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 |
|---|---|---|---|---|---|---|
57,679 | Is the word problem of CFLs in NC? | <p>Consider the membership problem for a context-free language. An instance of this problem can be described as pair $(G,w)$, where $G$ is a context-free grammar and $w$ is a string. </p>

<p>Lets say I have a PRAM and I want it to decide in $\log^k n$ time and $n^c$ space complexity whether $w$ is in $L(G)$ ($... | algorithms context free formal grammars parallel computing parsers | 1 | Is the word problem of CFLs in NC? -- (algorithms context free formal grammars parallel computing parsers)
<p>Consider the membership problem for a context-free language. An instance of this problem can be described as pair $(G,w)$, where $G$ is a context-free grammar and $w$ is a string. </p>

<p>Lets say I ha... | habedi/stack-exchange-dataset |
57,695 | What's the definition of ACTL? | <p>I have been looking for the definition of ACTL, but Google has given me very little to go with. </p>

<p>So far, I know ACTL is another form of CTL model checking, and CTL includes the following operators: </p>

<ul>
<li>Always </li>
<li>Exist</li>
<li>Global</li>
<li>Finally</li>
... | model checking temporal logic | 1 | What's the definition of ACTL? -- (model checking temporal logic)
<p>I have been looking for the definition of ACTL, but Google has given me very little to go with. </p>

<p>So far, I know ACTL is another form of CTL model checking, and CTL includes the following operators: </p>

<ul>
<li>Always </l... | habedi/stack-exchange-dataset |
57,707 | Finding simple cycle of minimal weight in directed bipartite complete graph with negative cycles | <p>Given a weighted complete bipartite directed graph K_{m,n}, is it possible to find a simple cycle (every node is visited at most a single time) with minimal weight in polynomial time (in m*n) when there exist simple cycles with negative weight? </p>

<p>For general graphs this problem is NP-complete (<a href... | algorithms complexity theory graphs optimization | 1 | Finding simple cycle of minimal weight in directed bipartite complete graph with negative cycles -- (algorithms complexity theory graphs optimization)
<p>Given a weighted complete bipartite directed graph K_{m,n}, is it possible to find a simple cycle (every node is visited at most a single time) with minimal weight in... | habedi/stack-exchange-dataset |
57,716 | The transition function in a Markov decision process | <p>A Markov decision process is typically described as a tuple $\langle A,U,T,R \rangle $ where </p>

<ul>
<li>$A$ is the state space</li>
<li>$U$ is the action space</li>
<li>$T: A \times U \times A \mapsto [0,\infty) $ is the state transition probability function</li>
<li>$R:A \times U \times ... | probability theory markov chains | 1 | The transition function in a Markov decision process -- (probability theory markov chains)
<p>A Markov decision process is typically described as a tuple $\langle A,U,T,R \rangle $ where </p>

<ul>
<li>$A$ is the state space</li>
<li>$U$ is the action space</li>
<li>$T: A \times U \times A \mapsto [... | habedi/stack-exchange-dataset |
57,719 | Convex hull algorithm in $O(\min(mn, n\log n))$ | <p>I am looking for an algorithm to compute the convex hull of a set of $n$ points $P$. The hull should contains $m$ points. This algorithm should work in time $O(\min(mn,n \log n))$.</p>

<p>My first guess was QuickHull, which has a best case running time of $O(n \log n ) $ and a worst case running time time o... | algorithms computational geometry convex hull | 1 | Convex hull algorithm in $O(\min(mn, n\log n))$ -- (algorithms computational geometry convex hull)
<p>I am looking for an algorithm to compute the convex hull of a set of $n$ points $P$. The hull should contains $m$ points. This algorithm should work in time $O(\min(mn,n \log n))$.</p>

<p>My first guess was Qu... | habedi/stack-exchange-dataset |
57,724 | What Exactly Does the Term "Key" Mean with Regards to a Hash Table? | <p>I know it is supposed to be some arbitrary term that is a stand-in for a large class of possible objects.</p>

<p>But I still don't understand what part of the array the term "key" is meant to represent or denote.</p>

<p>Does it mean an element of the array? The index of the element of the array? So... | terminology hash hash tables | 1 | What Exactly Does the Term "Key" Mean with Regards to a Hash Table? -- (terminology hash hash tables)
<p>I know it is supposed to be some arbitrary term that is a stand-in for a large class of possible objects.</p>

<p>But I still don't understand what part of the array the term "key" is meant to represent or d... | habedi/stack-exchange-dataset |
57,726 | Why does merging two sorted arrays take 2N - 1 comparisons? | <p>A friend of mine asked me a question on how to prove that merging two sorted arrays requires at least 2N - 1 comparisons</p>

<blockquote>
 <p>Prove that merging two sorted arrays of N items requires at least 2N-1 comparisons.</p>
</blockquote>

<pre><code> /*
 * An example program that ... | algorithm analysis runtime analysis sorting arrays | 1 | Why does merging two sorted arrays take 2N - 1 comparisons? -- (algorithm analysis runtime analysis sorting arrays)
<p>A friend of mine asked me a question on how to prove that merging two sorted arrays requires at least 2N - 1 comparisons</p>

<blockquote>
 <p>Prove that merging two sorted arrays of N ite... | habedi/stack-exchange-dataset |
57,730 | Order classic notions of computability by power | <p>I need some help with a question. I'm currently studying for an exam and I could therefore use some help with this following question:</p>

<p><strong>Order the following formalisms (but one) according to their expressive power: placing A before B means that any language definable by A is definable by B. Als... | formal languages turing machines automata finite automata | 1 | Order classic notions of computability by power -- (formal languages turing machines automata finite automata)
<p>I need some help with a question. I'm currently studying for an exam and I could therefore use some help with this following question:</p>

<p><strong>Order the following formalisms (but one) accord... | habedi/stack-exchange-dataset |
57,732 | Voronoi Diagram: Exactly 2n-5 vertices | <p>I want to find some characteristics for a set of points $S$ which contains $n$ points and has some Voronoi Diagram $V(S)$. This diagram should have exactly $2n-5$ vertices.</p>

<p>I tried to use the Euler formula for planar graphs which says $v-e+f = 2$:</p>

<p>$\Rightarrow 2n -5 -e + n = 2 \Righta... | graphs computational geometry voronoi diagrams | 1 | Voronoi Diagram: Exactly 2n-5 vertices -- (graphs computational geometry voronoi diagrams)
<p>I want to find some characteristics for a set of points $S$ which contains $n$ points and has some Voronoi Diagram $V(S)$. This diagram should have exactly $2n-5$ vertices.</p>

<p>I tried to use the Euler formula for ... | habedi/stack-exchange-dataset |
57,739 | Theoretical justification of "halting problem avoidance" | <p>The wikipedia page for the <a href="https://en.wikipedia.org/wiki/Halting_problem" rel="nofollow noreferrer">Halting problem</a> mentioned <em>practical solutions</em> to avoiding the halting problem such as avoiding infinite loops. And there is a mention that "by restricting the capabilities of general-purpose (Tur... | computability computation models halting problem | 1 | Theoretical justification of "halting problem avoidance" -- (computability computation models halting problem)
<p>The wikipedia page for the <a href="https://en.wikipedia.org/wiki/Halting_problem" rel="nofollow noreferrer">Halting problem</a> mentioned <em>practical solutions</em> to avoiding the halting problem such a... | habedi/stack-exchange-dataset |
57,741 | Prove that language of possible stack content is regular | <p>So, here's the problem:</p>

<p>Suppose that $A=(Q,\Sigma,\Gamma,\delta,s,\bot, F)$ is a PDA, let
 $$L = \{ \gamma \in \Gamma^* \hspace{5pt}|\hspace{5pt} \exists_{x,y\in \Sigma^*} \exists_{q\in Q}: (s,x,\bot)\vdash_A^*(q,y,\gamma)\}$$</p>

<p>Show that $L$ is regular.</p>

<p>So far solut... | formal languages regular languages automata pushdown automata | 1 | Prove that language of possible stack content is regular -- (formal languages regular languages automata pushdown automata)
<p>So, here's the problem:</p>

<p>Suppose that $A=(Q,\Sigma,\Gamma,\delta,s,\bot, F)$ is a PDA, let
 $$L = \{ \gamma \in \Gamma^* \hspace{5pt}|\hspace{5pt} \exists_{x,y\in \Sigma^*} \... | habedi/stack-exchange-dataset |
57,760 | Computing losing positions in modified Wythoff's game efficiently | <blockquote>
 <p><a href="https://en.wikipedia.org/wiki/Wythoff%27s_game" rel="nofollow">Wythoff's</a> game is as follows: there are two players $A$ and $B$ ( $A$ being the first player ) and there are $2$ piles of stones. When his turn a player can remove one or more stones from anyone pile or same number of ston... | number theory game theory | 1 | Computing losing positions in modified Wythoff's game efficiently -- (number theory game theory)
<blockquote>
 <p><a href="https://en.wikipedia.org/wiki/Wythoff%27s_game" rel="nofollow">Wythoff's</a> game is as follows: there are two players $A$ and $B$ ( $A$ being the first player ) and there are $2$ piles of sto... | habedi/stack-exchange-dataset |
57,769 | What is the point of the "respect" requirement in cut property of minimum spanning tree? | <p>The cut property stated in terms of Theorem 23.1 in Section 23.1 of CLRS (2nd edition) is as follows.</p>

