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 |
|---|---|---|---|---|---|---|
24,180 | Proving that a language does not belong to a language class by using more specific instances of that language | <p>You have a description of a language that you have to prove is regular, context free, or other. In order to prove that it does <em>not</em> belong to a certain class of languages, you might think that it will be more convenient to prove it by using a subset of that language. The problem is that a subset of a languag... | formal languages proof techniques | 1 | Proving that a language does not belong to a language class by using more specific instances of that language -- (formal languages proof techniques)
<p>You have a description of a language that you have to prove is regular, context free, or other. In order to prove that it does <em>not</em> belong to a certain class of... | habedi/stack-exchange-dataset |
24,184 | Turing machine with repeated strings | <p>How would I go about making a Turing machine to accept the following language L?</p>

<p>$$L = \{ www \mid w = \{0,1\}^* \text{ and } w > 0\}$$</p>

<p>I was thinking counting the number of symbols in the input string and then dividing by three to find the beginning of each instance of <em>w</em> ... | formal languages turing machines automata strings | 1 | Turing machine with repeated strings -- (formal languages turing machines automata strings)
<p>How would I go about making a Turing machine to accept the following language L?</p>

<p>$$L = \{ www \mid w = \{0,1\}^* \text{ and } w > 0\}$$</p>

<p>I was thinking counting the number of symbols in the i... | habedi/stack-exchange-dataset |
24,185 | Inclusion of complexity classes (Deterministic Turing Machine) | <p>I can't understand what my professor wrote about these inclusions concerning deterministic classes:</p>

<p>$$
DTIME(f) \subseteq DSPACE(f) \subseteq \sum_{c\in\Bbb N}DTIME(2^{c(log+f)}) 
$$</p>

<p>I understood the first inclusion:</p>

<blockquote>
 <p>The Turing Machine needs... | turing machines time complexity space complexity complexity classes | 1 | Inclusion of complexity classes (Deterministic Turing Machine) -- (turing machines time complexity space complexity complexity classes)
<p>I can't understand what my professor wrote about these inclusions concerning deterministic classes:</p>

<p>$$
DTIME(f) \subseteq DSPACE(f) \subseteq \sum_{c\in\Bbb N}DT... | habedi/stack-exchange-dataset |
24,186 | Operator overloading: Java vs. Python | <p>Why <a href="http://en.wikipedia.org/wiki/Operator_overloading" rel="nofollow">operator overloading</a> was included in Python and not in Java?
How does one decide to include or exclude operator overloading in a programming language?</p>

<p>It is said <a href="http://javarevisited.blogspot.in/2011/08/wh... | programming languages api design | 1 | Operator overloading: Java vs. Python -- (programming languages api design)
<p>Why <a href="http://en.wikipedia.org/wiki/Operator_overloading" rel="nofollow">operator overloading</a> was included in Python and not in Java?
How does one decide to include or exclude operator overloading in a programming language?</p>... | habedi/stack-exchange-dataset |
24,195 | Just another Divide-And-Conquer question - but somehow different | <p>Please consider the following Divide-And-Conquer Problem:</p>

<blockquote>
 <p>You’re consulting for a small computation-intensive investment
 company, and they have the following type of problem that they want to
 solve over and over. A typical instance of the problem is the
 following.... | algorithms algorithm analysis divide and conquer | 1 | Just another Divide-And-Conquer question - but somehow different -- (algorithms algorithm analysis divide and conquer)
<p>Please consider the following Divide-And-Conquer Problem:</p>

<blockquote>
 <p>You’re consulting for a small computation-intensive investment
 company, and they have the following... | habedi/stack-exchange-dataset |
24,199 | Hardness of approximating hitting set | <p>Consider the <a href="http://www.nada.kth.se/~viggo/wwwcompendium/node149.html" rel="nofollow">hitting set problem</a> with $n$ elements and $m$ sets. I gather from the linked page as well as <a href="http://people.csail.mit.edu/dmoshkov/papers/set-cover/set-cover-full.pdf" rel="nofollow">this</a> that </p>

... | np hard approximation | 1 | Hardness of approximating hitting set -- (np hard approximation)
<p>Consider the <a href="http://www.nada.kth.se/~viggo/wwwcompendium/node149.html" rel="nofollow">hitting set problem</a> with $n$ elements and $m$ sets. I gather from the linked page as well as <a href="http://people.csail.mit.edu/dmoshkov/papers/set-cov... | habedi/stack-exchange-dataset |
24,209 | Why does an acceptor send the highest numbered proposal with number less than n as a response to prepare(n) in paxos? | <p>I was reading the Paxos notes from yale from the following link:</p>

<p><a href="http://pine.cs.yale.edu/pinewiki/Paxos" rel="nofollow">http://pine.cs.yale.edu/pinewiki/Paxos</a></p>

<p>Recall that Paxos is a distributed system algorithm with the goal that the processes participating in its protoco... | algorithms algorithm analysis distributed systems | 1 | Why does an acceptor send the highest numbered proposal with number less than n as a response to prepare(n) in paxos? -- (algorithms algorithm analysis distributed systems)
<p>I was reading the Paxos notes from yale from the following link:</p>

<p><a href="http://pine.cs.yale.edu/pinewiki/Paxos" rel="nofollow"... | habedi/stack-exchange-dataset |
24,217 | Bloom filter variant | <p>I've been playing around with a simple probabilistic data structure which is very similar to a Bloom filter. Where a Bloom filter would use $k$ independent hash functions to choose $k$ of the $m$ bits to set, this structure uses $m$ hash functions, and sets each bit with probability $p$.</p>

<p>This structu... | reference request data structures probabilistic algorithms bloom filters dictionaries | 1 | Bloom filter variant -- (reference request data structures probabilistic algorithms bloom filters dictionaries)
<p>I've been playing around with a simple probabilistic data structure which is very similar to a Bloom filter. Where a Bloom filter would use $k$ independent hash functions to choose $k$ of the $m$ bits to s... | habedi/stack-exchange-dataset |
24,225 | Robot follows a path near an obstacle without colliding | <p>I have a problem that I would like to solve it. A robot have to move near an obstacle (e.g a wall) without colliding. He should also try to be always near the obstacle.
The following picture can help you to understand what I need to do:</p>

<p><img src="https://i.stack.imgur.com/zYBcI.png" alt="enter im... | artificial intelligence | 1 | Robot follows a path near an obstacle without colliding -- (artificial intelligence)
<p>I have a problem that I would like to solve it. A robot have to move near an obstacle (e.g a wall) without colliding. He should also try to be always near the obstacle.
The following picture can help you to understand what I nee... | habedi/stack-exchange-dataset |
24,226 | regular expression: sum of positive fixed point decimal numbers | <p>I need help with this exercise. </p>

<p>Indicate the regular expression for the following Languages. Explain your expression in one sentence and indicate the basis form of the alphabet. Indicate also every assumption you make.</p>

<p>i) Sums of positive fixed-point decimal numbers. The following S... | formal languages regular expressions | 1 | regular expression: sum of positive fixed point decimal numbers -- (formal languages regular expressions)
<p>I need help with this exercise. </p>

<p>Indicate the regular expression for the following Languages. Explain your expression in one sentence and indicate the basis form of the alphabet. Indicate also e... | habedi/stack-exchange-dataset |
24,231 | Given a complete, weighted and undirected graph $G$, complexity of finding a path with a specific cost | <p>Given a fully connected graph $G$, suppose that we are searching for a simple path $P$ with a specific cost $c$. </p>

<p>Is answering to that problem <em>yes</em> or <em>no</em> equivalent to subset-sum problem?
What would be the complexity of finding such path?</p>

<p>I have made a reduction f... | algorithms graphs decision problem | 1 | Given a complete, weighted and undirected graph $G$, complexity of finding a path with a specific cost -- (algorithms graphs decision problem)
<p>Given a fully connected graph $G$, suppose that we are searching for a simple path $P$ with a specific cost $c$. </p>

<p>Is answering to that problem <em>yes</em> or... | habedi/stack-exchange-dataset |
24,232 | Minimum weighted arithmetic mean partion? | <p>Assume I have some positive numbers $a_1,\ldots,a_n$ and a number $k \in \mathbb{N}$. </p>

<p>I want to partition these numbers into exactly $k$ sets $A_1,\ldots,A_k$ such that the weighted arithmetic mean</p>

<p>$$\text{cost}(A_i,\ldots,A_k)=\sum_{i=1}^{k}\frac{|A_i|}{n}c(A_i)$$</p>

<p>is... | optimization np hard np partitions | 1 | Minimum weighted arithmetic mean partion? -- (optimization np hard np partitions)
<p>Assume I have some positive numbers $a_1,\ldots,a_n$ and a number $k \in \mathbb{N}$. </p>

<p>I want to partition these numbers into exactly $k$ sets $A_1,\ldots,A_k$ such that the weighted arithmetic mean</p>

<p>$$\t... | habedi/stack-exchange-dataset |
24,235 | Tree data structure for fast merges | <p>I need trees that have the following properties:</p>

