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 |
|---|---|---|---|---|---|---|
11,413 | What is the difference between the semantic and syntactic views of function types? | <p><strong>Edit:</strong> My original question referred to <em>nonconstructive</em> and <em>constructive</em> definitions of function types. I changed the terminology in the question and the title to <em>semantic</em> and <em>syntactic</em>, which the answer indicates is the correct terminology for this distinction.</... | terminology programming languages type theory | 1 | What is the difference between the semantic and syntactic views of function types? -- (terminology programming languages type theory)
<p><strong>Edit:</strong> My original question referred to <em>nonconstructive</em> and <em>constructive</em> definitions of function types. I changed the terminology in the question an... | habedi/stack-exchange-dataset |
11,418 | FFT-less $O(n\log n)$ algorithm for pairwise sums | <p>Suppose we are given $n$ distinct integers $a_1, a_2, \dots, a_n$, such that $0 \le a_i \le kn$ for some constant $k \gt 0$, and for all $i$.</p>

<p>We are interested in finding the counts of all the possible pairwise sums $S_{ij} = a_i + a_j$. ($i = j$ is allowed).</p>

<p>One algorithm is to const... | algorithms time complexity fourier transform | 1 | FFT-less $O(n\log n)$ algorithm for pairwise sums -- (algorithms time complexity fourier transform)
<p>Suppose we are given $n$ distinct integers $a_1, a_2, \dots, a_n$, such that $0 \le a_i \le kn$ for some constant $k \gt 0$, and for all $i$.</p>

<p>We are interested in finding the counts of all the possible... | habedi/stack-exchange-dataset |
11,424 | Time Complexity of a selection problem | <p>I wonder what's the time complexity of the following selection problem I found while thinking of a string-matching problem.</p>

<p>[Assuming operations on integers take $O(1)$ time]</p>

<p>We are Given $m$ sets, with $n$ integer numbers each. We want to select exactly one integer from each set, to ... | complexity theory time complexity set cover | 1 | Time Complexity of a selection problem -- (complexity theory time complexity set cover)
<p>I wonder what's the time complexity of the following selection problem I found while thinking of a string-matching problem.</p>

<p>[Assuming operations on integers take $O(1)$ time]</p>

<p>We are Given $m$ sets,... | habedi/stack-exchange-dataset |
11,427 | Route on a square grid with only (x,y) → (x,x+y) and (x,y) → (x+y,y) moves | <p>This problem is about finding a route on a square grid.
The starting point is $(1,1)$ and the target point $(n,m)$.
I can move each step from my current point $(x,y)$ either to $(x+y,y)$ or $(x,y+x)$.
Now I need to determine if there is a path from $(1,1)$ to $(n,m)$, and if so to return the shortest one... | algorithms graphs shortest path square grid | 1 | Route on a square grid with only (x,y) → (x,x+y) and (x,y) → (x+y,y) moves -- (algorithms graphs shortest path square grid)
<p>This problem is about finding a route on a square grid.
The starting point is $(1,1)$ and the target point $(n,m)$.
I can move each step from my current point $(x,y)$ either to $(x+y,y)... | habedi/stack-exchange-dataset |
11,428 | Bellman-Ford parent pointer (?) negative cycle | <p>First of all, let me preface by saying that this question is not completly new but the original question hasn't been answered. More important, this is only basic question on understanding the proof itself.</p>

<p>So after some search in the site I found the following question : <a href="https://cs.stackexch... | algorithms graphs shortest path | 1 | Bellman-Ford parent pointer (?) negative cycle -- (algorithms graphs shortest path)
<p>First of all, let me preface by saying that this question is not completly new but the original question hasn't been answered. More important, this is only basic question on understanding the proof itself.</p>

<p>So after so... | habedi/stack-exchange-dataset |
11,441 | Converting CFG to PDA | <p>I have the following CFG,</p>

<p>$S \rightarrow CB$<br>
$C \rightarrow aCa \text{ }|\text{ } bCb \text{ }|\text{ } \text{#}B$<br>
$B \rightarrow AB \text{ }|\text{ } \varepsilon$<br>
$A \rightarrow a\text{ }|\text{ }b$</p>

<p>This is the CFG for the following language:</p>

<p>$... | context free formal grammars pushdown automata | 1 | Converting CFG to PDA -- (context free formal grammars pushdown automata)
<p>I have the following CFG,</p>