<blockquote>
 <p><strong><em>Theorem 23.1</em></strong> Let $G = (V, E)$ be a connected, undirected graph with a real-valued weight function $w$ defined on $E$. Let $A$ be a subset of $E$ that is i... | algorithms graphs correctness proof minimum spanning tree | 1 | What is the point of the "respect" requirement in cut property of minimum spanning tree? -- (algorithms graphs correctness proof minimum spanning tree)
<p>The cut property stated in terms of Theorem 23.1 in Section 23.1 of CLRS (2nd edition) is as follows.</p>

<blockquote>
 <p><strong><em>Theorem 23.1</em... | habedi/stack-exchange-dataset |
57,773 | Densely connected non overlapping subgraph | <p>I'm trying to detect quasi cliques in an undirected graph. My problem is that I don't want any overlap between cluster. </p>

<p>I'm currently trying to detect community using Louvain algorithm, but it detects subgraphs with a low clustering coefficient (0.60) and when I detect maximal or quasi cliques they ... | algorithms graphs optimization social networks clustering | 1 | Densely connected non overlapping subgraph -- (algorithms graphs optimization social networks clustering)
<p>I'm trying to detect quasi cliques in an undirected graph. My problem is that I don't want any overlap between cluster. </p>

<p>I'm currently trying to detect community using Louvain algorithm, but it d... | habedi/stack-exchange-dataset |
57,780 | Of which Chomsky-type is the language $L = \{a^jb^ic^{2i} | i,j \in \mathbb{N}^0\}$? | <p>At first I thought the language would be context sensitive because it seems that it can be shown with the pumping lemma for regular languages, that it's not a regular language and analogously with the pumping lemma for context free languages, that it is not context free. But it upon further pondering I came up with ... | formal languages chomsky hierarchy | 1 | Of which Chomsky-type is the language $L = \{a^jb^ic^{2i} | i,j \in \mathbb{N}^0\}$? -- (formal languages chomsky hierarchy)
<p>At first I thought the language would be context sensitive because it seems that it can be shown with the pumping lemma for regular languages, that it's not a regular language and analogously ... | habedi/stack-exchange-dataset |
57,788 | How to calculate IV, EV and optimal k for K-means? | <p>Could someone explain how to calculate the following 3 evaluative properties:</p>

<ul>
<li>Intercluster Variability (IV) - How different are the data points within the same cluster</li>
<li>Extracluster Variability (EV) - How different are the data points that are in distinct clusters</li>
<li>O... | optimization machine learning statistics cluster clustering | 1 | How to calculate IV, EV and optimal k for K-means? -- (optimization machine learning statistics cluster clustering)
<p>Could someone explain how to calculate the following 3 evaluative properties:</p>

<ul>
<li>Intercluster Variability (IV) - How different are the data points within the same cluster</li>&#x... | habedi/stack-exchange-dataset |
57,792 | Shortest path from that passes through a set of edges once | <p>Given a graph with weighted edges. How to find the shortest path from vertex $A$ to vertex $B$ that passes through a set of edges $X$ at most once? $X$ can be big.</p>

<p>Slow solution:
Finding shortest path from $A$ to each edge of $X$ and shortest path from each edge to $B$ in graph $G\setminus{X}$. C... | algorithms graphs optimization shortest path | 1 | Shortest path from that passes through a set of edges once -- (algorithms graphs optimization shortest path)
<p>Given a graph with weighted edges. How to find the shortest path from vertex $A$ to vertex $B$ that passes through a set of edges $X$ at most once? $X$ can be big.</p>

<p>Slow solution:
Finding s... | habedi/stack-exchange-dataset |
57,807 | Why %RSD of execution times, while sorting hundreds of arrays, is lower for larger arrays of random integers? | <p>I am experimenting with the sorting of arrays and their execution times.
While using <code>bubblesort</code>, <code>insertsort</code> and <code>quicksort</code>, I have observed that relative standard deviation (%RSD) of execution times, for five hundred arrays of the same size containing random integers, decrea... | algorithm analysis runtime analysis sorting quicksort | 1 | Why %RSD of execution times, while sorting hundreds of arrays, is lower for larger arrays of random integers? -- (algorithm analysis runtime analysis sorting quicksort)
<p>I am experimenting with the sorting of arrays and their execution times.
While using <code>bubblesort</code>, <code>insertsort</code> and <code>... | habedi/stack-exchange-dataset |
57,817 | What does the number of bit of microprocessor mean? | <p>Intel 8085 is a 8 bit processor whereas 8086 is a 16 bit processor,what does the number of bit specify?</p>
 | computer architecture | 1 | What does the number of bit of microprocessor mean? -- (computer architecture)
<p>Intel 8085 is a 8 bit processor whereas 8086 is a 16 bit processor,what does the number of bit specify?</p>
 | habedi/stack-exchange-dataset |
57,829 | Prove that there is no computable enumeration of all decidable languages | <p><strong>The question:</strong></p>

<blockquote>
 <p>Let $L_1,L_2,...$ be an enumeration of $\mathcal{R}$ and define $A_i = \{\langle M\rangle \ | \ L(M) = L_i\}$. Let $L$ be a language in $\mathcal{RE}$ such that $L \subset \{\langle M\rangle \ | \ \text{M is a TM that always halts}\}$. Prove that
... | computability turing machines undecidability | 1 | Prove that there is no computable enumeration of all decidable languages -- (computability turing machines undecidability)
<p><strong>The question:</strong></p>

<blockquote>
 <p>Let $L_1,L_2,...$ be an enumeration of $\mathcal{R}$ and define $A_i = \{\langle M\rangle \ | \ L(M) = L_i\}$. Let $L$ be a lang... | habedi/stack-exchange-dataset |
57,837 | What type of an algorithm is being used for directory structure scanning? | <p>So after learning about DFS and BFS yesterday in my class I was curious as to how is scanning on various file system being done. I spent quite a bit of time trying to look for some references on the web, but so far I have failed in doing so. I'm assuming that either DFS or BFS are behind the core "scanning" in some ... | operating systems search algorithms filesystems | 1 | What type of an algorithm is being used for directory structure scanning? -- (operating systems search algorithms filesystems)
<p>So after learning about DFS and BFS yesterday in my class I was curious as to how is scanning on various file system being done. I spent quite a bit of time trying to look for some reference... | habedi/stack-exchange-dataset |
57,841 | Concurrency: Is it order-independability or interruptibility of tasks? | <p>After researching concurrency I am unable to discern if it is either of these specifically or it encapsulates both?</p>

<p>I was also wondering if someone could provide some programming applications/real world examples I am struggling to grasp the concepts entirely and it feels like every where I look peopl... | concurrency | 1 | Concurrency: Is it order-independability or interruptibility of tasks? -- (concurrency)
<p>After researching concurrency I am unable to discern if it is either of these specifically or it encapsulates both?</p>

<p>I was also wondering if someone could provide some programming applications/real world examples I... | habedi/stack-exchange-dataset |
57,844 | Wikipedia does not list insertion complexity for arrays - why? | <p>Wikipedia does not list insertion complexity for arrays in the <a href="https://en.wikipedia.org/wiki/Linked_list#Tradeoffs" rel="nofollow">list of linked-list implementations</a>.</p>

<p>Is this because insertion operations are not defined on the array ADT?</p>
 | data structures arrays | 1 | Wikipedia does not list insertion complexity for arrays - why? -- (data structures arrays)
<p>Wikipedia does not list insertion complexity for arrays in the <a href="https://en.wikipedia.org/wiki/Linked_list#Tradeoffs" rel="nofollow">list of linked-list implementations</a>.</p>

<p>Is this because insertion ope... | habedi/stack-exchange-dataset |
57,873 | Maximum subset pairwise not divisible by $K$ | <p>I have a set of numbers, and want to calculate the maximum subset such that the sum of any two of it's elements is not divisible by an integer $K$.
I tried to solve this problem, but I have found the quadratic solution, which is not efficient response.<br>
$K < 100, N < 10000$, where $N$ is the number ... | algorithms efficiency | 1 | Maximum subset pairwise not divisible by $K$ -- (algorithms efficiency)
<p>I have a set of numbers, and want to calculate the maximum subset such that the sum of any two of it's elements is not divisible by an integer $K$.
I tried to solve this problem, but I have found the quadratic solution, which is not efficien... | habedi/stack-exchange-dataset |
57,884 | ordered uniform distribution | <p>We are given $n$ objects with individual weights $w_1 , w_2 , \ldots , w_n$ and $m$ buckets in which these objects are to be inserted but in order. Here order means if object $i$ goes in bucket $m_i$ and if object $j$ goes in bucket $m_j$ then if $i < j$ then $m_i \le m_j$.
Objective of the problem is the min... | algorithms optimization mathematical programming packing | 1 | ordered uniform distribution -- (algorithms optimization mathematical programming packing)
<p>We are given $n$ objects with individual weights $w_1 , w_2 , \ldots , w_n$ and $m$ buckets in which these objects are to be inserted but in order. Here order means if object $i$ goes in bucket $m_i$ and if object $j$ goes in ... | habedi/stack-exchange-dataset |
57,889 | Is DTIME(n) = DTIME(2n) true? (unlike Rosenberg's results) | <p>I'm reading Homer and Selman's "Computability and Complexity" book. In some Corollary 5.3 it says: </p>