<ol>
<li><p>Each node in the tree has two values associated with it - a key and an associated opaque data element.</p></li>
<li><p>An internal node in the tree has unbounded number of children. The tree reflects a real world hierarchy that is in f... | data structures trees dictionaries | 1 | Tree data structure for fast merges -- (data structures trees dictionaries)
<p>I need trees that have the following properties:</p>

<ol>
<li><p>Each node in the tree has two values associated with it - a key and an associated opaque data element.</p></li>
<li><p>An internal node in the tree has unbound... | habedi/stack-exchange-dataset |
24,237 | Where/when did Stephen Kleene first define the Kleene closure/star? | <p>I'm working on a paper and would like to review the origins of <a href="http://en.wikipedia.org/wiki/Kleene_star">Kleene's closure</a>. I am unable to find any article of Kleene's that has the original definition of the Kleene closure.</p>

<p>Is there a paper by Kleene in which he first defines the Kleene c... | formal languages reference request automata | 1 | Where/when did Stephen Kleene first define the Kleene closure/star? -- (formal languages reference request automata)
<p>I'm working on a paper and would like to review the origins of <a href="http://en.wikipedia.org/wiki/Kleene_star">Kleene's closure</a>. I am unable to find any article of Kleene's that has the origina... | habedi/stack-exchange-dataset |
24,243 | Constructing an unrestricted grammar for a^n b^m c^n d^m | <p>I've been trying to construct an unrestricted grammar which has the language:</p>

<p><code>L = {a^n b^m c^n d^m | n>0, m>0}</code></p>

<p>But I can't seem to figure it out without making the derivations run an unreasonably long amount of time. Can anyone help me devise an elegant way to crea... | formal languages formal grammars | 1 | Constructing an unrestricted grammar for a^n b^m c^n d^m -- (formal languages formal grammars)
<p>I've been trying to construct an unrestricted grammar which has the language:</p>

<p><code>L = {a^n b^m c^n d^m | n>0, m>0}</code></p>

<p>But I can't seem to figure it out without making the derivat... | habedi/stack-exchange-dataset |
24,246 | Why is the k-bounded spanning tree problem NP-complete? | <p>The $k$-bounded spanning tree problem is where you have an undirected graph $G(V,E)$ and you have to decide whether or not it has a spanning tree such that each vertex has a degree of at most $k$.</p>

<p>I realize that for the case $k=2$, this is the Hamiltonian path problem. However I'm having trouble with... | spanning trees | 1 | Why is the k-bounded spanning tree problem NP-complete? -- (spanning trees)
<p>The $k$-bounded spanning tree problem is where you have an undirected graph $G(V,E)$ and you have to decide whether or not it has a spanning tree such that each vertex has a degree of at most $k$.</p>

<p>I realize that for the case ... | habedi/stack-exchange-dataset |
24,255 | What does it mean that a value can only be incremented after it's been loaded into a register? | <p>Consider the following program:</p>

<pre><code>const int n = 50;
int tally;

void total() {
 int count;
 for (count = 1; count <= n; count++){
 tally++;
 }
}

void main() {
 tally = 0;
 parbegin (total (), total ());
 write (tally);
}
<... | terminology concurrency semantics | 1 | What does it mean that a value can only be incremented after it's been loaded into a register? -- (terminology concurrency semantics)
<p>Consider the following program:</p>

<pre><code>const int n = 50;
int tally;

void total() {
 int count;
 for (count = 1; count <= n; count++){
 ... | habedi/stack-exchange-dataset |
24,256 | How does one figure out where a class of languages falls under some complexity class? | <p><img src="https://i.imgur.com/fKkk9Aq.png" alt="enter image description here"></p>

<p>I was wondering how can someone prove that one class of languages is of a certain complexity? For example, how could I show the Turing-recognizable languages are in P?</p>

<p>Would I have to come up with an algori... | complexity theory formal languages proof techniques | 1 | How does one figure out where a class of languages falls under some complexity class? -- (complexity theory formal languages proof techniques)
<p><img src="https://i.imgur.com/fKkk9Aq.png" alt="enter image description here"></p>

<p>I was wondering how can someone prove that one class of languages is of a certa... | habedi/stack-exchange-dataset |
24,261 | Is the class NP closed under complement? | <p>Is the class $\sf NP$ closed under complement or is it unknown? I have looked online, but I couldn't find anything. </p>
 | complexity theory closure properties complexity classes np | 1 | Is the class NP closed under complement? -- (complexity theory closure properties complexity classes np)
<p>Is the class $\sf NP$ closed under complement or is it unknown? I have looked online, but I couldn't find anything. </p>
 | habedi/stack-exchange-dataset |
24,264 | are NP Complete languages closed under any regular operations? | <p>I have tried looking online, but I couldn't find any definitive statements. It would make sense to me that Union and Intersection of two NPC languages would produce a language not necessarily in NPC. Is it also true that NPC languages are not closed under the complement, concatenation, and kleene star operations?</p... | complexity theory np complete closure properties | 1 | are NP Complete languages closed under any regular operations? -- (complexity theory np complete closure properties)
<p>I have tried looking online, but I couldn't find any definitive statements. It would make sense to me that Union and Intersection of two NPC languages would produce a language not necessarily in NPC. ... | habedi/stack-exchange-dataset |
24,269 | An $O(n)$ algorithm to FFT-evaluate an FFT evaluation | <p>This question is from a practice exam in my algorithms class. I'm posting the question and the answer listed in that practice exam:</p>

<blockquote>
 <p>Let $W$ be an $n\times n$ matrix whose $(i,j)$-th entry is $\omega_n^{ij}$, where $\omega_n$ is a principal $n$th root of unity. Let $X=(X_0,\dots,X_{... | algorithms algorithm analysis fourier transform | 1 | An $O(n)$ algorithm to FFT-evaluate an FFT evaluation -- (algorithms algorithm analysis fourier transform)
<p>This question is from a practice exam in my algorithms class. I'm posting the question and the answer listed in that practice exam:</p>

<blockquote>
 <p>Let $W$ be an $n\times n$ matrix whose $(i,... | habedi/stack-exchange-dataset |
24,279 | How to find partition set of a Partition Problem using its decision problem | <p>I understand Partition Problem is NP-complete.</p>

<p>Given we have a magic black box that can answer Yes or No for the partition problem. I was wondering how to come up with a polynomial time algorithm to find the actual set using this black box. </p>

<p>Thank you. </p>
 | complexity theory np complete partition problem | 1 | How to find partition set of a Partition Problem using its decision problem -- (complexity theory np complete partition problem)
<p>I understand Partition Problem is NP-complete.</p>

<p>Given we have a magic black box that can answer Yes or No for the partition problem. I was wondering how to come up with a po... | habedi/stack-exchange-dataset |
24,290 | Solving the recurrence T(n) = 3T(n-2) with iterative method | <p>It's been a while since I had to solve a recurrence and I wanted to make sure I understood the iterative method of solving these problems. Given:</p>

<p>$$T(n) = 3T(n-2)$$</p>

<p>My first step was to iteratively substitute terms to arrive at a general form:</p>

<p>$$T(n-2) = 3T(n-2 -2) = 3... | asymptotics recurrence relation | 1 | Solving the recurrence T(n) = 3T(n-2) with iterative method -- (asymptotics recurrence relation)
<p>It's been a while since I had to solve a recurrence and I wanted to make sure I understood the iterative method of solving these problems. Given:</p>

<p>$$T(n) = 3T(n-2)$$</p>

<p>My first step was to it... | habedi/stack-exchange-dataset |
24,293 | regular expression in license plates | <p>I'm trying to write a regular expression for some particular license plates. They consist of one up to three capital letters, a hyphen, one up to two capitol letters and one up to four numbers. The license plate should not exceed the 8 symbols.</p>

<p>Example: AA-AA123</p>

<p>What I have until now ... | formal languages regular expressions | 1 | regular expression in license plates -- (formal languages regular expressions)
<p>I'm trying to write a regular expression for some particular license plates. They consist of one up to three capital letters, a hyphen, one up to two capitol letters and one up to four numbers. The license plate should not exceed the 8 sy... | habedi/stack-exchange-dataset |
24,312 | What would show a human mind is/is not reducible to a Turing machine? | <p>In computer science it is often assumed that a human mind can be reduced to a Turing machine. This is the assumption that underlies the field of artificial intelligence.</p>

<p>However, it is an assumption, one that has neither been proven or disproven.</p>

<p>Is there any kind of test within our ... | turing machines artificial intelligence computer vs human | 1 | What would show a human mind is/is not reducible to a Turing machine? -- (turing machines artificial intelligence computer vs human)
<p>In computer science it is often assumed that a human mind can be reduced to a Turing machine. This is the assumption that underlies the field of artificial intelligence.</p>

... | habedi/stack-exchange-dataset |
24,314 | How to evaluate all derivatives of a polynomial at a point with FFT? | <p>I found <a href="http://staff.ustc.edu.cn/~csli/graduate/algorithms/book6/chap32.htm" rel="nofollow noreferrer">this problem</a>:</p>