<p>$S \rightarrow CB$<br>
$C \rightarrow aCa \text{ }|\text{ } bCb \text{ }|\text{ } \text{#}B$<br>
$B \rightarrow AB \text{ }|\text{ } \varepsilon$<br>
$A \rightarrow a\text{ }|\text{ }b$</p>... | habedi/stack-exchange-dataset |
11,448 | What makes lambda calculus relevant to study? | <p>I'm starting an undergraduate computer science course next fall, but I can't really understand λ-calculus in the context of functional programming. I may be misinterpreting this completely, but based on this <a href="http://plato.stanford.edu/entries/lambda-calculus/" rel="noreferrer">definition</a> from the Stanfor... | programming languages lambda calculus | 1 | What makes lambda calculus relevant to study? -- (programming languages lambda calculus)
<p>I'm starting an undergraduate computer science course next fall, but I can't really understand λ-calculus in the context of functional programming. I may be misinterpreting this completely, but based on this <a href="http://plat... | habedi/stack-exchange-dataset |
11,453 | NP hardness through Restriction | <p>Let's say I have a decision problem $P$ on graphs for which I know that it is NP-hard on graphs with maximum degree $d$. Does this then imply that it is NP-hard on $d$-regular graphs? Although it might seem obviously true, maybe it is inherent in the reduction to show that $P$ is hard, that some vertices have degre... | complexity theory reductions np hard | 1 | NP hardness through Restriction -- (complexity theory reductions np hard)
<p>Let's say I have a decision problem $P$ on graphs for which I know that it is NP-hard on graphs with maximum degree $d$. Does this then imply that it is NP-hard on $d$-regular graphs? Although it might seem obviously true, maybe it is inheren... | habedi/stack-exchange-dataset |
11,458 | Quicksort Partitioning: Hoare vs. Lomuto | <p>There are two quicksort partition methods mentioned in Cormen:</p>

<p>(the argument <code>A</code> is the array, and <code>[p, r]</code> is the range, inclusive, to perform the partition on. The returned value is the index to the pivot after the partition.)</p>

<pre><code>Hoare-Partition(A, p, r)&#... | algorithms sorting quicksort | 1 | Quicksort Partitioning: Hoare vs. Lomuto -- (algorithms sorting quicksort)
<p>There are two quicksort partition methods mentioned in Cormen:</p>

<p>(the argument <code>A</code> is the array, and <code>[p, r]</code> is the range, inclusive, to perform the partition on. The returned value is the index to the piv... | habedi/stack-exchange-dataset |
11,462 | Is there a difference between pure binary and binary? | <p>In some books and on the internet I occasionally find "pure binary" and "binary" on its own, is there a difference between these two terms? If so, can someone describe briefly what they are?</p>
 | terminology encoding scheme | 1 | Is there a difference between pure binary and binary? -- (terminology encoding scheme)
<p>In some books and on the internet I occasionally find "pure binary" and "binary" on its own, is there a difference between these two terms? If so, can someone describe briefly what they are?</p>
 | habedi/stack-exchange-dataset |
11,463 | Prove NP-completeness of deciding whether there is an edge-tour of at most a given length | <p>We are given a graph G, integer b < |E|, and subset F in E. The problem is to detect whether there is a cycle in the graph with length at most b and includes each edge in F. Prove that this is NP Complete. </p>

<p>I'm thinking of reducing from Hamiltonian Path, but still can't think of the appropriate tr... | complexity theory np complete reductions | 1 | Prove NP-completeness of deciding whether there is an edge-tour of at most a given length -- (complexity theory np complete reductions)
<p>We are given a graph G, integer b < |E|, and subset F in E. The problem is to detect whether there is a cycle in the graph with length at most b and includes each edge in F. Prov... | habedi/stack-exchange-dataset |
11,471 | The difference between a bit and a Qubit | <p>Ok, I have done a lot of research on Quantum computers. I understand that they are possibly the future of computers and may be commonplace in approximately 30-50 years time.</p>

<p>I know that a Binary is either 0 or 1, but a Qubit can be 0 or 1. But what I don't understand is how it can be anything other t... | terminology quantum computing | 1 | The difference between a bit and a Qubit -- (terminology quantum computing)
<p>Ok, I have done a lot of research on Quantum computers. I understand that they are possibly the future of computers and may be commonplace in approximately 30-50 years time.</p>

<p>I know that a Binary is either 0 or 1, but a Qubit ... | habedi/stack-exchange-dataset |
11,475 | Are all Integer Linear Programming problems NP-Hard? | <p>As I understand, the <a href="http://en.wikipedia.org/wiki/Assignment_problem" rel="noreferrer">assignment problem</a> is in P as the Hungarian algorithm can solve it in polynomial time - O(n<sup>3</sup>). I also understand that the assignment problem is an <a href="http://en.wikipedia.org/wiki/Integer_programming" ... | complexity theory complexity classes linear programming integer programming | 1 | Are all Integer Linear Programming problems NP-Hard? -- (complexity theory complexity classes linear programming integer programming)
<p>As I understand, the <a href="http://en.wikipedia.org/wiki/Assignment_problem" rel="noreferrer">assignment problem</a> is in P as the Hungarian algorithm can solve it in polynomial ti... | habedi/stack-exchange-dataset |
11,489 | Identifying an object in an image based on color (AI ?) | <p><em>First off, I am not sure if this is the correct stackexchange site to ask this question on, so moderators can feel free to move it.</em></p>