<blockquote>
 <p>For all ε > 0, DTIME(O(n)) = DTIME( (1+ε) n).</p>
</blockquote>

<p>Now I'm confused with this corollary and Rosenberg's result (p87 in the same book):</p>

<b... | complexity theory time complexity complexity classes | 1 | Is DTIME(n) = DTIME(2n) true? (unlike Rosenberg's results) -- (complexity theory time complexity complexity classes)
<p>I'm reading Homer and Selman's "Computability and Complexity" book. In some Corollary 5.3 it says: </p>

<blockquote>
 <p>For all ε > 0, DTIME(O(n)) = DTIME( (1+ε) n).</p>
</blockq... | habedi/stack-exchange-dataset |
57,894 | Longest path in a cyclic, directed and weighted graph | <p>I am looking for the longest simple path in a directed, cyclic and weighted graph with positive and negative weights.</p>

<p>In my research so far I have found out that you need to generate <code>-G</code> from graph <code>G</code> and then run a shortest path algorithm on it to find the longest path in <co... | algorithms graphs | 1 | Longest path in a cyclic, directed and weighted graph -- (algorithms graphs)
<p>I am looking for the longest simple path in a directed, cyclic and weighted graph with positive and negative weights.</p>

<p>In my research so far I have found out that you need to generate <code>-G</code> from graph <code>G</code>... | habedi/stack-exchange-dataset |
57,897 | Linearity of Expectation | <p>I'm taking a course on Coursera about approximation algorithms for fun and one of the modules uses probability to analyze the cost of a linear program with randomized rounding solution to the set cover problem.</p>

<p>One of the problem set questions is a basic probability question and is as follows:</p>&#x... | algorithm analysis | 1 | Linearity of Expectation -- (algorithm analysis)
<p>I'm taking a course on Coursera about approximation algorithms for fun and one of the modules uses probability to analyze the cost of a linear program with randomized rounding solution to the set cover problem.</p>

<p>One of the problem set questions is a bas... | habedi/stack-exchange-dataset |
57,900 | Modelling a dependency of multiple transitions on data in one place | <p>We are modeling our process using a colored Petri net. One of the limitations we have is that when multiple transitions depend on one place, only one of those transitions will fire because then the token and data is consumed.</p>

<p>How can we model our process, or what type of Petri net property can we use... | modelling petri nets | 1 | Modelling a dependency of multiple transitions on data in one place -- (modelling petri nets)
<p>We are modeling our process using a colored Petri net. One of the limitations we have is that when multiple transitions depend on one place, only one of those transitions will fire because then the token and data is consume... | habedi/stack-exchange-dataset |
57,904 | Why do we have to trade abstraction for speed? | <p>Why can high-level languages seemingly never reach lower-level languages in terms of speed? Examples of high-level languages would be Python, Haskell, and Java. Low-level languages would be trickier to define, but let's say C. Comparisons can be found all around the Internet$^1$ and they all agree that C is a lot fa... | programming languages performance | 1 | Why do we have to trade abstraction for speed? -- (programming languages performance)
<p>Why can high-level languages seemingly never reach lower-level languages in terms of speed? Examples of high-level languages would be Python, Haskell, and Java. Low-level languages would be trickier to define, but let's say C. Comp... | habedi/stack-exchange-dataset |
57,908 | Is a PDA's stack size linear bounded in input size? | <p>I was thinking as follows: At each step, a PDA can put arbitrary many symbols onto the stack. But this number is constant for every individual PDA, so it can't be more than, say, $k$ symbols per step. Using only regular transitions, the stack can rise to maximally (more or less) $kn$ symbols in a run on an input siz... | automata pushdown automata | 1 | Is a PDA's stack size linear bounded in input size? -- (automata pushdown automata)
<p>I was thinking as follows: At each step, a PDA can put arbitrary many symbols onto the stack. But this number is constant for every individual PDA, so it can't be more than, say, $k$ symbols per step. Using only regular transitions, ... | habedi/stack-exchange-dataset |
57,910 | Suggest a data-structure that supports the following operations with time complexity of $ O(log(n)) $ | <p>Iv'e been struggling a lot with this one.
I am looking for a data-structure (could be a modification of an existing type of data-structure, or a combination of more than one data-structure), which supports the following methods, all with time complexity (at worst-case) of $O(log(n))$:</p>

<ol>
<li>I... | data structures dictionaries | 1 | Suggest a data-structure that supports the following operations with time complexity of $ O(log(n)) $ -- (data structures dictionaries)
<p>Iv'e been struggling a lot with this one.
I am looking for a data-structure (could be a modification of an existing type of data-structure, or a combination of more than one dat... | habedi/stack-exchange-dataset |
57,921 | Why is the set of perfect squares in P? | <p>I am reading an article by Cook [1]. In it he writes:</p>

<blockquote>
 <p>The set of perfect squares is in P, since Newton's method can be used to efficiently approximate square roots.</p>
</blockquote>

<p>I can see how to use Newton's method to decide whether a natural number is a
pe... | complexity theory time complexity polynomial time number theory | 1 | Why is the set of perfect squares in P? -- (complexity theory time complexity polynomial time number theory)
<p>I am reading an article by Cook [1]. In it he writes:</p>

<blockquote>
 <p>The set of perfect squares is in P, since Newton's method can be used to efficiently approximate square roots.</p>
... | habedi/stack-exchange-dataset |
57,926 | NFA to accept strings where the third AND the third-last element are b | <p>Alphabet is {a,b}, the third element from the start must be "b" (e.g: aab..., abb...) and the third-last element must also be "b" (e.g: ...baa, ...bbb). I can do them separately but at the same time I don't know where to start. Help please.</p>
 | automata finite automata | 1 | NFA to accept strings where the third AND the third-last element are b -- (automata finite automata)
<p>Alphabet is {a,b}, the third element from the start must be "b" (e.g: aab..., abb...) and the third-last element must also be "b" (e.g: ...baa, ...bbb). I can do them separately but at the same time I don't know wher... | habedi/stack-exchange-dataset |
57,936 | Taking intersection in large search | <p>As I understand, you can build the the word -> pages index in Google or large SQL database since indexed search has complexity O(1) -- lookup gives you a billion-page result at once</p>

<pre><code>сomputer -> About 2.14 bln results 
science -> About 1.93 bln results
</code></pre>

<hr>... | search algorithms big data search | 1 | Taking intersection in large search -- (search algorithms big data search)
<p>As I understand, you can build the the word -> pages index in Google or large SQL database since indexed search has complexity O(1) -- lookup gives you a billion-page result at once</p>

<pre><code>сomputer -> About 2.14 bln result... | habedi/stack-exchange-dataset |
57,937 | Are all functions with constant space complexity in $REG$? | <p>The <a href="https://en.wikipedia.org/wiki/Regular_language" rel="nofollow">Wikipedia article</a> about regular languages mentions that $DSPACE(O(1))$ is equal to $REG$. Can I conclude from this that every function in $R$ with constant space complexity is in $REG$?</p>
 | complexity theory computability regular languages primitive recursion | 1 | Are all functions with constant space complexity in $REG$? -- (complexity theory computability regular languages primitive recursion)
<p>The <a href="https://en.wikipedia.org/wiki/Regular_language" rel="nofollow">Wikipedia article</a> about regular languages mentions that $DSPACE(O(1))$ is equal to $REG$. Can I conclud... | habedi/stack-exchange-dataset |
57,946 | Why are regular expressions defined with union, concatenation and star operations? | <p>A <em>regular expresssion</em> is defined recursively as</p>

<ol>
<li>$a$ for some $a \in \Sigma$ is a regular expression,</li>
<li>$\varepsilon$ is a regular expression,</li>
<li>$\emptyset$ is a regular expression,</li>
<li>$(R_1 \cup R_2)$ where $R_1$ and $R_2$ are regular expressions is ... | formal languages regular languages regular expressions | 1 | Why are regular expressions defined with union, concatenation and star operations? -- (formal languages regular languages regular expressions)
<p>A <em>regular expresssion</em> is defined recursively as</p>

<ol>
<li>$a$ for some $a \in \Sigma$ is a regular expression,</li>
<li>$\varepsilon$ is a regula... | habedi/stack-exchange-dataset |
57,949 | Does the Halting Problem prove that true Artificial Intelligence is impossible? | <p>The Halting Problem demonstrates that there are things that a machine can never be programmed to do. </p>