<blockquote>
 <p>Evaluating all derivatives of a polynomial at a point</p>
 
 <p>Given a polynomial A(x) of degree-bound n, its tth derivative is
 defined... | fourier transform | 1 | How to evaluate all derivatives of a polynomial at a point with FFT? -- (fourier transform)
<p>I found <a href="http://staff.ustc.edu.cn/~csli/graduate/algorithms/book6/chap32.htm" rel="nofollow noreferrer">this problem</a>:</p>

<blockquote>
 <p>Evaluating all derivatives of a polynomial at a point</p>&#x... | habedi/stack-exchange-dataset |
24,319 | Complexity of factoring products of distinct prime numbers | <p>Problem: Input is an integer number $x$ that we know factors as $p_{i_1}\cdot p_{i_2}\ldots p_{i_n}$, where the $p_{i_j}$'s are distinct prime numbers. Output is the above factorization of $x$.</p>

<p>Do you know any results/references for the time complexity of this factoring problem? </p>

<p>Note... | complexity theory reference request time complexity factoring | 1 | Complexity of factoring products of distinct prime numbers -- (complexity theory reference request time complexity factoring)
<p>Problem: Input is an integer number $x$ that we know factors as $p_{i_1}\cdot p_{i_2}\ldots p_{i_n}$, where the $p_{i_j}$'s are distinct prime numbers. Output is the above factorization of $x... | habedi/stack-exchange-dataset |
24,321 | Coq --- non-terminating programs | <p>People usually say Coq does not allow writing non-terminating functions. I have a question regarding that.</p>

<p>Does Coq allow writing exactly <strong>all</strong> terminating functions? In other words, what are the completeness and soundness properties of Coq's procedure for checking well-foundness of fi... | machine models coq | 1 | Coq --- non-terminating programs -- (machine models coq)
<p>People usually say Coq does not allow writing non-terminating functions. I have a question regarding that.</p>

<p>Does Coq allow writing exactly <strong>all</strong> terminating functions? In other words, what are the completeness and soundness proper... | habedi/stack-exchange-dataset |
24,326 | Is the complexity class NP computably enumerable? | <p>The definition of the complexity class $\mathsf{NP}$ seems to ensure (as good as possible) that it is computably enumerable. It looks as if the class could be enumerated by enumerating all Turing machines, and for each Turing machine report for each $k\in\mathbb{N}$ the language generated by stopping each computatio... | computability complexity classes np enumeration | 1 | Is the complexity class NP computably enumerable? -- (computability complexity classes np enumeration)
<p>The definition of the complexity class $\mathsf{NP}$ seems to ensure (as good as possible) that it is computably enumerable. It looks as if the class could be enumerated by enumerating all Turing machines, and for ... | habedi/stack-exchange-dataset |
24,336 | Are there any PSPACE problems that don't exist in NP-Hard? | <p>The question is in the title, I suppose. I am studying complexity classes, and I understand that NP-Hard is the set of problems that are at least as hard as the hardest problems in NP. Therefore, it will naturally contain PSPACE problems.</p>

<p>However, I was specifically wondering if there were any PSPACE... | complexity theory np hard complexity classes | 1 | Are there any PSPACE problems that don't exist in NP-Hard? -- (complexity theory np hard complexity classes)
<p>The question is in the title, I suppose. I am studying complexity classes, and I understand that NP-Hard is the set of problems that are at least as hard as the hardest problems in NP. Therefore, it will natu... | habedi/stack-exchange-dataset |
24,340 | Does "serializable" also mean that it's lockable | <p>Here's an final exam question for a Database Fundamentals class. I've read the book, stuff online.. I can't figure out if "<em>serializable</em>" also means that the schedule is <code>lockable</code> or not. What I mean is.. I understand that for the schedule to be isolated, you have to have non-conflicting <em>read... | concurrency databases | 1 | Does "serializable" also mean that it's lockable -- (concurrency databases)
<p>Here's an final exam question for a Database Fundamentals class. I've read the book, stuff online.. I can't figure out if "<em>serializable</em>" also means that the schedule is <code>lockable</code> or not. What I mean is.. I understand tha... | habedi/stack-exchange-dataset |
24,343 | Is dependency analysis required in order to type a program? | <p>I have seen stated in various places that in order to allow an "increase in polymorphism," functional dependency analysis should be performed, and type inference should be used for every declaration group in topological order. It seems like a well-known fact... except that nobody provides any reference or example.</... | functional programming typing type inference | 1 | Is dependency analysis required in order to type a program? -- (functional programming typing type inference)
<p>I have seen stated in various places that in order to allow an "increase in polymorphism," functional dependency analysis should be performed, and type inference should be used for every declaration group in... | habedi/stack-exchange-dataset |
24,345 | Automata with no transition for some character | <p>Given an automaton and an alphabet $\{a, b\} $, and the language accepted by the automaton is $ab^*$. </p>

<p>Such an automata can be found here:</p>

<p><img src="https://i.stack.imgur.com/Vmutm.gif" alt="an automaton"></p>

<p>My question is: this automaton cannot process the word $ba$ fo... | terminology automata finite automata | 1 | Automata with no transition for some character -- (terminology automata finite automata)
<p>Given an automaton and an alphabet $\{a, b\} $, and the language accepted by the automaton is $ab^*$. </p>

<p>Such an automata can be found here:</p>

<p><img src="https://i.stack.imgur.com/Vmutm.gif" alt="an a... | habedi/stack-exchange-dataset |
24,346 | Can not follow the example for max-flow-min-cut on Wikipedia | <p>This <a href="http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem#Example" rel="nofollow noreferrer">Wikipedia</a> example is very confusing. Its saying the max flow = min cut. But I see the max flow = 9 and the min cut = 7. If not, how does the capacity =min cut here? Which is the max flow min cut theorem. </p>&#... | algorithms graphs network flow | 1 | Can not follow the example for max-flow-min-cut on Wikipedia -- (algorithms graphs network flow)
<p>This <a href="http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem#Example" rel="nofollow noreferrer">Wikipedia</a> example is very confusing. Its saying the max flow = min cut. But I see the max flow = 9 and the min cu... | habedi/stack-exchange-dataset |
24,355 | Can we create binomial heaps in linear time? | <p>I'm studying binomial heaps in anticipation for my finals and the <a href="http://en.wikipedia.org/wiki/CLRS" rel="nofollow">CLRS</a> book tells me that insertion in a binomial heap takes $\Theta(\log n)$ time. So given an array of numbers it would take $\Theta(n\log n)$ time to convert it a a binomial heap. To me t... | data structures efficiency heaps priority queues | 1 | Can we create binomial heaps in linear time? -- (data structures efficiency heaps priority queues)
<p>I'm studying binomial heaps in anticipation for my finals and the <a href="http://en.wikipedia.org/wiki/CLRS" rel="nofollow">CLRS</a> book tells me that insertion in a binomial heap takes $\Theta(\log n)$ time. So give... | habedi/stack-exchange-dataset |
24,361 | Relation between RAM and Turing machine | <p>Denote $D$ a set of finite sequences of integers. In Papadimitriou's "Computational Complexity" in theorem 2.5 it is proved that if a RAM program $\Pi$ computes a function $\phi$ from $D$ to integers in time $f(n)$, then there is a $7$-string Turing machine $M$, which computes $\phi$ in time $O(f(n)^3)$.</p>
&#x... | turing machines time complexity simulation computation models | 1 | Relation between RAM and Turing machine -- (turing machines time complexity simulation computation models)
<p>Denote $D$ a set of finite sequences of integers. In Papadimitriou's "Computational Complexity" in theorem 2.5 it is proved that if a RAM program $\Pi$ computes a function $\phi$ from $D$ to integers in time $f... | habedi/stack-exchange-dataset |
24,364 | Definition of “c-competitive” algorithm | <p>What is the definition of a "c-competitive" algorithm? For example what does it mean, if we say that there is a 2-competitive algorithm for packet routing?</p>
 | algorithms terminology performance | 1 | Definition of “c-competitive” algorithm -- (algorithms terminology performance)
<p>What is the definition of a "c-competitive" algorithm? For example what does it mean, if we say that there is a 2-competitive algorithm for packet routing?</p>
 | habedi/stack-exchange-dataset |
24,381 | Is there C++ code that takes infinite time to compile? | <p>Is C++ as a formal language recursively enumerable? If yes, is there any invalid C++ code that takes "infinite" time to compile?</p>
 | computability compilers semi decidability | 1 | Is there C++ code that takes infinite time to compile? -- (computability compilers semi decidability)
<p>Is C++ as a formal language recursively enumerable? If yes, is there any invalid C++ code that takes "infinite" time to compile?</p>
 | habedi/stack-exchange-dataset |
24,390 | Why is the set of NFA that accept all words in co-NPSPACE? | <p>In Sipser's book there is a section describing how to decide </p>