<p>I am working on an application that identifies an object in an image. For example, let's say that the object is an apple, and the apple can be green, red, or b... | algorithms artificial intelligence image processing | 1 | Identifying an object in an image based on color (AI ?) -- (algorithms artificial intelligence image processing)
<p><em>First off, I am not sure if this is the correct stackexchange site to ask this question on, so moderators can feel free to move it.</em></p>

<p>I am working on an application that identifies ... | habedi/stack-exchange-dataset |
11,492 | Computing number of block reads given relational algebra statement | <p>So I'm just starting to learn about query processing and such in databases and I'm having some trouble. I don't really understand how to compute the minimum number of block reads given a relation and a query I guess you could say. If anyone could help me out, it'd be much appreciated. Here is an example that I'm ... | database theory databases relational algebra | 1 | Computing number of block reads given relational algebra statement -- (database theory databases relational algebra)
<p>So I'm just starting to learn about query processing and such in databases and I'm having some trouble. I don't really understand how to compute the minimum number of block reads given a relation and... | habedi/stack-exchange-dataset |
11,498 | How to distinguish empty cells from cells outside of the input cells? | <p><strong>Setup</strong></p>

<p>I need to develop a Turing Machine that accepts a string m that has the same number of a's and b's.
My alphabet is {a,b}, and we use a diamond in class to represent an empty space.</p>

<p><strong>Problem</strong></p>

<p>The part I'm having trouble with is ... | turing machines discrete mathematics | 1 | How to distinguish empty cells from cells outside of the input cells? -- (turing machines discrete mathematics)
<p><strong>Setup</strong></p>

<p>I need to develop a Turing Machine that accepts a string m that has the same number of a's and b's.
My alphabet is {a,b}, and we use a diamond in class to represe... | habedi/stack-exchange-dataset |
11,505 | Proving that finding wheel subgraphs is NP-complete | <p>Can you help me with this problem ?</p>

<blockquote>
 <p>Given an undirected graph $G$ and an integer $n$, prove that determining whether the graph has wheel on $n$ vertices $W_{n}$ (a wheel $W_{i}$ is such that $i$ nodes form a cycle and a $i+1$st node is connected to all other nodes, resulting in $2i... | complexity theory graphs np complete | 1 | Proving that finding wheel subgraphs is NP-complete -- (complexity theory graphs np complete)
<p>Can you help me with this problem ?</p>

<blockquote>
 <p>Given an undirected graph $G$ and an integer $n$, prove that determining whether the graph has wheel on $n$ vertices $W_{n}$ (a wheel $W_{i}$ is such th... | habedi/stack-exchange-dataset |
11,514 | Does our PC work as Turing Machine? | <p>Does our PC work as Turing Machine? The model of a Turing Machine consists of infinite memory tape, which means infinite states. But suppose if our PC has 128 MB memory and 30GB disk it would have 256^30128000000 states and thus, it has finite states.</p>

<p>I know that we can write a type of program that,... | complexity theory computability turing machines automata | 1 | Does our PC work as Turing Machine? -- (complexity theory computability turing machines automata)
<p>Does our PC work as Turing Machine? The model of a Turing Machine consists of infinite memory tape, which means infinite states. But suppose if our PC has 128 MB memory and 30GB disk it would have 256^30128000000 state... | habedi/stack-exchange-dataset |
11,518 | Finding the largest 3-clique-free induced subgraph | <p>Consider this problem:</p>
<blockquote>
<p>Given an undirected graph <span class="math-container">$G = (V, E)$</span>, find <span class="math-container">$G' = (V', E')$</span> such that:</p>
<ol>
<li><span class="math-container">$G'$</span> is an induced subgraph of <span class="math-container">$G$</... | algorithms graphs optimization | 1 | Finding the largest 3-clique-free induced subgraph -- (algorithms graphs optimization)
<p>Consider this problem:</p>
<blockquote>
<p>Given an undirected graph <span class="math-container">$G = (V, E)$</span>, find <span class="math-container">$G' = (V', E')$</span> such that:</p>
<ol>
<li><span class="m... | habedi/stack-exchange-dataset |
11,519 | Null Hypothesis in Analysis and Testing | <p>I have my end of year exams next Thursday. I'm generally doing fine but I am having some major issues with this strand of my course, this has to be the biggest issue I have. So, here is the question in the past paper:</p>

<blockquote>
 <p>You have been tasked with determining the validity of a 
 ... | probability theory statistics reliability | 1 | Null Hypothesis in Analysis and Testing -- (probability theory statistics reliability)
<p>I have my end of year exams next Thursday. I'm generally doing fine but I am having some major issues with this strand of my course, this has to be the biggest issue I have. So, here is the question in the past paper:</p>

... | habedi/stack-exchange-dataset |
11,525 | Prove that context free languages are not closed under swapping prefixes and suffixes | <p>Prove that context free languages aren't closed under this operation: $ A(L) = \{ zyx \mid x,y,z \in \{0,1 \}^*, xyz \in L \} $</p>

<p>Obviously, we need to find a context free language $L$ such that $A(L)$ isn't context free. Here are some of my failed attempts:</p>