<p>Is this proof that true Artificial Intelligence - that is, the ability for a machine to think and reason like humans - is not possible?</p>
 | artificial intelligence halting problem | 1 | Does the Halting Problem prove that true Artificial Intelligence is impossible? -- (artificial intelligence halting problem)
<p>The Halting Problem demonstrates that there are things that a machine can never be programmed to do. </p>

<p>Is this proof that true Artificial Intelligence - that is, the ability for... | habedi/stack-exchange-dataset |
57,955 | How to compute the sum of this series involving golden ratio, efficiently? | <p><strong>Definitions</strong><br></p>

<ol>
<li>Let $\tau$ be a function on natural numbers defined as $\tau(n)=\lceil n*\phi^2\rceil$ where $n$ is some natural number and $\phi=\frac{1+\sqrt{5}}{2}$ is the golden ratio. This series can also be looked up here : <a href="https://oeis.org/A004957">A004957</... | time complexity number theory | 1 | How to compute the sum of this series involving golden ratio, efficiently? -- (time complexity number theory)
<p><strong>Definitions</strong><br></p>

<ol>
<li>Let $\tau$ be a function on natural numbers defined as $\tau(n)=\lceil n*\phi^2\rceil$ where $n$ is some natural number and $\phi=\frac{1+\sqrt{5}}{... | habedi/stack-exchange-dataset |
57,960 | exercise on Huffman encode | <p>I have these 4 symbols with their probabilities:</p>

<pre><code> x P(x)
 --------
 1 0.3
 2 0.3
 3 0.2
 4 0.2
</code></pre>

<p>I built the Huffman tree in this way:</p>

<p><a href="https://i.stack.imgur.com/Dq6GM.png" rel="nofollow noreferrer"><img src="ht... | huffman coding | 1 | exercise on Huffman encode -- (huffman coding)
<p>I have these 4 symbols with their probabilities:</p>

<pre><code> x P(x)
 --------
 1 0.3
 2 0.3
 3 0.2
 4 0.2
</code></pre>

<p>I built the Huffman tree in this way:</p>

<p><a href="https://i.stack.imgur.com/Dq... | habedi/stack-exchange-dataset |
57,970 | How can time complexities be elements of others? | <p>I have a problem that I solved, but I'm unsure if my answers are correct or not. I've never seen the implementation of time complexities as elements of others.</p>

<pre><code>f(n) element of O(log(n))
g(n) element of theta(n)
</code></pre>

<p>Prove if the below are true are false, provide a... | asymptotics | 1 | How can time complexities be elements of others? -- (asymptotics)
<p>I have a problem that I solved, but I'm unsure if my answers are correct or not. I've never seen the implementation of time complexities as elements of others.</p>

<pre><code>f(n) element of O(log(n))
g(n) element of theta(n)
</code><... | habedi/stack-exchange-dataset |
57,974 | Set of vertex-disjoint cycles maximizing different colored vertices | <p>Let $G=(V,E)$ be a directed graph whose vertices $v \in V$ have colors and its edges $e\in E$ have costs $cost(e)$.</p>

<p>I am looking to find a set of vertex-disjoint cycles that:</p>

<ol>
<li>First maximizes the number of differently colored covered vertices.</li>
<li>In case of ties, br... | network flow matching | 1 | Set of vertex-disjoint cycles maximizing different colored vertices -- (network flow matching)
<p>Let $G=(V,E)$ be a directed graph whose vertices $v \in V$ have colors and its edges $e\in E$ have costs $cost(e)$.</p>

<p>I am looking to find a set of vertex-disjoint cycles that:</p>

<ol>
<li>First... | habedi/stack-exchange-dataset |
57,977 | Hadamard gate on entangled qubit | <p><strong>TL;DR:</strong> If you have two entangled qubits in the state $|00\rangle + |11\rangle$, what is the result of applying the Hadamard gate on the second qubit, and why?</p>

<hr>

<p>I am trying to understand <a href="https://cs.uwaterloo.ca/~watrous/Papers/PSPACEinQIP3.pdf" rel="nofollow">$\t... | quantum computing | 1 | Hadamard gate on entangled qubit -- (quantum computing)
<p><strong>TL;DR:</strong> If you have two entangled qubits in the state $|00\rangle + |11\rangle$, what is the result of applying the Hadamard gate on the second qubit, and why?</p>

<hr>

<p>I am trying to understand <a href="https://cs.uwaterloo... | habedi/stack-exchange-dataset |
57,978 | Classify the set of all TMs whose languages from the accepting problem | <p>Let $$L = \{ \langle M \rangle \mid M \text{ is a Turing machine so } A_{TM} \leq_m L(M) \}$$
The question is whether $L$ is in $\mathcal{R}, \mathcal{RE}, co-\mathcal{RE}$ or in $\overline{\mathcal{RE} \cup co-\mathcal{RE}}$ ?</p>

<p><br><br><br><br>
I gained some progrees showing $L \notin co- \... | computability turing machines undecidability | 1 | Classify the set of all TMs whose languages from the accepting problem -- (computability turing machines undecidability)
<p>Let $$L = \{ \langle M \rangle \mid M \text{ is a Turing machine so } A_{TM} \leq_m L(M) \}$$
The question is whether $L$ is in $\mathcal{R}, \mathcal{RE}, co-\mathcal{RE}$ or in $\overline{\... | habedi/stack-exchange-dataset |
57,980 | Number of winning combination in Nim | <p>I am studying game theory and I am wondering how many winning combinations are possible for Nim game? Suppose, stones = 500 and piles = 5. With these number, there are many initial game positions are possible. like [1, 2, 4, 3, 490], [100, 100, 100, 100, 100], [100, 200, 100, 100], [0, 200, 200, 50, 50] and so on. S... | algorithms game theory | 1 | Number of winning combination in Nim -- (algorithms game theory)
<p>I am studying game theory and I am wondering how many winning combinations are possible for Nim game? Suppose, stones = 500 and piles = 5. With these number, there are many initial game positions are possible. like [1, 2, 4, 3, 490], [100, 100, 100, 10... | habedi/stack-exchange-dataset |
57,982 | All output functions of a truth table | <blockquote>
 <p><a href="http://www.cim.mcgill.ca/~langer/273/3-notes.pdf" rel="nofollow noreferrer">http://www.cim.mcgill.ca/~langer/273/3-notes.pdf</a>
 <a href="https://i.stack.imgur.com/UNbvZ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/UNbvZ.png" alt="enter image description here">... | propositional logic | 1 | All output functions of a truth table -- (propositional logic)
<blockquote>
 <p><a href="http://www.cim.mcgill.ca/~langer/273/3-notes.pdf" rel="nofollow noreferrer">http://www.cim.mcgill.ca/~langer/273/3-notes.pdf</a>
 <a href="https://i.stack.imgur.com/UNbvZ.png" rel="nofollow noreferrer"><img src="https://i... | habedi/stack-exchange-dataset |
57,988 | How to prove the following xor equation? | <p>In a test paper, a question is given as :</p>

<pre><code>Let, x1^x2^x3^x4 =0 where x1, x2, x3, x4 are Boolean variables,and ^ is the XOR operator.

Which one of the following must always be TRUE?
(A) x1x2x3x4 = 0
(B) x1x3+x2 = 0
(C) x1'^x3' = x2'^x4'
(D) x1+x2+x3+x4 = 0

+ i... | boolean algebra | 1 | How to prove the following xor equation? -- (boolean algebra)
<p>In a test paper, a question is given as :</p>

<pre><code>Let, x1^x2^x3^x4 =0 where x1, x2, x3, x4 are Boolean variables,and ^ is the XOR operator.

Which one of the following must always be TRUE?
(A) x1x2x3x4 = 0
(B) x1x3+x2 = 0&#... | habedi/stack-exchange-dataset |
57,989 | Why is BNF considered an unsatisfactory technique for describing a language? | <p>I was reading the paper <a href="http://dl.acm.org/citation.cfm?id=609208" rel="noreferrer">Fundamental Concepts in Programming Languages by C. Strachey</a> the other day, wherein I read something that was quite strange to me. Quoting directly (with the strange part highlighted by me):</p>

<blockquote>
... | formal grammars programming languages syntax | 1 | Why is BNF considered an unsatisfactory technique for describing a language? -- (formal grammars programming languages syntax)
<p>I was reading the paper <a href="http://dl.acm.org/citation.cfm?id=609208" rel="noreferrer">Fundamental Concepts in Programming Languages by C. Strachey</a> the other day, wherein I read som... | habedi/stack-exchange-dataset |
57,991 | Computing gaussian kernel for image blurring | <p>When I compute a gaussian kernel for image blurring should I normalize the 1D vectors? Because when I apply the raw values sometimes the image gets lighter or darker.
The function I'm using is $f(x) = \frac{1}{\sqrt{2\pi}\sigma}e^{\frac{-x^2}{2\sigma^2}}$ or the 2D function.
So, should I just apply the resul... | image processing computer vision | 1 | Computing gaussian kernel for image blurring -- (image processing computer vision)
<p>When I compute a gaussian kernel for image blurring should I normalize the 1D vectors? Because when I apply the raw values sometimes the image gets lighter or darker.
The function I'm using is $f(x) = \frac{1}{\sqrt{2\pi}\sigma}e^... | habedi/stack-exchange-dataset |
58,004 | Check whether an undirected graph contains a simple cycle of length four using the "Squares" method | <p>The following problem is exercise 4.3 of the book <a href="http://rads.stackoverflow.com/amzn/click/0073523402" rel="nofollow noreferrer">"Algorithms"</a> by S. Dasgupta, C. Papadimitriou, and U. Vazirani.</p>