<p>$\qquad\displaystyle \mathrm{ALL}_\mathrm{NFA} = \{ \langle N \rangle \mid N \text{ is an NFA}, L(N) = \Sigma^*\}$ </p>

<p>in polynomial space. To do so, it shows $\overline{\mathrm{ALL}_\mathrm{NFA} }$ is in NPSPACE. </p>
&#x... | complexity theory space complexity | 1 | Why is the set of NFA that accept all words in co-NPSPACE? -- (complexity theory space complexity)
<p>In Sipser's book there is a section describing how to decide </p>

<p>$\qquad\displaystyle \mathrm{ALL}_\mathrm{NFA} = \{ \langle N \rangle \mid N \text{ is an NFA}, L(N) = \Sigma^*\}$ </p>

<p>in polyn... | habedi/stack-exchange-dataset |
24,395 | Which NP-Complete problem has the fastest known algorithm? | <p>In terms of worst-case asymptotic runtime, which NP-complete problem has the fastest-known (exact) algorithm and what is the algorithm? Is there something known that is faster than $O(n^2*2^n)$?</p>
 | algorithms reference request np complete | 1 | Which NP-Complete problem has the fastest known algorithm? -- (algorithms reference request np complete)
<p>In terms of worst-case asymptotic runtime, which NP-complete problem has the fastest-known (exact) algorithm and what is the algorithm? Is there something known that is faster than $O(n^2*2^n)$?</p>
 | habedi/stack-exchange-dataset |
24,406 | Is there a canonical definition of “pure” function? | <p>StackOverflow pointed me here, so the question might be a bit in a layman's terms.</p>

<p>Wikipedia defines <a href="http://en.wikipedia.org/wiki/Pure_function">pure functions</a> as</p>

<blockquote>
 <p>In computer programming, a function may be described as a pure
 function if both thes... | terminology functional programming semantics | 1 | Is there a canonical definition of “pure” function? -- (terminology functional programming semantics)
<p>StackOverflow pointed me here, so the question might be a bit in a layman's terms.</p>

<p>Wikipedia defines <a href="http://en.wikipedia.org/wiki/Pure_function">pure functions</a> as</p>

<blockquot... | habedi/stack-exchange-dataset |
24,407 | Relationship between graph expansion and conductance | <p>I'm quite confused about the exact relationship between the expansion of a graph and its conductance. My first question is:</p>

<ul>
<li>Could someone point me to a reference that discusses <em>both</em> of these notions? (I've found various lecture notes on related topics but these seem to focus either... | graphs reference request combinatorics expanders | 1 | Relationship between graph expansion and conductance -- (graphs reference request combinatorics expanders)
<p>I'm quite confused about the exact relationship between the expansion of a graph and its conductance. My first question is:</p>

<ul>
<li>Could someone point me to a reference that discusses <em>bot... | habedi/stack-exchange-dataset |
24,414 | Recurrence doesn't add up | <p>I made a recurrence tree and guessed that solution to $T(n)=2T(n-2)+n$ is $O(2^{n/2})$ and I am now trying to prove this through substitution. These are my steps so far, but I can't get it to pass for some reason:</p>

<p>\begin{align}
T(n-2) &\leq c2^{(n-2)/2}\\
T(n) &= 2(c2^{(n-2)/2})+n\\&#... | recurrence relation | 1 | Recurrence doesn't add up -- (recurrence relation)
<p>I made a recurrence tree and guessed that solution to $T(n)=2T(n-2)+n$ is $O(2^{n/2})$ and I am now trying to prove this through substitution. These are my steps so far, but I can't get it to pass for some reason:</p>

<p>\begin{align}
T(n-2) &\leq c... | habedi/stack-exchange-dataset |
24,415 | Reducibility in Computability Theory | <p>In Sipser's book of Theory of Computation, related to Reducibility, it's written </p>

<blockquote>
 <p>if A is undecidable and reducible to B, B is undecidable.</p>
</blockquote>

<p>The confusion is, only a solution to B determines a solution to A, if i'm not wrong.
So, for instance if... | computability reductions | 1 | Reducibility in Computability Theory -- (computability reductions)
<p>In Sipser's book of Theory of Computation, related to Reducibility, it's written </p>

<blockquote>
 <p>if A is undecidable and reducible to B, B is undecidable.</p>
</blockquote>

<p>The confusion is, only a solution to B de... | habedi/stack-exchange-dataset |
24,426 | Need of reducing problems if we already know that a problem is undecidable | <p>In the Reducibility chapter of Sipser's Theory of Computation book, an example is: </p>

<p>We reduce A(TM) to HALT(TM). And then we claim that if H decides HALT(TM), then A decides A(TM), but since A(TM) is undecidable, so is HALT(TM)</p>

<p>My question is, if we already know that A(TM) is undecida... | computability reductions | 1 | Need of reducing problems if we already know that a problem is undecidable -- (computability reductions)
<p>In the Reducibility chapter of Sipser's Theory of Computation book, an example is: </p>

<p>We reduce A(TM) to HALT(TM). And then we claim that if H decides HALT(TM), then A decides A(TM), but since A(TM)... | habedi/stack-exchange-dataset |
24,434 | Find a maximal subgraph on a tree with conditions | <p>Given a tree, find a path on which every vertex has at most 4 leaves (can have 0 as well) and is the "biggest" (has the maximum amount of vertices possible - including the leaves).
Time complexity: $O(n)$.</p>

<p>I'm getting nowhere with this problem. I have tried BFS/DFS (seemed like such an obvious me... | graphs trees graph traversal | 1 | Find a maximal subgraph on a tree with conditions -- (graphs trees graph traversal)
<p>Given a tree, find a path on which every vertex has at most 4 leaves (can have 0 as well) and is the "biggest" (has the maximum amount of vertices possible - including the leaves).
Time complexity: $O(n)$.</p>

<p>I'm get... | habedi/stack-exchange-dataset |
24,436 | Optimal Algorithm for checking if a number is a multiple of three | <p>I'm just starting a course on Computational Number Theory and have very little Computer Science background but definitely know enough about the big-O notation.</p>

<p>I currently have an assignment to work on:</p>

<blockquote>
 <p>An algorithm reads in the binary digits of a positive integer $... | algorithm analysis runtime analysis arithmetic | 1 | Optimal Algorithm for checking if a number is a multiple of three -- (algorithm analysis runtime analysis arithmetic)
<p>I'm just starting a course on Computational Number Theory and have very little Computer Science background but definitely know enough about the big-O notation.</p>

<p>I currently have an ass... | habedi/stack-exchange-dataset |
24,446 | Why does introsort use heapsort rather than mergesort? | <p>As part of a homework assignment covering implementation of <a href="http://en.wikipedia.org/wiki/Introsort">introsort</a> I'm asked why heapsort is used rather than mergesort (or other $O(n\log(n))$ algorithms for that matter). </p>

<blockquote>
 <p>Introsort is a hybrid sorting algorithm that provid... | algorithms algorithm analysis sorting | 1 | Why does introsort use heapsort rather than mergesort? -- (algorithms algorithm analysis sorting)
<p>As part of a homework assignment covering implementation of <a href="http://en.wikipedia.org/wiki/Introsort">introsort</a> I'm asked why heapsort is used rather than mergesort (or other $O(n\log(n))$ algorithms for that... | habedi/stack-exchange-dataset |
24,450 | NP Completeness of 3-SAT problem | <p>I have started reading on algorithmic complexity for my thesis work. Already have studied on Polynomial time reducibility, NP-Complete, NP-Hard. Now trying to prove NP completeness of some of the classical problems. I have started with 3-SAT problem.</p>
<p>3-SAT problem — was shown to be NP-complete:</p>
<b... | complexity theory np complete reductions satisfiability 3 sat | 1 | NP Completeness of 3-SAT problem -- (complexity theory np complete reductions satisfiability 3 sat)
<p>I have started reading on algorithmic complexity for my thesis work. Already have studied on Polynomial time reducibility, NP-Complete, NP-Hard. Now trying to prove NP completeness of some of the classical problems. I... | habedi/stack-exchange-dataset |
24,457 | Mutual Information in a Binary Erasure Channel | <p>Imagine a Binary Erasure Channel as depicted on <a href="http://en.wikipedia.org/wiki/Binary_erasure_channel" rel="nofollow">Wikipedia</a>.</p>

<p>One equation describing the mutual information is:</p>

<p>$$
\begin{align*}I(x;y) 
 &= H(x) - H(x|y) \\
 &= H(x) - p(y=0) \cdot 0 - ... | information theory | 1 | Mutual Information in a Binary Erasure Channel -- (information theory)
<p>Imagine a Binary Erasure Channel as depicted on <a href="http://en.wikipedia.org/wiki/Binary_erasure_channel" rel="nofollow">Wikipedia</a>.</p>