<p>Take the language $ L = \{\ ... | formal languages context free closure properties pumping lemma | 1 | Prove that context free languages are not closed under swapping prefixes and suffixes -- (formal languages context free closure properties pumping lemma)
<p>Prove that context free languages aren't closed under this operation: $ A(L) = \{ zyx \mid x,y,z \in \{0,1 \}^*, xyz \in L \} $</p>

<p>Obviously, we need ... | habedi/stack-exchange-dataset |
11,536 | How to prove Transitive property of Reducibility with a TM? | <p>How can we prove that $h(x) = g(f(x))$ is a reduction function for $A \leq_m C$,</p>

<p>if $f$ is the reduction function of $A \leq_m B$ and $g$ is the reduction function for $B \leq_m C$</p>

<p>The given Proposition is: $A \leq_m B, B \leq_m C \Rightarrow A \leq_m C$</p>

<p>I was thinki... | computability turing machines reductions | 1 | How to prove Transitive property of Reducibility with a TM? -- (computability turing machines reductions)
<p>How can we prove that $h(x) = g(f(x))$ is a reduction function for $A \leq_m C$,</p>

<p>if $f$ is the reduction function of $A \leq_m B$ and $g$ is the reduction function for $B \leq_m C$</p>

... | habedi/stack-exchange-dataset |
11,541 | Reduction from 3-SAT to a graph problem | <p>I have a question, i was trying to reduce 3-SAT to a particular graph problem and i'm not quite sure about a thing i used in the reduction.
In fact the reduction build a bipartite graph, the edge $(x_1,c_1)$ exist if the variable $x_1$ is in the clause number 1, the costs on that edge are dependent on the truthf... | complexity theory graphs np complete reductions 3 sat | 1 | Reduction from 3-SAT to a graph problem -- (complexity theory graphs np complete reductions 3 sat)
<p>I have a question, i was trying to reduce 3-SAT to a particular graph problem and i'm not quite sure about a thing i used in the reduction.
In fact the reduction build a bipartite graph, the edge $(x_1,c_1)$ exist ... | habedi/stack-exchange-dataset |
11,542 | How to construct and write down a Turing machine for a given language? | <p>In my class we just started learning about Turing machines. I think I understand the concept but am unsure how to syntactically solve any problem related to one. I am presented with the problem:</p>

<blockquote>
 <p>Build a Turing machine accepting $(b + c)^+$$\#a^+$ (Please comment your
 code.... | turing machines | 1 | How to construct and write down a Turing machine for a given language? -- (turing machines)
<p>In my class we just started learning about Turing machines. I think I understand the concept but am unsure how to syntactically solve any problem related to one. I am presented with the problem:</p>

<blockquote>&#x... | habedi/stack-exchange-dataset |
11,545 | Find maximum element in sorted arrays in logarithmic time | <p>Been stuck on this for a while, would really appreciate some help:</p>

<blockquote>
 <p>Suppose you are given an array A[1...n] of sorted integers that has been circularly shifted k positions to the right. For example, [35,42,5,15,27,29] is a sorted array that has been circularly shifted k = 2 position... | algorithms search algorithms arrays | 1 | Find maximum element in sorted arrays in logarithmic time -- (algorithms search algorithms arrays)
<p>Been stuck on this for a while, would really appreciate some help:</p>

<blockquote>
 <p>Suppose you are given an array A[1...n] of sorted integers that has been circularly shifted k positions to the right... | habedi/stack-exchange-dataset |
11,558 | Prove NP-completeness of deciding satisfiability of monotone boolean formula | <p>I am trying to solve this problem and I am really struggling.</p>

<p>A <em>monotone boolean formula</em> is a formula in propositional logic where all the literals are positive. For example, </p>

<p>$\qquad (x_1 \lor x_2) \land (x_1 \lor x_3) \land (x_3 \lor x_4 \lor x_5)$ </p>

<p>is a mon... | complexity theory np complete satisfiability | 1 | Prove NP-completeness of deciding satisfiability of monotone boolean formula -- (complexity theory np complete satisfiability)
<p>I am trying to solve this problem and I am really struggling.</p>

<p>A <em>monotone boolean formula</em> is a formula in propositional logic where all the literals are positive. For... | habedi/stack-exchange-dataset |
11,561 | Proving that Turing Machine M runs in time $O(2^{dn})$ | <p>I'm trying to solve this question in order to review for my exam, and this one has got me a bit stumped. From the looks of it, it seems like a fairly straight-forward question, but I can't figure out what steps to begin with.</p>
<blockquote>
<p>Let <span class="math-container">$M$</span> be a linear-space T... | turing machines space complexity | 1 | Proving that Turing Machine M runs in time $O(2^{dn})$ -- (turing machines space complexity)
<p>I'm trying to solve this question in order to review for my exam, and this one has got me a bit stumped. From the looks of it, it seems like a fairly straight-forward question, but I can't figure out what steps to begin with... | habedi/stack-exchange-dataset |
11,564 | Is there a name for complement of recursively enumerable set? | <p>If there is a recursive function
$$
f(x) = 
\begin{cases}
1 & \text{if $x \notin A$}\\
\text{undefined} & \text{if $x \in A$}\\
\end{cases}
$$</p>