<blockquote>
 <p><em>Squares.</em> Design and analyze an algorithm that takes as input an und... | algorithms graphs | 1 | Check whether an undirected graph contains a simple cycle of length four using the "Squares" method -- (algorithms graphs)
<p>The following problem is exercise 4.3 of the book <a href="http://rads.stackoverflow.com/amzn/click/0073523402" rel="nofollow noreferrer">"Algorithms"</a> by S. Dasgupta, C. Papadimitriou, and U... | habedi/stack-exchange-dataset |
58,009 | Is EXPTIME "solvable" or "checkable" in exponential time? | <p>According to <a href="https://youtu.be/YX40hbAHx3s?t=8m24s">this</a> video, EXP has problems that are exponentially difficult to check.</p>

<p>But according to <a href="https://youtu.be/moPtwq_cVH8?t=2m39s">this</a> video, EXP are problems that are exponentially difficult to solve.</p>

<p>It would ... | complexity theory algorithm analysis np | 1 | Is EXPTIME "solvable" or "checkable" in exponential time? -- (complexity theory algorithm analysis np)
<p>According to <a href="https://youtu.be/YX40hbAHx3s?t=8m24s">this</a> video, EXP has problems that are exponentially difficult to check.</p>

<p>But according to <a href="https://youtu.be/moPtwq_cVH8?t=2m39s... | habedi/stack-exchange-dataset |
58,013 | Is it possible to derive a deterministic CSPRNG given two functions, at least one of which is a CSPRNG? | <p>Let <code>f</code> and <code>g</code> be two functions with integer range <code>0..m-1</code>. They may keep state and interact with the world (for example setting a seed or reading the current time), calling them multiple times may produce different results. <code>f</code> and <code>g</code> can see each other's st... | discrete mathematics cryptography randomness pseudo random generators | 1 | Is it possible to derive a deterministic CSPRNG given two functions, at least one of which is a CSPRNG? -- (discrete mathematics cryptography randomness pseudo random generators)
<p>Let <code>f</code> and <code>g</code> be two functions with integer range <code>0..m-1</code>. They may keep state and interact with the w... | habedi/stack-exchange-dataset |
58,019 | Union of a Deterministic Context-free language and a Regular Language is a Deterministic Context-free Language | <p>In formal language theory, deterministic context-free languages (DCFL) are a proper subset of context-free languages. They are the context-free languages that can be accepted by a deterministic pushdown automaton. </p>

<p>Now Assume that $R$ is a regular language and $D$ is a deterministic context-free l... | context free automata pushdown automata | 1 | Union of a Deterministic Context-free language and a Regular Language is a Deterministic Context-free Language -- (context free automata pushdown automata)
<p>In formal language theory, deterministic context-free languages (DCFL) are a proper subset of context-free languages. They are the context-free languages that ca... | habedi/stack-exchange-dataset |
58,021 | Flaw in linear programming solution for multi-commodity flow problem? | <p>The multi-commodity flow problem problem statement - <a href="https://en.wikipedia.org/wiki/Multi-commodity_flow_problem" rel="nofollow noreferrer">wiki</a></p>

<p>According to constraints of multi-commodity flow problem a given material must start at source <em>s</em> with demand <em>d</em> and end up at i... | algorithms graphs np complete linear programming | 1 | Flaw in linear programming solution for multi-commodity flow problem? -- (algorithms graphs np complete linear programming)
<p>The multi-commodity flow problem problem statement - <a href="https://en.wikipedia.org/wiki/Multi-commodity_flow_problem" rel="nofollow noreferrer">wiki</a></p>

<p>According to constra... | habedi/stack-exchange-dataset |
58,027 | is this NPC Prob? Minimum count of distinct values at all matrix columns provided only in-row swap operation | <p>I am searching for an algorithm for this! Cannot find anything useful in textbook so far. Thanks in advance! </p>

<blockquote>
 <p>Question: The input is a $N \times K$ matrix, where $N$ and $K$ are positive numbers( usually $N$ is a large number, $K$ is a small number). Each row of the matrix contains... | algorithms combinatorics matrices | 1 | is this NPC Prob? Minimum count of distinct values at all matrix columns provided only in-row swap operation -- (algorithms combinatorics matrices)
<p>I am searching for an algorithm for this! Cannot find anything useful in textbook so far. Thanks in advance! </p>

<blockquote>
 <p>Question: The input is a... | habedi/stack-exchange-dataset |
58,028 | Number of possible programs in a language | <p>Is the number of possible programs usually finite or infinite? I'm playing with the idea of generating all possible programs for a language - is that even a finite number or must we be more specific, finite RAM etc?</p>
 | programming languages | 1 | Number of possible programs in a language -- (programming languages)
<p>Is the number of possible programs usually finite or infinite? I'm playing with the idea of generating all possible programs for a language - is that even a finite number or must we be more specific, finite RAM etc?</p>
 | habedi/stack-exchange-dataset |
58,031 | What is the difference between oblivious and non-oblivious merging, sorting etc | <p>Algorithms can either be oblivious or non-oblivious, but what is the actual difference between the two?</p>
 | algorithms complexity theory sorting | 1 | What is the difference between oblivious and non-oblivious merging, sorting etc -- (algorithms complexity theory sorting)
<p>Algorithms can either be oblivious or non-oblivious, but what is the actual difference between the two?</p>
 | habedi/stack-exchange-dataset |
58,033 | Is there a way to reflect small edge-weight changes after computing Floyd-Warshall on a large graph? | <p>I am working on a hex-based game in which I'm trying to pre-calculate pathfinding for a given map using the Floyd-Warshall algorithm. The map size is on the order of thousands of hexes (so maximum tens of thousands of edges).</p>

<p>The map represents an arena in which two teams fight, and both have the abi... | graphs shortest path | 1 | Is there a way to reflect small edge-weight changes after computing Floyd-Warshall on a large graph? -- (graphs shortest path)
<p>I am working on a hex-based game in which I'm trying to pre-calculate pathfinding for a given map using the Floyd-Warshall algorithm. The map size is on the order of thousands of hexes (so m... | habedi/stack-exchange-dataset |
58,045 | Common subset sum fast algorithm | <p>Suppose of I two sets of $n$ integers bounded in $[-B,B]$. The integers are $$a_1,\dots,a_n$$
$$b_1,\dots,b_n$$</p>

<p>I want to find if there is a common subset $I\subseteq\{1,\dots,n\}$ such that $$\sum_{i\in I}a_i=0$$$$\sum_{i\in I}b_i=0$$</p>

<p>This problem is $NP$-complete.</p>

<... | algorithms pseudo polynomial | 1 | Common subset sum fast algorithm -- (algorithms pseudo polynomial)
<p>Suppose of I two sets of $n$ integers bounded in $[-B,B]$. The integers are $$a_1,\dots,a_n$$
$$b_1,\dots,b_n$$</p>

<p>I want to find if there is a common subset $I\subseteq\{1,\dots,n\}$ such that $$\sum_{i\in I}a_i=0$$$$\sum_{i\in I}b_... | habedi/stack-exchange-dataset |
58,065 | What is the archive attribute for windows files? | <p>What is the archive attribute for windows files.
What is Archive in file details?</p>
 | attribute grammars | 1 | What is the archive attribute for windows files? -- (attribute grammars)
<p>What is the archive attribute for windows files.
What is Archive in file details?</p>
 | habedi/stack-exchange-dataset |
58,085 | How can I study the nature of the structure of evaluation of function in lambda calculus? | <p>I am specifically focusing on lambda calculus, following this paper: <a href="http://www.inf.fu-berlin.de/lehre/WS03/alpi/lambda.pdf" rel="nofollow">A Tutorial Introduction to the Lambda Calculus</a>.</p>