<p>One equation describing the mutual information is:</p>

<p>$$
\begin{align*}I(... | habedi/stack-exchange-dataset |
24,459 | Show that the running time of the build_heap function is $O(n)$ | <blockquote>
 <p>Given the following two functions, prove that the build_heap function, which transforms an array A into a max-heap-sorted array A' runs in $O(n)$.</p>

<pre><code>heapify(A, i):

Input: array A of length n, index i

left = 2i + 1 (left child node) 
right = 2i + 2 (right... | algorithm analysis data structures heaps | 1 | Show that the running time of the build_heap function is $O(n)$ -- (algorithm analysis data structures heaps)
<blockquote>
 <p>Given the following two functions, prove that the build_heap function, which transforms an array A into a max-heap-sorted array A' runs in $O(n)$.</p>

<pre><code>heapify(A, i):&#x... | habedi/stack-exchange-dataset |
24,464 | Minimising height of a 2-3-4 tree | <p>I'm wondering how a set of keys could be assigned to nodes in a 2-3-4 tree in order to minimize the height of the tree?</p>

<p>Does the sequence of insertion matter with 2-3-4 trees?</p>
 | data structures search trees | 1 | Minimising height of a 2-3-4 tree -- (data structures search trees)
<p>I'm wondering how a set of keys could be assigned to nodes in a 2-3-4 tree in order to minimize the height of the tree?</p>

<p>Does the sequence of insertion matter with 2-3-4 trees?</p>
 | habedi/stack-exchange-dataset |
24,469 | Algorithm to match numbers with minimum number of moves | <p>This is a sort of edit-distance question, and is very easy. I am just quite brain dead on this subject and can't figure it out so far.</p>

<hr>

<p>Given a series of numbers, e.g.</p>

<pre><code>[3, 1, 1, 1]
</code></pre>

<p>How would one most efficiently turn all of the number... | algorithms optimization | 1 | Algorithm to match numbers with minimum number of moves -- (algorithms optimization)
<p>This is a sort of edit-distance question, and is very easy. I am just quite brain dead on this subject and can't figure it out so far.</p>

<hr>

<p>Given a series of numbers, e.g.</p>

<pre><code>[3, 1, 1, 1... | habedi/stack-exchange-dataset |
24,470 | Is polynomial time reducibility reversible? | <p>If a language $A$ is reducible to some language $B$, does it follow that $B$ is reducible to $A$?</p>

<p>My guess is no, it having something to do with the function $f$ in the definition of $A$ reducing to $B$ needing to be invertible.</p>
 | complexity theory reductions polynomial time | 1 | Is polynomial time reducibility reversible? -- (complexity theory reductions polynomial time)
<p>If a language $A$ is reducible to some language $B$, does it follow that $B$ is reducible to $A$?</p>

<p>My guess is no, it having something to do with the function $f$ in the definition of $A$ reducing to $B$ need... | habedi/stack-exchange-dataset |
24,475 | NP hardness of Partition | <p>I'm trying to show that PARTITION is NP-hard. I'm not sure if what I have is correct so I'll write what I have. I tried to reduce it from SUBSET_SUM:</p>

<p>$$PART= \{S\subset\mathbb{Z}|\exists C \subset S: \sum_{x\in C} x=\sum_{x\in S-C}x\} $$
$$SUBSET SUM = \{\langle T,u\rangle| T\subset \mathbb{N}, u... | algorithms complexity theory np complete np hard | 1 | NP hardness of Partition -- (algorithms complexity theory np complete np hard)
<p>I'm trying to show that PARTITION is NP-hard. I'm not sure if what I have is correct so I'll write what I have. I tried to reduce it from SUBSET_SUM:</p>

<p>$$PART= \{S\subset\mathbb{Z}|\exists C \subset S: \sum_{x\in C} x=\sum_{... | habedi/stack-exchange-dataset |
24,478 | How can an LBA check legality of TM transitions without extra memory? | <p>In Sipser's book there is a proof that an emptiness of LBA is undecidable, with the help of reduction to A_$_{\text{TM}}$.</p>

<p>The reduction is proposed in the following manner:
we receive a TM $M$ and a word $w$, and build an LBA $B$ that accepts if is fed an accepting computation history of $M$ on ... | computability undecidability linear bounded automata | 1 | How can an LBA check legality of TM transitions without extra memory? -- (computability undecidability linear bounded automata)
<p>In Sipser's book there is a proof that an emptiness of LBA is undecidable, with the help of reduction to A_$_{\text{TM}}$.</p>

<p>The reduction is proposed in the following manner:... | habedi/stack-exchange-dataset |
24,484 | Can't understand why the DP Subset Sum algorithm is not polynomial | <p>I can not understand why the dynamic programming algorithm for the Subset Sum, is not polynomial. </p>

<p>Even though the sum to find 'T' is greater than the total sum of the 'n' elements of the set , the number of iterations is always (T * n) and not exponential I'm not understanding it.</p>

<p>T... | complexity theory terminology np complete dynamic programming polynomial time | 1 | Can't understand why the DP Subset Sum algorithm is not polynomial -- (complexity theory terminology np complete dynamic programming polynomial time)
<p>I can not understand why the dynamic programming algorithm for the Subset Sum, is not polynomial. </p>

<p>Even though the sum to find 'T' is greater than the ... | habedi/stack-exchange-dataset |
24,491 | NFAs with more than one initial state | <p>I'm trying to give a meaningful definition for NFAs with more than one initial state. I know from the <a href="http://en.wikipedia.org/wiki/Nondeterministic_finite_automaton#Formal_definition" rel="nofollow">formal definition</a> in Wikipedia that it is possible to have more than one initial state, it mentions that ... | terminology automata finite automata | 1 | NFAs with more than one initial state -- (terminology automata finite automata)
<p>I'm trying to give a meaningful definition for NFAs with more than one initial state. I know from the <a href="http://en.wikipedia.org/wiki/Nondeterministic_finite_automaton#Formal_definition" rel="nofollow">formal definition</a> in Wiki... | habedi/stack-exchange-dataset |
24,494 | Automata Theory Questions: Rule Trees, Context-Free Grammar, Proving Ambiguity | <p>I'm currently taking a class in Automata Theory and it's kicking my butt. I have an assignment that my teacher gave me that consists of three questions. I have no idea where to start. My teacher and I have a language barrier that I can't seem to break. If anyone could help me understand how to solve the following pr... | context free automata trees | 1 | Automata Theory Questions: Rule Trees, Context-Free Grammar, Proving Ambiguity -- (context free automata trees)
<p>I'm currently taking a class in Automata Theory and it's kicking my butt. I have an assignment that my teacher gave me that consists of three questions. I have no idea where to start. My teacher and I have... | habedi/stack-exchange-dataset |
24,500 | Filing systems using index blocks | <p>I know that a disadvantage of the index block system is that it can be wasteful of space if the files involved are mostly small in size, as index blocks are allocated from free space as required and at least one index block is needed for each file regardless of size. On average there is ½ block wastage per file in t... | operating systems filesystems | 1 | Filing systems using index blocks -- (operating systems filesystems)
<p>I know that a disadvantage of the index block system is that it can be wasteful of space if the files involved are mostly small in size, as index blocks are allocated from free space as required and at least one index block is needed for each file ... | habedi/stack-exchange-dataset |
24,503 | Minimizing Cost by minimizing delay | <p>There is a complete binary tree with its leaves as components of some system
<img src="https://i.stack.imgur.com/xSP4r.jpg" alt="enter image description here"></p>

<p>The values from one node to another gives propagation time for a signal to propagate from one junction to another 
For the signal to ... | algorithms optimization greedy algorithms | 1 | Minimizing Cost by minimizing delay -- (algorithms optimization greedy algorithms)
<p>There is a complete binary tree with its leaves as components of some system
<img src="https://i.stack.imgur.com/xSP4r.jpg" alt="enter image description here"></p>

<p>The values from one node to another gives propagation ... | habedi/stack-exchange-dataset |
24,504 | Is the reversal of a minimal DFA also minimal? | <p>The question is pretty much in the title. Is there ever a time where some language $L$ can be accepted by a minimal DFA with $n$ states, but $L^R$, the reversal of $L$, can be accepted by a DFA with $m$ states, where $m<n$?</p>
 | formal languages reference request automata finite automata | 1 | Is the reversal of a minimal DFA also minimal? -- (formal languages reference request automata finite automata)
<p>The question is pretty much in the title. Is there ever a time where some language $L$ can be accepted by a minimal DFA with $n$ states, but $L^R$, the reversal of $L$, can be accepted by a DFA with $m$ st... | habedi/stack-exchange-dataset |
24,526 | Can someone show me step-by-step how to calculate the primitive operations of this algorithm? | <p>See the example algorithm below from my course notes, I don't follow the operation counting in the inner loop. Can someone walk me through this step-by-step?</p>

<p>Here's the algorithm:</p>

<pre><code>Algorithm PrefixAverages1(A, n):
 Input: An integer array A of size n.
 Output: An... | algorithms algorithm analysis | 1 | Can someone show me step-by-step how to calculate the primitive operations of this algorithm? -- (algorithms algorithm analysis)
<p>See the example algorithm below from my course notes, I don't follow the operation counting in the inner loop. Can someone walk me through this step-by-step?</p>