<p>Is there a special name for the class of sets like $A$?</p>
 | terminology computability undecidability | 1 | Is there a name for complement of recursively enumerable set? -- (terminology computability undecidability)
<p>If there is a recursive function
$$
f(x) = 
\begin{cases}
1 & \text{if $x \notin A$}\\
\text{undefined} & \text{if $x \in A$}\\
\end{cases}
$$</p>

<p>Is there a spe... | habedi/stack-exchange-dataset |
11,565 | Best problems that are prone to parallelization? | <p>What are some problems that are prone to parallelization? When I think about this, the first thing that comes to my mind is matrix multiplication, which yields to faster calculations, meaning you can get speed ups easily. Any other examples like this?</p>
 | parallel computing | 1 | Best problems that are prone to parallelization? -- (parallel computing)
<p>What are some problems that are prone to parallelization? When I think about this, the first thing that comes to my mind is matrix multiplication, which yields to faster calculations, meaning you can get speed ups easily. Any other examples lik... | habedi/stack-exchange-dataset |
11,579 | Determining if a TM decidable or not, with limited information | <p>Were being asked to determine the whether this Turing Machine is decidable or not</p>

<p>"Given a two way, one-tape DTM $M$ whose tape set is $\Gamma=${$a,b,B$} and a string $x\in${$a,b$}*, determine whether $M$ will ever overwrite a symbol $a$ by a symbol $b$ in its computation on <em>input</em> $x$"</p>&#... | turing machines undecidability | 1 | Determining if a TM decidable or not, with limited information -- (turing machines undecidability)
<p>Were being asked to determine the whether this Turing Machine is decidable or not</p>

<p>"Given a two way, one-tape DTM $M$ whose tape set is $\Gamma=${$a,b,B$} and a string $x\in${$a,b$}*, determine whether $... | habedi/stack-exchange-dataset |
11,586 | How are two layer feed-forward neural networks universal? | <p>Across my studies I have noticed the following statement in my Subject Guide; namely, that two-layer feed-forward neural networks using the sigmoidal activation function are universal. My question is how are the networks 'universal' and what does 'universal' actually mean in this instance?</p>

<p>Thanks in ... | neural networks | 1 | How are two layer feed-forward neural networks universal? -- (neural networks)
<p>Across my studies I have noticed the following statement in my Subject Guide; namely, that two-layer feed-forward neural networks using the sigmoidal activation function are universal. My question is how are the networks 'universal' and w... | habedi/stack-exchange-dataset |
11,588 | Proving language in Space Complexity | <p>I'd like to know if I have the right intuition and my answer is headed the correct way.</p>

<p>I am given a function
$ f = \{0, 1\}^* \rightarrow \{0, 1\}^* $ that is computable in space $O(\log n)$ assume that for every $x \in \{0, 1\}^*$, $f$ is length preserving, $|f(x)| = |x|$.</p>

<p>Defi... | space complexity | 1 | Proving language in Space Complexity -- (space complexity)
<p>I'd like to know if I have the right intuition and my answer is headed the correct way.</p>

<p>I am given a function
$ f = \{0, 1\}^* \rightarrow \{0, 1\}^* $ that is computable in space $O(\log n)$ assume that for every $x \in \{0, 1\}^*$, $f$... | habedi/stack-exchange-dataset |
11,590 | Algorithm of Communication with Failures | <p>I am interested in Distributed Algorithms especially in communication in network with failures.</p>

<p>I look for the proof of the following randomized algorithm of communication in network with failures. For me it seems like very general result in the communication, nevertheless I haven’t found the proof y... | algorithms distributed systems | 1 | Algorithm of Communication with Failures -- (algorithms distributed systems)
<p>I am interested in Distributed Algorithms especially in communication in network with failures.</p>

<p>I look for the proof of the following randomized algorithm of communication in network with failures. For me it seems like very ... | habedi/stack-exchange-dataset |
11,592 | Prove that $L_1$ is regular if $L_2$, $L_1L_2$, $L_2L_1$ are regular | <p>Prove that $L_1$ is regular if $L_2$, $L_1L_2$, $L_2L_1$ are regular.</p>

<p>These are the things that I would use to start.</p>

<ul>
<li>As $L_1L_2$ is regular, then the homomorphism $h(L_1L_2)$ is regular.</li>
<li>Let $h(L_1) = L_2$ and $h(L_2) = L_1$, then $h(L_1L_2) = L_2L_1$ is regula... | regular languages finite automata proof techniques closure properties | 1 | Prove that $L_1$ is regular if $L_2$, $L_1L_2$, $L_2L_1$ are regular -- (regular languages finite automata proof techniques closure properties)
<p>Prove that $L_1$ is regular if $L_2$, $L_1L_2$, $L_2L_1$ are regular.</p>