<p>Suppose we have three functions that represent the natural numbers 0 and 1, and a successor function... | lambda calculus church numerals | 1 | How can I study the nature of the structure of evaluation of function in lambda calculus? -- (lambda calculus church numerals)
<p>I am specifically focusing on lambda calculus, following this paper: <a href="http://www.inf.fu-berlin.de/lehre/WS03/alpi/lambda.pdf" rel="nofollow">A Tutorial Introduction to the Lambda Cal... | habedi/stack-exchange-dataset |
58,096 | Permutation on matrix to fill main diagonal with non-zero values | <p>I am currently working on some sparse non-singular matrices. One of the algorithms I use requires divisions by the elements on the main diagonal so I have to ensure that my main diagonal is filled with non-zero values. My matrices represent a set of linear equations and there is no problem to use permutations betwee... | graphs matrices linear algebra permutations sparse matrices | 1 | Permutation on matrix to fill main diagonal with non-zero values -- (graphs matrices linear algebra permutations sparse matrices)
<p>I am currently working on some sparse non-singular matrices. One of the algorithms I use requires divisions by the elements on the main diagonal so I have to ensure that my main diagonal ... | habedi/stack-exchange-dataset |
58,102 | operator precendence grammar | <p>According to this post <a href="https://stackoverflow.com/questions/28397767/computing-leading-and-trailing-sets-for-context-free-grammar">https://stackoverflow.com/questions/28397767/computing-leading-and-trailing-sets-for-context-free-grammar</a> while constructing operator precendence parser we have to create tab... | terminology formal grammars parsers | 1 | operator precendence grammar -- (terminology formal grammars parsers)
<p>According to this post <a href="https://stackoverflow.com/questions/28397767/computing-leading-and-trailing-sets-for-context-free-grammar">https://stackoverflow.com/questions/28397767/computing-leading-and-trailing-sets-for-context-free-grammar</a... | habedi/stack-exchange-dataset |
58,110 | Is there a relationship between "sound and complete" in logic and "type safety" in PLs? | <p>I've been wondering if there's a connection between "good logics" and "good programming languages". It seems that logics are shown to be "locally sound and complete" whereas programming languages are shown to be "type safe" (preservation and progress).</p>

<p>If there's a relationship could you please expla... | programming languages logic type theory | 1 | Is there a relationship between "sound and complete" in logic and "type safety" in PLs? -- (programming languages logic type theory)
<p>I've been wondering if there's a connection between "good logics" and "good programming languages". It seems that logics are shown to be "locally sound and complete" whereas programmin... | habedi/stack-exchange-dataset |
58,116 | How do we know for sure that EXPTIME ≠ P? | <p>I'm a beginner in learning about computational complexity and this has stumped me. I've read that by the time hierarchy theorem, it's known that EXP-complete problems are not in P. <a href="https://en.wikipedia.org/wiki/EXPTIME">(Wikipedia)</a> It makes absolute sense <em>intuitively</em> that this is the case, as d... | complexity theory np complete np nondeterminism polynomial time | 1 | How do we know for sure that EXPTIME ≠ P? -- (complexity theory np complete np nondeterminism polynomial time)
<p>I'm a beginner in learning about computational complexity and this has stumped me. I've read that by the time hierarchy theorem, it's known that EXP-complete problems are not in P. <a href="https://en.wikip... | habedi/stack-exchange-dataset |
58,120 | Is there any example of Regression Tree driven optimization (or active learning)? | <p>Bayesian Optimization is the classic example of meta-model driven optimization where new observations are used to train a Gaussian process that provides a clue to where to optimize next.</p>

<p>LEM (Learnable Evolution Models) are evolutionary models where rather than recombining observations (like GAs) a p... | optimization machine learning bayesian statistics | 1 | Is there any example of Regression Tree driven optimization (or active learning)? -- (optimization machine learning bayesian statistics)
<p>Bayesian Optimization is the classic example of meta-model driven optimization where new observations are used to train a Gaussian process that provides a clue to where to optimize... | habedi/stack-exchange-dataset |
58,132 | Maximize cost in graph with variable costs | <p>Consider the following problem. A prisoner eats once a day, he can either have a low, or a high calorie dish. In order to be allowed to eat the high calorie dish, he must not have eaten the previous day. The prisoner knows the calories of each dish for the full week, and wishes to maximize his calorie intake for the... | graphs dynamic programming weighted graphs | 1 | Maximize cost in graph with variable costs -- (graphs dynamic programming weighted graphs)
<p>Consider the following problem. A prisoner eats once a day, he can either have a low, or a high calorie dish. In order to be allowed to eat the high calorie dish, he must not have eaten the previous day. The prisoner knows the... | habedi/stack-exchange-dataset |
58,133 | Does P=NP imply polynomial solutions to #P? | <p>Is it true that $\#P$-complete problems could possibly be solved in polynomial time if P=NP? I know that even some counting problems related to polynomial time decision problems are $\#P$-complete, so even if P=NP it may not necessarily be true. My confusion is over how we write the answer to a $\#P$-complete probl... | complexity theory time complexity polynomial time | 1 | Does P=NP imply polynomial solutions to #P? -- (complexity theory time complexity polynomial time)
<p>Is it true that $\#P$-complete problems could possibly be solved in polynomial time if P=NP? I know that even some counting problems related to polynomial time decision problems are $\#P$-complete, so even if P=NP it m... | habedi/stack-exchange-dataset |
58,137 | Why is bipartite graph matching hard? | <p>I am reading on how solving maximum flow (Ford-Fulkerson) can be also used to solve unweighted bipartite graph matching problem. I think I don't understand the essence of this problem, because to me it seems trivial.</p>

<p>The method of solving the problem says to convert the original bipartite graph into ... | algorithms graphs optimization bipartite matching | 1 | Why is bipartite graph matching hard? -- (algorithms graphs optimization bipartite matching)
<p>I am reading on how solving maximum flow (Ford-Fulkerson) can be also used to solve unweighted bipartite graph matching problem. I think I don't understand the essence of this problem, because to me it seems trivial.</p>
... | habedi/stack-exchange-dataset |
58,140 | RISC machines have register renaming? | <p>I know that one of the techniques used by RISC machines to improve the pipeline is the delayed branch, but what other techniques do they employ, namely, can they use register renaming?</p>

<p>I know that Superscalar processors have register renaming, but a Superscalar processor can only be a CISC machine, r... | computer architecture cpu pipelines | 1 | RISC machines have register renaming? -- (computer architecture cpu pipelines)
<p>I know that one of the techniques used by RISC machines to improve the pipeline is the delayed branch, but what other techniques do they employ, namely, can they use register renaming?</p>

<p>I know that Superscalar processors ha... | habedi/stack-exchange-dataset |
58,146 | Is better than O(n^2) possible for getting pairs that sum to a multiple of 10? | <p>Is it possible to solve a problem with a worse case less than $O(n^2)$, when the input is an an array of numbers and the output is all pairs that sum to a number divisible by 10? for example</p>

<pre><code>int [] a = {1, 2, 15, 25, 28};
// would produce [2, 28], [15, 25]
</code></pre>

<p>I... | complexity theory time complexity arrays | 1 | Is better than O(n^2) possible for getting pairs that sum to a multiple of 10? -- (complexity theory time complexity arrays)
<p>Is it possible to solve a problem with a worse case less than $O(n^2)$, when the input is an an array of numbers and the output is all pairs that sum to a number divisible by 10? for example<... | habedi/stack-exchange-dataset |
58,149 | Find a DFA for a finite set of palindromes | <p>Since every finite language is regular, I'm trying to find how would a DFA for the following language $\{xx^R \mid x \in \{a,b\}^*, |x| = \ell\}$ look like.
Would there be one DFA for all words of length $\ell$ or one DFA per word? </p>
 | regular languages automata finite automata | 1 | Find a DFA for a finite set of palindromes -- (regular languages automata finite automata)
<p>Since every finite language is regular, I'm trying to find how would a DFA for the following language $\{xx^R \mid x \in \{a,b\}^*, |x| = \ell\}$ look like.
Would there be one DFA for all words of length $\ell$ or one DFA ... | habedi/stack-exchange-dataset |
58,154 | How does (non)deterministic time relate to verifiability? | <p>So far, from all the research I've done, I've come across 2 different ways that NP time is explained. One is that a nondeterministic turing machine is able to solve the problem in polynomial time. It seems like this is the exact same as being able to verify that a result is correct in polynomial time, but not necess... | complexity theory np | 1 | How does (non)deterministic time relate to verifiability? -- (complexity theory np)
<p>So far, from all the research I've done, I've come across 2 different ways that NP time is explained. One is that a nondeterministic turing machine is able to solve the problem in polynomial time. It seems like this is the exact same... | habedi/stack-exchange-dataset |
58,156 | What complexity class would this version of generalized chess fall? | <p>By now I understand that generalized chess is harder than NP, and is EXPTIME-complete for the decision problem "Given an nxn board with a given position, can white <em>force</em> a win?" because the proof would require an exponential amount of steps to show that each branch of the tree eventually leads to a win. The... | complexity theory time complexity np nondeterminism board games | 1 | What complexity class would this version of generalized chess fall? -- (complexity theory time complexity np nondeterminism board games)
<p>By now I understand that generalized chess is harder than NP, and is EXPTIME-complete for the decision problem "Given an nxn board with a given position, can white <em>force</em> a... | habedi/stack-exchange-dataset |
58,172 | How can I reduce a product of transpositions? | <p>I'm looking for an algorithm to solve the following task:</p>

<p>Input: a set $T$ of transpositions; a permutation $\pi$ expressed as a product of transpositions from $T$<br>
Desired output: express $\pi$ as the shortest possible product of transpositions from $T$.</p>

<p>In other words, the ou... | algorithms optimization permutations | 1 | How can I reduce a product of transpositions? -- (algorithms optimization permutations)
<p>I'm looking for an algorithm to solve the following task:</p>

