>

<p><span class="math-container">$\frac{P}{C}$</... | habedi/stack-exchange-dataset |
107,438 | Is this problem that's similar to integer linear programming also an NP-complete problem? | <p>I've come across this problem while trying to work out a table-formatting algorithm.</p>

<p>It's very similar to standard linear programming (though it uses <span class="math-container">$>$</span> instead of <span class="math-container">$<$</span>; I'm not extremely familiar with linear programming, b... | np complete integer programming constraint satisfaction | 1 | Is this problem that's similar to integer linear programming also an NP-complete problem? -- (np complete integer programming constraint satisfaction)
<p>I've come across this problem while trying to work out a table-formatting algorithm.</p>

<p>It's very similar to standard linear programming (though it uses ... | habedi/stack-exchange-dataset |
107,439 | What is a 'Key' in computer science? | <p>I'm a bit confused on what exactly the meaning of a 'key' is in computer science. I understand key-value pairs, primary keys, etc... But I can't find a definition of what the term 'key' means by itself.</p>

<p>As far as I can tell it just means a piece of data. In CLRS, data associated with tree nodes are r... | terminology | 1 | What is a 'Key' in computer science? -- (terminology)
<p>I'm a bit confused on what exactly the meaning of a 'key' is in computer science. I understand key-value pairs, primary keys, etc... But I can't find a definition of what the term 'key' means by itself.</p>

<p>As far as I can tell it just means a piece o... | habedi/stack-exchange-dataset |
108,451 | 3-DNF proves the algorithm is in P class | <p><a href="https://cs.stackexchange.com/questions/107183/will-this-algorithm-always-solve-a-constrained-sudoku-puzzle-in-quadratic-time">To understand fully, please read link</a></p>

<p>After, reading the link we will take a look at how we recover our solutions to a constrained Sudoku Puzzle.</p>

<p>... | satisfiability decision problem | 1 | 3-DNF proves the algorithm is in P class -- (satisfiability decision problem)
<p><a href="https://cs.stackexchange.com/questions/107183/will-this-algorithm-always-solve-a-constrained-sudoku-puzzle-in-quadratic-time">To understand fully, please read link</a></p>

<p>After, reading the link we will take a look at... | habedi/stack-exchange-dataset |
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