<p>These are the things that I would use to start.</p>

<ul>
<li>As $L_1L_2$ i... | habedi/stack-exchange-dataset |
11,598 | prove no DPDA accepts language of even-lengthed palindromes | <p>How do you prove that the language of even-lengthed palindromes, i.e.,
$L=\left\{ ww^R \mid w\in \left\lbrace 0,1 \right\}^* \right\}$, can not be accepted by a determinsitc Push-Down-Automaton?</p>

<p>Is there any general way to prove that a context-free language can not be accepted by a deterministic ... | context free pushdown automata | 1 | prove no DPDA accepts language of even-lengthed palindromes -- (context free pushdown automata)
<p>How do you prove that the language of even-lengthed palindromes, i.e.,
$L=\left\{ ww^R \mid w\in \left\lbrace 0,1 \right\}^* \right\}$, can not be accepted by a determinsitc Push-Down-Automaton?</p>

<p>Is the... | habedi/stack-exchange-dataset |
11,607 | Finding a tree that approximates the distances and total weights | <p>Given an undirected graph $G=(V,E)$ could we build a tree $T$ that approximates the distances from given vertex $r$ and the total weight, i.e. $\forall x \in V, d_G(r,x) \le d_T(r,x) \le 3 \cdot d_G(r,x)$ and $w(T) \le 3\cdot w(\text{MST}(G))$, where $\text{MST}$ is the minimum spanning tree and $w(\cdot)$ is the we... | algorithms approximation | 1 | Finding a tree that approximates the distances and total weights -- (algorithms approximation)
<p>Given an undirected graph $G=(V,E)$ could we build a tree $T$ that approximates the distances from given vertex $r$ and the total weight, i.e. $\forall x \in V, d_G(r,x) \le d_T(r,x) \le 3 \cdot d_G(r,x)$ and $w(T) \le 3\c... | habedi/stack-exchange-dataset |
11,611 | Can all permutations of a set or string be generated in O(n log n) time? | <p>I was looking over <a href="https://stackoverflow.com/q/352203/2327689">this question</a> requesting an algorithm to generate all permutations of a given string. A comment in the answer caught my eye:</p>

<p><em>It might seem that it can take O(n) time per permutation, but if you think about it more careful... | algorithms complexity theory time complexity | 1 | Can all permutations of a set or string be generated in O(n log n) time? -- (algorithms complexity theory time complexity)
<p>I was looking over <a href="https://stackoverflow.com/q/352203/2327689">this question</a> requesting an algorithm to generate all permutations of a given string. A comment in the answer caught m... | habedi/stack-exchange-dataset |
11,619 | Is the language $a^{3}b^{+}$ the same as $\{a^{3}b^{n}, n \geq 1\}$ ? and what is the result of pumping this? | <p>The regular expression $a^{3}b^{+}$ is indeed regular because we can define an automata $M$. But I see that $\mathcal{L} = \{a^{3}b^{n}, n \geq 1\}$ may generate the same strings, but using the pumping lemma with constant $N$ for a substring $\alpha\beta = a^{3}b^{t},|\alpha\beta| \leq N$, let $\alpha = a$ and $\bet... | regular languages finite automata regular expressions pumping lemma | 1 | Is the language $a^{3}b^{+}$ the same as $\{a^{3}b^{n}, n \geq 1\}$ ? and what is the result of pumping this? -- (regular languages finite automata regular expressions pumping lemma)
<p>The regular expression $a^{3}b^{+}$ is indeed regular because we can define an automata $M$. But I see that $\mathcal{L} = \{a^{3}b^{n... | habedi/stack-exchange-dataset |
11,630 | What does the posterior probability of a variable mean in the Bayes' rule? | <p>I have been studying Artificial Intelligence and I have noticed that the Bayes' rule allows us to infer the posterior probability if a variable. But, my question is, what does the word, or phrase, 'posterior' mean in this context with regard to the Bayes' rule?</p>
 | artificial intelligence probability theory | 1 | What does the posterior probability of a variable mean in the Bayes' rule? -- (artificial intelligence probability theory)
<p>I have been studying Artificial Intelligence and I have noticed that the Bayes' rule allows us to infer the posterior probability if a variable. But, my question is, what does the word, or phras... | habedi/stack-exchange-dataset |
11,635 | Particularly Tricky Recurrence Relation (Master's Theorem) | <p>Master's theorem is shown below,</p>

<p><img src="https://i.stack.imgur.com/OtLdE.png" alt="enter image description here"></p>

<p>The recursive function to be solved is shown below,</p>

<p><img src="https://i.stack.imgur.com/qu9VR.png" alt="enter image description here"></p>

<p>I ... | recursion | 1 | Particularly Tricky Recurrence Relation (Master's Theorem) -- (recursion)
<p>Master's theorem is shown below,</p>

<p><img src="https://i.stack.imgur.com/OtLdE.png" alt="enter image description here"></p>