<p>Input: a set $T$ of transpositions; a permutation $\pi$ expressed as a product of transpositions from $T$<br>
Desired output: express $\pi$ as the shor... | habedi/stack-exchange-dataset |
58,180 | What is the difference in 'logical array blocked' and array list B, and what do they represent? | <p>In Johnson's 1975 Paper <a href="http://epubs.siam.org/doi/abs/10.1137/0204007?journalCode=smjcat" rel="nofollow">'Finding All the Elementary Circuits of a Directed Graph',</a> his psuedocode refers to two separate data structures, logical array blocked and list array B. What is the difference in them and what do th... | graphs discrete mathematics graph traversal | 1 | What is the difference in 'logical array blocked' and array list B, and what do they represent? -- (graphs discrete mathematics graph traversal)
<p>In Johnson's 1975 Paper <a href="http://epubs.siam.org/doi/abs/10.1137/0204007?journalCode=smjcat" rel="nofollow">'Finding All the Elementary Circuits of a Directed Graph',... | habedi/stack-exchange-dataset |
58,183 | Does there always exist equivalent (M)(I)LPs with and without objective functions? | <p>For computing pure Nash equilibria (game theory), there exists a MILP method in literature (<a href="http://www.hindawi.com/journals/mpe/2014/640960/" rel="nofollow">clicky</a>).</p>

<p>In the proposed MILP, there is no objective function. A solution is a pure Nash equilibrium if it is a feasible solution o... | reductions linear programming | 1 | Does there always exist equivalent (M)(I)LPs with and without objective functions? -- (reductions linear programming)
<p>For computing pure Nash equilibria (game theory), there exists a MILP method in literature (<a href="http://www.hindawi.com/journals/mpe/2014/640960/" rel="nofollow">clicky</a>).</p>

<p>In t... | habedi/stack-exchange-dataset |
58,185 | The longest subarray sum divisible by $5$ in $O(n)$ time | <blockquote>
 <p>Given an array of non negative integers 
 Find the longest continuous sub array which it's sum is divisible by 5.</p>
</blockquote>

<p>For example if the array is:
[1,3,9,2,1,5,0,1]</p>

<p>A continuous subarray which it's sum is divisible by 5 for example is:
[3,... | algorithms arrays maximum subarray | 1 | The longest subarray sum divisible by $5$ in $O(n)$ time -- (algorithms arrays maximum subarray)
<blockquote>
 <p>Given an array of non negative integers 
 Find the longest continuous sub array which it's sum is divisible by 5.</p>
</blockquote>

<p>For example if the array is:
[1,3,9,2,1,5,0,... | habedi/stack-exchange-dataset |
58,194 | How are games like chess provably harder than NP? | <p>From <a href="https://cs.stackexchange.com/questions/58156/what-complexity-class-would-this-version-of-generalized-chess-fall?noredirect=1#comment123371_58156">this</a> question, I had the debate about how problems harder than NP are proved.</p>
<p>I said that intuitively I understand it as (from <a href="https:... | complexity theory time complexity np complete np nondeterminism | 1 | How are games like chess provably harder than NP? -- (complexity theory time complexity np complete np nondeterminism)
<p>From <a href="https://cs.stackexchange.com/questions/58156/what-complexity-class-would-this-version-of-generalized-chess-fall?noredirect=1#comment123371_58156">this</a> question, I had the debate ab... | habedi/stack-exchange-dataset |
58,223 | Red-blue intersection requirements | <p>In the red-blue line segments intersection problem, what does it mean that the red-red (and blue-blue) lines cannot intersect? Does mean mean that the algorithms wont work correctly or does it mean that these kind of intersections will be simply ignored?</p>

<p>In other words, do the fast intersection algor... | algorithms computational geometry | 1 | Red-blue intersection requirements -- (algorithms computational geometry)
<p>In the red-blue line segments intersection problem, what does it mean that the red-red (and blue-blue) lines cannot intersect? Does mean mean that the algorithms wont work correctly or does it mean that these kind of intersections will be simp... | habedi/stack-exchange-dataset |
58,255 | Why DCFL is not closed under kleene star? | <p>I have read somewhere that DCFL is not closed under kleene star. but I haven't found any example</p>
 | formal languages context free closure properties pushdown automata | 1 | Why DCFL is not closed under kleene star? -- (formal languages context free closure properties pushdown automata)
<p>I have read somewhere that DCFL is not closed under kleene star. but I haven't found any example</p>
 | habedi/stack-exchange-dataset |
58,263 | My algorithm is different from CLRS' -- is it wrong? | <p>Exercise 2.3-7 from "Introduction to Algorithms" by Cormen et al. Third Edition, states:</p>
<blockquote>
<p>Describe a O(n lg n)-time algorithm that, given a set <em>S</em> of <em>n</em> integers and another integer <em>x</em>, determines whether of not there exist two elements in <em>S</em> whose... | algorithms algorithm analysis sets | 1 | My algorithm is different from CLRS' -- is it wrong? -- (algorithms algorithm analysis sets)
<p>Exercise 2.3-7 from "Introduction to Algorithms" by Cormen et al. Third Edition, states:</p>
<blockquote>
<p>Describe a O(n lg n)-time algorithm that, given a set <em>S</em> of <em>n</em> integers and anoth... | habedi/stack-exchange-dataset |
58,264 | Does a shift operation distribute over XOR | <p><em>In this question, we abuse the mathematical notation to express bitwise operations in the following way:</em></p>

<ul>
<li><em>$\ll$ is a binary left shift</em></li>
<li><em>$\oplus$ is a bitwise XOR</em></li>
<li><em>$0b1, 0b110, 0b10 \ldots$ are used to denote raw bits</em></li>
<li><e... | arithmetic | 1 | Does a shift operation distribute over XOR -- (arithmetic)
<p><em>In this question, we abuse the mathematical notation to express bitwise operations in the following way:</em></p>

<ul>
<li><em>$\ll$ is a binary left shift</em></li>
<li><em>$\oplus$ is a bitwise XOR</em></li>
<li><em>$0b1, 0b110, 0b... | habedi/stack-exchange-dataset |
59,292 | Side effect and recursion | <p>My algorithm professor said a recursive function should not have side-effects since it's a methodological error because recursion is "pure".
Anyway I don't understand why, even because I find side-effects useful and difficult to replace a recursive side-effect function with a "pure" one.</p>
 | recursion software engineering recursion theory | 1 | Side effect and recursion -- (recursion software engineering recursion theory)
<p>My algorithm professor said a recursive function should not have side-effects since it's a methodological error because recursion is "pure".
Anyway I don't understand why, even because I find side-effects useful and difficult to repla... | habedi/stack-exchange-dataset |
59,294 | runtime of problems vs algorithms | <p>I know that a solving a specific problem can have different runtimes on different models of computation. But can a specific algorithm have different runtimes on different models of computation?</p>

<p>Also, would an algorithm be considered the high level description or the implementation level description o... | algorithms runtime analysis computation models | 1 | runtime of problems vs algorithms -- (algorithms runtime analysis computation models)
<p>I know that a solving a specific problem can have different runtimes on different models of computation. But can a specific algorithm have different runtimes on different models of computation?</p>

<p>Also, would an algori... | habedi/stack-exchange-dataset |
59,295 | Is this an instance of a well-known problem? | <h1>Context</h1>

<p>I am developing an application and came across a problem that seemed difficult to solve. Before attempting to reinvent the wheel (and trying to solve an NP complete problem on my own), I would like to get some feedback. Below you will find an abstract version of the problem.</p>

<h... | complexity theory optimization np complete | 1 | Is this an instance of a well-known problem? -- (complexity theory optimization np complete)
<h1>Context</h1>

<p>I am developing an application and came across a problem that seemed difficult to solve. Before attempting to reinvent the wheel (and trying to solve an NP complete problem on my own), I would like ... | habedi/stack-exchange-dataset |
59,299 | Complexity of testing membership in a disjoint set | <p>I have a disjoint set data structure (sometimes known as a union-find data structure) where I store a value in each "node". I want to look up a node by value. How can I do this?</p>

<p>The representations normally discussed in literature, both linked list and forests, deal with operations being given node... | data structures dictionaries union find | 1 | Complexity of testing membership in a disjoint set -- (data structures dictionaries union find)
<p>I have a disjoint set data structure (sometimes known as a union-find data structure) where I store a value in each "node". I want to look up a node by value. How can I do this?</p>

<p>The representations norma... | habedi/stack-exchange-dataset |
59,304 | What are these questions in the PoplMark challenge asking? | <p>I was reading the paper <em>Mechanized Metatheory for the Masses: the PoplMark Challenge</em> by Aydemir et al (<a href="http://research.microsoft.com/en-us/people/dimitris/poplmark.pdf" rel="nofollow">PDF</a>) and I found the following three questions on page 13 of the PDF a bit confusing. </p>