<p>Here's the al... | habedi/stack-exchange-dataset |
24,529 | Is there an O(n log n) algorithm for 4D line simplification? | <p>The <a href="http://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm">Ramer-Douglas-Peucker algorithm</a> for line simplification has worst-case $O(n^2)$ runtime. For suitably distributed random inputs, it has expected $O(n \log n)$ runtime complexity. In 2D, there are other algorithms with wors... | reference request computational geometry randomized algorithms | 1 | Is there an O(n log n) algorithm for 4D line simplification? -- (reference request computational geometry randomized algorithms)
<p>The <a href="http://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm">Ramer-Douglas-Peucker algorithm</a> for line simplification has worst-case $O(n^2)$ runtime. For ... | habedi/stack-exchange-dataset |
24,531 | Why addition algorithm is not pseudo- polynomial? | <p>There is something I don't understand. </p>

<p>In the Subset Sum problem, in the Dynamic Programming solution, because of binary representation of the sum T, we say it is pseudo-polynomial in run time; we must sum in the worst case from 1 to T.</p>

<p>So I don't understand why the Addition algorit... | algorithm analysis arithmetic pseudo polynomial | 1 | Why addition algorithm is not pseudo- polynomial? -- (algorithm analysis arithmetic pseudo polynomial)
<p>There is something I don't understand. </p>

<p>In the Subset Sum problem, in the Dynamic Programming solution, because of binary representation of the sum T, we say it is pseudo-polynomial in run time; we... | habedi/stack-exchange-dataset |
24,549 | What is the reason that is FFT multiplication slower than other methods for small N? | <p>I've seen plenty of statements in papers and on websites that Fast Fourier Transform-based multiplication algorithms are slower than other multiplication algorithms for relatively small input size N, and I've seen plenty of data in papers and on websites demonstrating that this is the case, but nothing I've come acr... | algorithms algorithm analysis fourier transform | 1 | What is the reason that is FFT multiplication slower than other methods for small N? -- (algorithms algorithm analysis fourier transform)
<p>I've seen plenty of statements in papers and on websites that Fast Fourier Transform-based multiplication algorithms are slower than other multiplication algorithms for relatively... | habedi/stack-exchange-dataset |
24,550 | Turing-unrecognizable language - what TM does? | <p>I have a problem giving "intuitive" explanation to turing-unrecognizable languages.</p>

<p>We can prove that, say, ${\overline{A_{TM}}}$ is not turing-recognizable, because that would make ${{A_{TM}}}$ decidable, but what would the $TM$ do if it doesn't accept, reject of loop?</p>
 | computability turing machines | 1 | Turing-unrecognizable language - what TM does? -- (computability turing machines)
<p>I have a problem giving "intuitive" explanation to turing-unrecognizable languages.</p>

<p>We can prove that, say, ${\overline{A_{TM}}}$ is not turing-recognizable, because that would make ${{A_{TM}}}$ decidable, but what woul... | habedi/stack-exchange-dataset |
24,560 | Find $k$ subsets containing a particular element quickly | <p>Suppose there are $n$ subsets of $U$. I want to quickly (in terms of average-case) find k $ (< n)$ subsets that contain $e \in U$ (call this <em>Extraction(e)</em>). Elements are integers.</p>

<p>To that effect, I want to preprocess/encode the $n$ subsets so that this extraction operation can occur relat... | reference request data structures sets hash average case | 1 | Find $k$ subsets containing a particular element quickly -- (reference request data structures sets hash average case)
<p>Suppose there are $n$ subsets of $U$. I want to quickly (in terms of average-case) find k $ (< n)$ subsets that contain $e \in U$ (call this <em>Extraction(e)</em>). Elements are integers.</p>&#x... | habedi/stack-exchange-dataset |
24,569 | Solution of complex recurrence relation | <p>Do anyone have any idea how to solve this recurrence?$$T(k) = \sum_{i=1}^{k/2} {k \choose i}T(i)T(k-i)$$ </p>

<p>I am working with this kind of recurrence for the first time and don't have much idea of how to proceed. But, for beginning I was trying to guess the solution and use substitution method. But, in... | combinatorics recurrence relation | 1 | Solution of complex recurrence relation -- (combinatorics recurrence relation)
<p>Do anyone have any idea how to solve this recurrence?$$T(k) = \sum_{i=1}^{k/2} {k \choose i}T(i)T(k-i)$$ </p>

<p>I am working with this kind of recurrence for the first time and don't have much idea of how to proceed. But, for be... | habedi/stack-exchange-dataset |
24,574 | What are appropriate isomorphisms between formal languages? | <p>A <a href="http://en.wikipedia.org/wiki/Formal_language#Definition" rel="nofollow noreferrer"><em>formal language</em></a> $L$ over an alphabet $\Sigma$ is a subset of $\Sigma^*$, that is, a set of words over that alphabet. Two formal languages $L$ and $L'$ are equal, if the corresponding sets are extensionally equa... | complexity theory formal languages reference request | 1 | What are appropriate isomorphisms between formal languages? -- (complexity theory formal languages reference request)
<p>A <a href="http://en.wikipedia.org/wiki/Formal_language#Definition" rel="nofollow noreferrer"><em>formal language</em></a> $L$ over an alphabet $\Sigma$ is a subset of $\Sigma^*$, that is, a set of w... | habedi/stack-exchange-dataset |
24,576 | What is the regular expression to the given language? | <p>I can't really find out, how can the following given Language be written down with regular expressions</p>

<p>$
L = \{ a^{3k-1} b^n a^{2t} \mid n > 0; k, t\ge1 \}
$</p>

<p>I had some guesses, but I don't know how to express the part $a^{3k-1}$ of the Language.
Probably it should look... | formal languages regular languages regular expressions | 1 | What is the regular expression to the given language? -- (formal languages regular languages regular expressions)
<p>I can't really find out, how can the following given Language be written down with regular expressions</p>

<p>$
L = \{ a^{3k-1} b^n a^{2t} \mid n > 0; k, t\ge1 \}
$</p>

<p>I ... | habedi/stack-exchange-dataset |
24,594 | Number of Final States Subset Construction for NFA to DFA | <p><strong>"Suppose we use the subset construction to convert a $7$-state NFA $M = (Q,\Sigma, \delta, q_0, F)$ into a DFA $M' = (Q', \Sigma, \delta', q_0, F')$ for the same language. Then $M'$ will have $|Q'| = 128$ states. If $|F| = 2$, then $M'$ will have $|F'| = 96$ final states."</strong></p>

<p>From the s... | finite automata | 1 | Number of Final States Subset Construction for NFA to DFA -- (finite automata)
<p><strong>"Suppose we use the subset construction to convert a $7$-state NFA $M = (Q,\Sigma, \delta, q_0, F)$ into a DFA $M' = (Q', \Sigma, \delta', q_0, F')$ for the same language. Then $M'$ will have $|Q'| = 128$ states. If $|F| = 2$, the... | habedi/stack-exchange-dataset |
24,596 | Hash tables - probing for collisions run time | <p>The question is a true or false question:</p>

<p><strong>Hash tables using probing for collisions run in constant time with respect to how many items are in the hash but are at least linearly dependent on how full the hash is.</strong></p>

<p>I think it's true but I don't fully understand why and I... | algorithms algorithm analysis hash tables | 1 | Hash tables - probing for collisions run time -- (algorithms algorithm analysis hash tables)
<p>The question is a true or false question:</p>

<p><strong>Hash tables using probing for collisions run in constant time with respect to how many items are in the hash but are at least linearly dependent on how full t... | habedi/stack-exchange-dataset |
24,597 | Proof or refute $n^n = \Omega(n!)$ with the help of Stirling's approximation | <p>I'm trying to proof/refute the following equation:</p>

<p>$$n^n = \Omega(n!)$$</p>

<p>Generally I would try to use Convergence Criteria and or <a href="http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule" rel="nofollow">l'Hôpital's rule</a> to solve such a problem.</p>

<p>$$\lim_{n\to \... | asymptotics check my answer | 1 | Proof or refute $n^n = \Omega(n!)$ with the help of Stirling's approximation -- (asymptotics check my answer)
<p>I'm trying to proof/refute the following equation:</p>

<p>$$n^n = \Omega(n!)$$</p>

<p>Generally I would try to use Convergence Criteria and or <a href="http://en.wikipedia.org/wiki/L%27H%C3... | habedi/stack-exchange-dataset |
24,599 | Which architecture do modern computers use? | <p>Is it one of:</p>

<ul>
<li>Harvard</li>
<li>Modified Harvard</li>
<li>von Neumann</li>
</ul>

<p>Or are they antiquated models that modern computers are only loosely based on?</p>

<p>If you asked Intel or AMD what would they say?</p>
 | computer architecture | 1 | Which architecture do modern computers use? -- (computer architecture)
<p>Is it one of:</p>