<p>The recursive function to be solved is shown below,</p>

<p><img src="https://i.stack.i... | habedi/stack-exchange-dataset |
11,643 | If $L = L(M)$ then $L$ is a subset of $L(M)$ and $L(M)$ is a subset of $L$ | <p>If $L = L(M)$ then $L$ is a subset of $L(M)$ and $L(M)$ is a subset of $L$.</p>

<p>Can anyone clarify what does this mean?</p>
 | terminology sets | 1 | If $L = L(M)$ then $L$ is a subset of $L(M)$ and $L(M)$ is a subset of $L$ -- (terminology sets)
<p>If $L = L(M)$ then $L$ is a subset of $L(M)$ and $L(M)$ is a subset of $L$.</p>

<p>Can anyone clarify what does this mean?</p>
 | habedi/stack-exchange-dataset |
11,645 | Can a runtime environment detect an infinite loop? | <p>Would it be possible for a runtime environment to detect infinite loops and subsequently stop the associated process, or would implementing such logic be equivalent to solving the halting problem?</p>

<p>For the purpose of this question, I define an "infinite loop" to mean a series of instructions and assoc... | halting problem | 1 | Can a runtime environment detect an infinite loop? -- (halting problem)
<p>Would it be possible for a runtime environment to detect infinite loops and subsequently stop the associated process, or would implementing such logic be equivalent to solving the halting problem?</p>

<p>For the purpose of this question... | habedi/stack-exchange-dataset |
11,654 | Cost at Each Level of a Recursion Tree | <p>Given a recursive function $T(n)=T(a_1\cdot n)+\dots +T(a_k\cdot n)+\Theta(n)$ such that $\forall a_i: 0<a_i<1$, what is the most general thing I can say about the sum of the cost of the nodes at each level of the recursion tree? I've looked at a few, and for the ones I've looked at it's always come out to $(... | recurrence relation | 1 | Cost at Each Level of a Recursion Tree -- (recurrence relation)
<p>Given a recursive function $T(n)=T(a_1\cdot n)+\dots +T(a_k\cdot n)+\Theta(n)$ such that $\forall a_i: 0<a_i<1$, what is the most general thing I can say about the sum of the cost of the nodes at each level of the recursion tree? I've looked at a... | habedi/stack-exchange-dataset |
11,656 | Resolving this recurrence equation | <p>I have this recurrence equation:</p>

<p>$T(n) = T(n/4) + T(3n/4) + \mathcal{O}(n)$</p>

<p>$T(1) = 1$</p>

<p>I know that the result is $\mathcal{O}(n \log n)$ but i don't know how to proceed.</p>
 | asymptotics runtime analysis recurrence relation recursion | 1 | Resolving this recurrence equation -- (asymptotics runtime analysis recurrence relation recursion)
<p>I have this recurrence equation:</p>

<p>$T(n) = T(n/4) + T(3n/4) + \mathcal{O}(n)$</p>

<p>$T(1) = 1$</p>

<p>I know that the result is $\mathcal{O}(n \log n)$ but i don't know how to proceed.<... | habedi/stack-exchange-dataset |
11,666 | Formalisms in concurrent and/or distributed programming? | <p>My background came from imperative languages, primarily C, C++, and Python. I picked up Scala, Erlang, and a bit of Haskell a few years later and have since become very interested in functional programming and the formalisms behind it.</p>

<p>I am also interested in concurrent and distributed programming an... | distributed systems concurrency | 1 | Formalisms in concurrent and/or distributed programming? -- (distributed systems concurrency)
<p>My background came from imperative languages, primarily C, C++, and Python. I picked up Scala, Erlang, and a bit of Haskell a few years later and have since become very interested in functional programming and the formalism... | habedi/stack-exchange-dataset |
11,667 | What is the difference between a 'page' of memory and a 'frame' of memory? | <p><a href="http://en.wikipedia.org/wiki/Page_frame" rel="noreferrer">WP</a> has an adequate discussion of <em>paging</em>, which I think I understand.. However I am confused by the articles repeated use of the term <em>Page Frame</em>.</p>