<blockquote... | programming languages semantics formal methods | 1 | What are these questions in the PoplMark challenge asking? -- (programming languages semantics formal methods)
<p>I was reading the paper <em>Mechanized Metatheory for the Masses: the PoplMark Challenge</em> by Aydemir et al (<a href="http://research.microsoft.com/en-us/people/dimitris/poplmark.pdf" rel="nofollow">PDF<... | habedi/stack-exchange-dataset |
59,307 | Common name for inverse of beta reduction | <p>For some transformation, I am currently working on, it is useful to "pull out" subexpressions and replacing them with variables.</p>

<p>i.e. $\textbf{transform}(42 + 3 * 4) = (\lambda x. 42 + x) (3*4)$ </p>

<p>This has, of course, the same result (if it does not extract bound variables and is corre... | terminology lambda calculus | 1 | Common name for inverse of beta reduction -- (terminology lambda calculus)
<p>For some transformation, I am currently working on, it is useful to "pull out" subexpressions and replacing them with variables.</p>

<p>i.e. $\textbf{transform}(42 + 3 * 4) = (\lambda x. 42 + x) (3*4)$ </p>

<p>This has, of c... | habedi/stack-exchange-dataset |
59,309 | Structure of a Pumping Lemma proof: contradiction or counterexample? | <p>This site is full of Pumping Lemma questions, and I do admit I've not read them all. I've tried some proofs myself and they seem to work, but I can't find anywhere what is the (general) exact structure of a proof where you show a language is not regular or context-free?</p>

<p>Wikipedia and most proofs star... | proof techniques pumping lemma | 1 | Structure of a Pumping Lemma proof: contradiction or counterexample? -- (proof techniques pumping lemma)
<p>This site is full of Pumping Lemma questions, and I do admit I've not read them all. I've tried some proofs myself and they seem to work, but I can't find anywhere what is the (general) exact structure of a proof... | habedi/stack-exchange-dataset |
59,317 | Can LOOP-Programm stop when its value goes below 0? | <p>I am wondering, if in the <a href="https://en.wikipedia.org/wiki/LOOP_%28programming_language%29" rel="nofollow">LOOP programing language</a>, whether instances of the <code>LOOP x DO P END</code> are defined to stop in the case $x < 0$.</p>

<p>The definition only says "Execute $P$, $x$ times" for the ab... | computability programming languages loops | 1 | Can LOOP-Programm stop when its value goes below 0? -- (computability programming languages loops)
<p>I am wondering, if in the <a href="https://en.wikipedia.org/wiki/LOOP_%28programming_language%29" rel="nofollow">LOOP programing language</a>, whether instances of the <code>LOOP x DO P END</code> are defined to stop i... | habedi/stack-exchange-dataset |
59,319 | Best starter resources for learning about AI | <p>I want to start learning of AI and have an idea to program "social evolution simulator" but want to hear any advice to avoid creation "well known bicycles" and get strong knowledge-base. Will be grateful for online resources and/or books. Thanks.</p>

<p>Also, I understand, that any programming language can ... | machine learning artificial intelligence | 1 | Best starter resources for learning about AI -- (machine learning artificial intelligence)
<p>I want to start learning of AI and have an idea to program "social evolution simulator" but want to hear any advice to avoid creation "well known bicycles" and get strong knowledge-base. Will be grateful for online resources a... | habedi/stack-exchange-dataset |
59,329 | Turing Machine remembering copied symbols | <p>So, I know that any multiple-tape TM can be in theory turned into a one-tape TM. However, it is too easy to copy, let's say, binary numbers from one tape to another. That's why I thought about putting a separator between the two copies and then taking symbols one after the other and writing them after the separator ... | turing machines automata | 1 | Turing Machine remembering copied symbols -- (turing machines automata)
<p>So, I know that any multiple-tape TM can be in theory turned into a one-tape TM. However, it is too easy to copy, let's say, binary numbers from one tape to another. That's why I thought about putting a separator between the two copies and then ... | habedi/stack-exchange-dataset |
59,358 | How do nondeterministic Turing machines compute general function problems? | <p>(Hope this hasn't been asked before, but I didn't find anything.)</p>

<p>In my understanding, nondeterminism applies to decision problems only, due to the requirement of the <strong>existence of an accepting path</strong>. In Wikipedia, the class $NP$-easy is defined to be solvable in deterministic poltime,... | turing machines computation models nondeterminism | 1 | How do nondeterministic Turing machines compute general function problems? -- (turing machines computation models nondeterminism)
<p>(Hope this hasn't been asked before, but I didn't find anything.)</p>

<p>In my understanding, nondeterminism applies to decision problems only, due to the requirement of the <str... | habedi/stack-exchange-dataset |
59,368 | Counting specific subgraphs | <p>For a given undirected graph <strong>G</strong>, I want to count all the subgraphs <strong>H</strong> that satisfies the following conditions:</p>

<ul>
<li><strong>H.V</strong> = <strong>G.V</strong> (The subgraph will containt all the original graph nodes)</li>
<li><strong>H</strong> is connected</... | algorithms graphs counting | 1 | Counting specific subgraphs -- (algorithms graphs counting)
<p>For a given undirected graph <strong>G</strong>, I want to count all the subgraphs <strong>H</strong> that satisfies the following conditions:</p>

<ul>
<li><strong>H.V</strong> = <strong>G.V</strong> (The subgraph will containt all the original... | habedi/stack-exchange-dataset |
59,381 | Choosing a non-cryptographic hash function for language with no unsigned integers | <p>I'm implementing a hash table in pure UnrealScript, which only has support for signed 32-bit integers. This means no 64-bit integers and no unsigned integers. I was in the middle of implementing an <a href="http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-param" rel="nofollow">FNV hash</a> function, but ran ... | hash | 1 | Choosing a non-cryptographic hash function for language with no unsigned integers -- (hash)
<p>I'm implementing a hash table in pure UnrealScript, which only has support for signed 32-bit integers. This means no 64-bit integers and no unsigned integers. I was in the middle of implementing an <a href="http://www.isthe.c... | habedi/stack-exchange-dataset |
59,382 | Show that P is closed against the Kleene star | <p>I have that question that looks kinda easy at first but it is quite hard.</p>

<blockquote>
 <p>Let <span class="math-container">$L\in P$</span>. Prove that <span class="math-container">$L^*\in P$</span></p>
</blockquote>

<p><strong>my approach:</strong></p>

<p>I tried to generate ... | complexity theory closure properties polynomial time | 1 | Show that P is closed against the Kleene star -- (complexity theory closure properties polynomial time)
<p>I have that question that looks kinda easy at first but it is quite hard.</p>

<blockquote>
 <p>Let <span class="math-container">$L\in P$</span>. Prove that <span class="math-container">$L^*\in P$</sp... | habedi/stack-exchange-dataset |
59,386 | Sipser exercise : variant of CNF is NL-complete | <p>I'm stuck rather badly on a Sipser exercise, 8.21 in my edition:</p>

<blockquote>
 <p><strong>8.21</strong> Let $CNF_{H1}$ = {<$\phi$> | $\phi$ is a satisfiable cnf-formula where each clause contains any number of positive literals and at most one negated literal. Furthermore, each negated literal h... | complexity theory | 1 | Sipser exercise : variant of CNF is NL-complete -- (complexity theory)
<p>I'm stuck rather badly on a Sipser exercise, 8.21 in my edition:</p>

<blockquote>
 <p><strong>8.21</strong> Let $CNF_{H1}$ = {<$\phi$> | $\phi$ is a satisfiable cnf-formula where each clause contains any number of positive litera... | habedi/stack-exchange-dataset |
59,389 | Evaluation functions of Minimax algorithm | <p>Let's say we have the following relationship between $f_1$ and $f_2$:</p>

<p>$$f_2(s) = \sqrt{1 + f_1(s)}$$</p>

<p>And $f_1$ returns a positive value. Why is it that <a href="https://en.wikipedia.org/wiki/Minimax" rel="nofollow">minimax</a> search using $f_2$ is guaranteed to the same action as usi... | artificial intelligence game theory | 1 | Evaluation functions of Minimax algorithm -- (artificial intelligence game theory)
<p>Let's say we have the following relationship between $f_1$ and $f_2$:</p>

<p>$$f_2(s) = \sqrt{1 + f_1(s)}$$</p>

<p>And $f_1$ returns a positive value. Why is it that <a href="https://en.wikipedia.org/wiki/Minimax" re... | habedi/stack-exchange-dataset |
59,396 | Example Turing Machine for a time-constructible function | <p>I am currently reading <a href="http://theory.cs.princeton.edu/complexity/book.pdf" rel="nofollow">"Computation Complexity: A Modern Approach"</a> by Arora and Barak and have a question about time-constructible functions. In particular, I can't construct a turing machine for a simple function $f(n)=n$ using the defi... | complexity theory turing machines time complexity | 1 | Example Turing Machine for a time-constructible function -- (complexity theory turing machines time complexity)
<p>I am currently reading <a href="http://theory.cs.princeton.edu/complexity/book.pdf" rel="nofollow">"Computation Complexity: A Modern Approach"</a> by Arora and Barak and have a question about time-construc... | habedi/stack-exchange-dataset |
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