<ul>
<li>Harvard</li>
<li>Modified Harvard</li>
<li>von Neumann</li>
</ul>

<p>Or are they antiquated models that modern computers are only loosely based on?</p>

<p>If you asked Intel or... | habedi/stack-exchange-dataset |
24,610 | Reduction from partition to multiprocessor scheduling | <p>I am kind of unsure about a reduction between two problems.
Here are the two problems:</p>

<p><strong>PARTITION:</strong>
Instance: A finite set of n positive integers $S= \{a_1,a_2,...a_n\}$.
Question: Can the set $S$ be partitioned into two subsets $S_1$,$S_2$, s.t. the sum of the numbers in $... | complexity theory reductions | 1 | Reduction from partition to multiprocessor scheduling -- (complexity theory reductions)
<p>I am kind of unsure about a reduction between two problems.
Here are the two problems:</p>

<p><strong>PARTITION:</strong>
Instance: A finite set of n positive integers $S= \{a_1,a_2,...a_n\}$.
Question: Can t... | habedi/stack-exchange-dataset |
24,638 | Computing FOLLOW sets for a LL(1) grammar | <p>I am trying to learn compiler design. But I get confused when I have to deal with computing the follow set specifically for the empty word. </p>

<p>Given the grammar:</p>

<pre><code>S-> ABC
A-> Aa|b
B-> Bc|d
C-> Ce|f
</code></pre>

<p>I've come up with the follow... | formal grammars compilers parsers | 1 | Computing FOLLOW sets for a LL(1) grammar -- (formal grammars compilers parsers)
<p>I am trying to learn compiler design. But I get confused when I have to deal with computing the follow set specifically for the empty word. </p>

<p>Given the grammar:</p>

<pre><code>S-> ABC
A-> Aa|b
B->... | habedi/stack-exchange-dataset |
24,645 | Denumerably many isomorphism types | <p><a href="http://f3.tiera.ru/2/M_Mathematics/MA_Algebra/MAml_Mathematical%20logic/Boolos%20G.,%20Burgess%20J.P.,%20Jeffrey%20R.C.%20Computability%20and%20logic%20%284ed.,%20CUP,%202002%29%28ISBN%200521007585%29%28370s%29_MAml_.pdf" rel="nofollow noreferrer">Computability and Logic by Boolos and Burgess</a> says that ... | first order logic | 1 | Denumerably many isomorphism types -- (first order logic)
<p><a href="http://f3.tiera.ru/2/M_Mathematics/MA_Algebra/MAml_Mathematical%20logic/Boolos%20G.,%20Burgess%20J.P.,%20Jeffrey%20R.C.%20Computability%20and%20logic%20%284ed.,%20CUP,%202002%29%28ISBN%200521007585%29%28370s%29_MAml_.pdf" rel="nofollow noreferrer">Co... | habedi/stack-exchange-dataset |
24,647 | Find MST based upon new definition | <p>Redefine the weight of a spanning tree to be the weight of the maximum weight edge in the tree (i.e. the weight of the tree is no longer the sum of the weights of all the edges in the tree, only the weight of the edge with the maximum weight). How would you derive an efficient algorithm to compute the minimum weight... | algorithms graphs trees spanning trees | 1 | Find MST based upon new definition -- (algorithms graphs trees spanning trees)
<p>Redefine the weight of a spanning tree to be the weight of the maximum weight edge in the tree (i.e. the weight of the tree is no longer the sum of the weights of all the edges in the tree, only the weight of the edge with the maximum wei... | habedi/stack-exchange-dataset |
24,652 | Proving a language is not decideable using a reduction from Busy Beaver? | <p>I was given this function:
$F(n)$ returns the smallest TM (measured in number of states) such that on input $\epsilon$, the TM makes at least $n$ steps before eventually halting ($n$ is a natural number). I was asked to prove that this function is uncomputable using a reduction from the Busy Beaver. I'm still ne... | formal languages turing machines reductions | 1 | Proving a language is not decideable using a reduction from Busy Beaver? -- (formal languages turing machines reductions)
<p>I was given this function:
$F(n)$ returns the smallest TM (measured in number of states) such that on input $\epsilon$, the TM makes at least $n$ steps before eventually halting ($n$ is a nat... | habedi/stack-exchange-dataset |
24,654 | Predicting target location given cursor speed and direction | <p>Do you guys know of any method or algorithm you are able to predict where a user is moving their cursor given its speed and bearing?</p>

<p>I'm trying to predict if and when users are moving their mouse to a certain part of the screen (address bar location).</p>

<p>Could I exploit Fitts's Law in th... | algorithms hci | 1 | Predicting target location given cursor speed and direction -- (algorithms hci)
<p>Do you guys know of any method or algorithm you are able to predict where a user is moving their cursor given its speed and bearing?</p>

<p>I'm trying to predict if and when users are moving their mouse to a certain part of the ... | habedi/stack-exchange-dataset |
24,657 | Visit all vertices on directed graph | <p>We are given a directed graph, the number of vertices and edges. We need to decide, whether there is a [starting] vertex where we can get started and visit all the vertices. You can revisit vertices, but can't "use" edges twice or more time. All this in linear time.</p>

<p>I was thinking about DFS - if the ... | algorithms graphs | 1 | Visit all vertices on directed graph -- (algorithms graphs)
<p>We are given a directed graph, the number of vertices and edges. We need to decide, whether there is a [starting] vertex where we can get started and visit all the vertices. You can revisit vertices, but can't "use" edges twice or more time. All this in lin... | habedi/stack-exchange-dataset |
24,661 | Red black tree partition to $\sqrt{n}$ trees | <p>This is a question I have stumbled upon in an old Algorithms test I found online:</p>

<blockquote>
 <p>A) Plan an algorithm that does the following:
 Input: Red-Black tree
 Output: $\sqrt{n}$ seperate trees, so that every tree has $\sqrt{n}$ nodes.
 What is the complexity of the Algorith... | algorithms trees | 1 | Red black tree partition to $\sqrt{n}$ trees -- (algorithms trees)
<p>This is a question I have stumbled upon in an old Algorithms test I found online:</p>

<blockquote>
 <p>A) Plan an algorithm that does the following:
 Input: Red-Black tree
 Output: $\sqrt{n}$ seperate trees, so that every tree... | habedi/stack-exchange-dataset |
24,674 | Training and testing image sizes for classification in computer vision | <p>When training a classifier for object detection using features extracted from images (eg HoG features), how important is it that the images used for training fed into the classifier in their natural aspect ratio?</p>

<p>For example, regardless of their aspect ratio, would a classifier work if all images wer... | image processing classification computer vision | 1 | Training and testing image sizes for classification in computer vision -- (image processing classification computer vision)
<p>When training a classifier for object detection using features extracted from images (eg HoG features), how important is it that the images used for training fed into the classifier in their na... | habedi/stack-exchange-dataset |
24,682 | Why can't we solve the dinner party problem by finding a maximum matching? | <p>Consider the following <em>dinner party problem</em>:</p>

<blockquote>
 <p>Given a list of acquaintances, and a list containing all pairs of individuals who are not on speaking terms with each other, find the largest set of acquaintances you can invite to a dinner party such that you do not invite any ... | algorithm analysis matching | 1 | Why can't we solve the dinner party problem by finding a maximum matching? -- (algorithm analysis matching)
<p>Consider the following <em>dinner party problem</em>:</p>

<blockquote>
 <p>Given a list of acquaintances, and a list containing all pairs of individuals who are not on speaking terms with each ot... | habedi/stack-exchange-dataset |
24,691 | NP-completeness: Reduce to or reduce from? | <p>Very simple question, but a mistake I make often enough that I'd love to have a standard reference.</p>

<p>I'm showing that a problem $P$ is NP-Hard by assuming I have a polynomial time algorithm to solve $P$, then showing that this solves another NP-Hard problem $Q$ in polynomial time.</p>

<p>Have... | complexity theory terminology np complete reductions polynomial time | 1 | NP-completeness: Reduce to or reduce from? -- (complexity theory terminology np complete reductions polynomial time)
<p>Very simple question, but a mistake I make often enough that I'd love to have a standard reference.</p>

<p>I'm showing that a problem $P$ is NP-Hard by assuming I have a polynomial time algor... | habedi/stack-exchange-dataset |
24,699 | Binary heap removal peculiar potential function analysis | <p>Given the potential function $\phi$, it seems that remove max may take $O(1)$ amoratized,
meaning that $n$ removals would take $O(n)$, which can't be, as it means we get a linear time comparison based sort if we build the heap in $O(n)$.</p>

<p>Where is the falling point in this potential function, and ... | heaps amortized analysis | 1 | Binary heap removal peculiar potential function analysis -- (heaps amortized analysis)
<p>Given the potential function $\phi$, it seems that remove max may take $O(1)$ amoratized,
meaning that $n$ removals would take $O(n)$, which can't be, as it means we get a linear time comparison based sort if we build the heap... | habedi/stack-exchange-dataset |
24,700 | Consistency and completeness imply soundness? | <p>I understand that soundness implies consistency. Also, I understand that consistency alone does not imply soundness. But shouldn't consistency + completeness imply soundness? Scott Aaronson in his <a href="http://www.scottaaronson.com/blog/?p=710" rel="nofollow">blog-post</a> hints otherwise. What am I exactly missi... | terminology logic | 1 | Consistency and completeness imply soundness? -- (terminology logic)
<p>I understand that soundness implies consistency. Also, I understand that consistency alone does not imply soundness. But shouldn't consistency + completeness imply soundness? Scott Aaronson in his <a href="http://www.scottaaronson.com/blog/?p=710" ... | habedi/stack-exchange-dataset |
24,706 | How can OS schedule disk requests efficiently without knowing the LBN to PBN mapping ? | <p>I learn from the OS schoolbook that the OS has the function that schedule the disk requests with the knowing algorithms such as SSTF, SCAN .. However, the date layout inner disk drives now is very complex that we may can't know. Disk zoning, disk skew, disk slipping and many other features of disk drives changes the... | operating systems scheduling | 1 | How can OS schedule disk requests efficiently without knowing the LBN to PBN mapping ? -- (operating systems scheduling)
<p>I learn from the OS schoolbook that the OS has the function that schedule the disk requests with the knowing algorithms such as SSTF, SCAN .. However, the date layout inner disk drives now is very... | habedi/stack-exchange-dataset |
24,718 | Can we represent all computer programs as graphs? | <p>I was thinking the other day, and it occurred to me that computer programs all seem to be representable as a graph (an abstract syntax tree for example), or, once common expressions are combined, an abstract syntax graph. </p>

<p>It occured to me that perhaps any computer program can be represented as one... | graphs turing machines machine models | 1 | Can we represent all computer programs as graphs? -- (graphs turing machines machine models)
<p>I was thinking the other day, and it occurred to me that computer programs all seem to be representable as a graph (an abstract syntax tree for example), or, once common expressions are combined, an abstract syntax graph. ... | habedi/stack-exchange-dataset |
24,722 | comparisons vs arithmetic complexity | <p>I'm trying to find out which operation is fast, evaluating a comparison vs doing an arithmetic option on a single word (e.g subtract, add). Can anyone point me in the right direction with some blogs, books and other material? </p>
 | algorithms complexity theory reference request | 1 | comparisons vs arithmetic complexity -- (algorithms complexity theory reference request)
<p>I'm trying to find out which operation is fast, evaluating a comparison vs doing an arithmetic option on a single word (e.g subtract, add). Can anyone point me in the right direction with some blogs, books and other material? </... | habedi/stack-exchange-dataset |
24,725 | Reducing A(TM) to some decidable problem | <p>We know that A(TM) is undecidable, what if we reduce A(TM) to A(DFA) which is decidable? How will we prove that A(DFA) is decidable?</p>

<p>I couldn't find an example or theory.</p>

<p>Thanks</p>
 | computability reductions undecidability | 1 | Reducing A(TM) to some decidable problem -- (computability reductions undecidability)
<p>We know that A(TM) is undecidable, what if we reduce A(TM) to A(DFA) which is decidable? How will we prove that A(DFA) is decidable?</p>

<p>I couldn't find an example or theory.</p>

<p>Thanks</p>
 | habedi/stack-exchange-dataset |
24,729 | Q-learning in a Dynamic environment | <p>I am new to reinforcement learning. Lately, I have learned Q-learning using the following <a href="http://mnemstudio.org/path-finding-q-learning-tutorial.htm" rel="nofollow">tutorial</a>.</p>

<p>Is Q-learning still possible if the environment is dynamic. Using the environment of the tutorial as an example,... | machine learning artificial intelligence reinforcement learning | 1 | Q-learning in a Dynamic environment -- (machine learning artificial intelligence reinforcement learning)
<p>I am new to reinforcement learning. Lately, I have learned Q-learning using the following <a href="http://mnemstudio.org/path-finding-q-learning-tutorial.htm" rel="nofollow">tutorial</a>.</p>

<p>Is Q-le... | habedi/stack-exchange-dataset |
24,735 | Eliminating Left Recursion | <p>Hello I have the above Context Free Grammar and I try to eliminate the left recursion so I can pass it to a tool. Any techniques I've read so far doesn't help me so a little help would be appreciated. </p>

<pre><code>exp -> num | exp op exp | (exp) 
op -> + | - | * | / 
</code></pre>&#... | context free | 1 | Eliminating Left Recursion -- (context free)
<p>Hello I have the above Context Free Grammar and I try to eliminate the left recursion so I can pass it to a tool. Any techniques I've read so far doesn't help me so a little help would be appreciated. </p>

<pre><code>exp -> num | exp op exp | (exp) 
op ... | habedi/stack-exchange-dataset |
24,742 | Reducing 3-colouring to planar 3-colouring | <p>I was reading <a href="http://www.cs.cmu.edu/afs/cs/academic/class/15451-s04/www/Lectures/chapter23.pdf" rel="nofollow">these lecture notes</a> and I'm trying to understand how one would formally describe reducing 3-colouring to planar 3-colouring. The link pretty much describes the process but understanding the mat... | algorithms graphs np complete | 1 | Reducing 3-colouring to planar 3-colouring -- (algorithms graphs np complete)
<p>I was reading <a href="http://www.cs.cmu.edu/afs/cs/academic/class/15451-s04/www/Lectures/chapter23.pdf" rel="nofollow">these lecture notes</a> and I'm trying to understand how one would formally describe reducing 3-colouring to planar 3-c... | habedi/stack-exchange-dataset |
24,745 | Cost of partitioning in quicksort | <p>I'm reading "Algorithms Fourth Edition" by Sedgewick & Wayne and am wondering if I have spotted an error in the book or if I just can't wrap my head around something so simple.</p>

<p>When talking about the complexity of quicksort, the book says that the cost of partitioning, measured in the number of c... | quicksort partitions comparison | 1 | Cost of partitioning in quicksort -- (quicksort partitions comparison)
<p>I'm reading "Algorithms Fourth Edition" by Sedgewick & Wayne and am wondering if I have spotted an error in the book or if I just can't wrap my head around something so simple.</p>

<p>When talking about the complexity of quicksort, t... | habedi/stack-exchange-dataset |
24,746 | Build a regular expression to define a regular language | <p>The language is an infinite set of chains that are defined by the next conditions.</p>

<p>Conditions:</p>

<pre><code>1) The language chains may consist of symbols from the set {1,a,b}. 
2) The language chains always start from subchain '1a'.
3) Every languange chain has to include at least ... | regular languages regular expressions | 1 | Build a regular expression to define a regular language -- (regular languages regular expressions)
<p>The language is an infinite set of chains that are defined by the next conditions.</p>

<p>Conditions:</p>

<pre><code>1) The language chains may consist of symbols from the set {1,a,b}. 
2) The lan... | habedi/stack-exchange-dataset |
24,750 | Local and Global storage with multithreading pools + locking threads | <p>I am having difficulty answering the following questions relating to the use of threading.</p>

<p>Question 1 is of relating to the possibility of a local storage per thread and a global storage accessible to all threads. Consider the following scenario; A program creates a series of threads each with their ... | space complexity threads | 1 | Local and Global storage with multithreading pools + locking threads -- (space complexity threads)
<p>I am having difficulty answering the following questions relating to the use of threading.</p>

<p>Question 1 is of relating to the possibility of a local storage per thread and a global storage accessible to a... | habedi/stack-exchange-dataset |
24,751 | Build a regular grammar for a regular language | <p>The language considered is the infinite set of all chains that meet the following conditions.</p>

<p>Conditions:</p>

<pre><code>1) They consist of symbols from the set {1,a,b}. 
2) They always start with the subchain '1a'.
3) They always include at least one subchain 'aa'.
</code></pre>... | regular languages formal grammars finite automata regular expressions | 1 | Build a regular grammar for a regular language -- (regular languages formal grammars finite automata regular expressions)
<p>The language considered is the infinite set of all chains that meet the following conditions.</p>

<p>Conditions:</p>

<pre><code>1) They consist of symbols from the set {1,a,b}. ... | habedi/stack-exchange-dataset |
24,761 | Introductory book on Logic and Computation | <p>Can you give me some suggestions about a good introductory (but comprehensive) book<br>about Logic and Computation?</p>

<p>Some fuzzy topics that I have in mind are:</p>

<ul>
<li>Presburger artihm., PA, ZF, ZFC, HOL</li>
<li>Set theory, Type theory</li>
<li>Modeling Computation (Turing ... | reference request logic books | 1 | Introductory book on Logic and Computation -- (reference request logic books)
<p>Can you give me some suggestions about a good introductory (but comprehensive) book<br>about Logic and Computation?</p>

<p>Some fuzzy topics that I have in mind are:</p>

<ul>
<li>Presburger artihm., PA, ZF, ZFC, HOL</... | habedi/stack-exchange-dataset |
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