<p>I thought frames and pages were different things. Could someone pl... | memory management | 1 | What is the difference between a 'page' of memory and a 'frame' of memory? -- (memory management)
<p><a href="http://en.wikipedia.org/wiki/Page_frame" rel="noreferrer">WP</a> has an adequate discussion of <em>paging</em>, which I think I understand.. However I am confused by the articles repeated use of the term <em>Pa... | habedi/stack-exchange-dataset |
11,678 | Upper bound on register machine contents | <p>I am doing some work on register machine theory which revolves around a 2-register register machine and attempting to show that it is not possible to compute an upper-bound on the final contents of its two registers on the basis of its program code and initial input, in halting configurations only. I believe this ca... | computability turing machines church turing thesis | 1 | Upper bound on register machine contents -- (computability turing machines church turing thesis)
<p>I am doing some work on register machine theory which revolves around a 2-register register machine and attempting to show that it is not possible to compute an upper-bound on the final contents of its two registers on t... | habedi/stack-exchange-dataset |
11,683 | proving $P \subseteq PCP(0,O(log(n))$ | <p>I was working on proving this one and I've solve one direction as follows :<br>
to prove that $P \subseteq PCP(0,logn)$ I said :<br>
let $M$ be deterministic polynomial TM that accepts $L \in P$ ,we want to show that we can there exists a proof system which consists of prover and deterministic polynomial ver... | complexity theory approximation | 1 | proving $P \subseteq PCP(0,O(log(n))$ -- (complexity theory approximation)
<p>I was working on proving this one and I've solve one direction as follows :<br>
to prove that $P \subseteq PCP(0,logn)$ I said :<br>
let $M$ be deterministic polynomial TM that accepts $L \in P$ ,we want to show that we can there exis... | habedi/stack-exchange-dataset |
11,687 | Is linear-time reduction symmetric? | <p>By reduction I mean the following:</p>

<blockquote>
 <p>Problem X linear reduces to problem Y if X can be solved with:<br>
 a) Linear number of standard computational steps.<br>
 b) Constant calls to subroutine for Y. </p>
</blockquote>

<p>If a problem X reduces to a problem Y, ... | complexity theory reductions | 1 | Is linear-time reduction symmetric? -- (complexity theory reductions)
<p>By reduction I mean the following:</p>

<blockquote>
 <p>Problem X linear reduces to problem Y if X can be solved with:<br>
 a) Linear number of standard computational steps.<br>
 b) Constant calls to subroutine for Y. </p>... | habedi/stack-exchange-dataset |
11,696 | Show that this language is in NP $\cap$ coNP | <p>Say $\ell: \{0,1\}^\ast \to \{0,1\}^\ast$ is a one-to-one polynomial-time computable function that preserves length. Consider the language $$L = \Bigl\{v \;\Big|\; \exists u: \bigl(u_1 = 1 ~~\text{and}~~ \ell(u) = v\bigr) \Bigr\}.$$ How do I prove that $L$ is in $\mathsf{NP} \cap \mathsf{coNP}$? Basically, what woul... | np hard np | 1 | Show that this language is in NP $\cap$ coNP -- (np hard np)
<p>Say $\ell: \{0,1\}^\ast \to \{0,1\}^\ast$ is a one-to-one polynomial-time computable function that preserves length. Consider the language $$L = \Bigl\{v \;\Big|\; \exists u: \bigl(u_1 = 1 ~~\text{and}~~ \ell(u) = v\bigr) \Bigr\}.$$ How do I prove that $L$... | habedi/stack-exchange-dataset |
11,697 | Is the problem of evaluating a boolean formula on a given assignment P-complete? | <p>I know that the CIRCUIT VALUE problem is P-complete.
In the CIRCUIT VALUE problem the input is a Boolean circuit together with an input to this circuit, and the answer is the evaluation of the given circuit on the given input.</p>

<p>I wish to know if the problem of evaluating a Boolean formula on a giv... | complexity theory time complexity complexity classes | 1 | Is the problem of evaluating a boolean formula on a given assignment P-complete? -- (complexity theory time complexity complexity classes)
<p>I know that the CIRCUIT VALUE problem is P-complete.
In the CIRCUIT VALUE problem the input is a Boolean circuit together with an input to this circuit, and the answer is the... | habedi/stack-exchange-dataset |
11,707 | What type of formal notation is being used here to represent functional algorithms? | <p>Interested in learning more about algorithm design in functional programming, I picked up Andrew Bird's <a href="http://rads.stackoverflow.com/amzn/click/0521513383" rel="nofollow noreferrer">Pearls of Functional Algorithm Design</a>. I have experience with a number of programming languages, but my only experience ... | algorithms formal languages functional programming notation | 1 | What type of formal notation is being used here to represent functional algorithms? -- (algorithms formal languages functional programming notation)
<p>Interested in learning more about algorithm design in functional programming, I picked up Andrew Bird's <a href="http://rads.stackoverflow.com/amzn/click/0521513383" re... | habedi/stack-exchange-dataset |
11,712 | Simulation BPP by Pseudorandom Generator | <p>I use the following scribe to study <a href="http://people.seas.harvard.edu/~salil/pseudorandomness/prgs.pdf" rel="nofollow">Pseudorandom Generators</a>.</p>

<p>The most intriguing question for me is how exactly PRG can be used in order to simulate BPP.</p>

<p>Let $A(x,r) \in BPP$, where $x$ is pr... | complexity theory | 1 | Simulation BPP by Pseudorandom Generator -- (complexity theory)
<p>I use the following scribe to study <a href="http://people.seas.harvard.edu/~salil/pseudorandomness/prgs.pdf" rel="nofollow">Pseudorandom Generators</a>.</p>

<p>The most intriguing question for me is how exactly PRG can be used in order to sim... | habedi/stack-exchange-dataset |
11,715 | Performance differences between Go-Back-N and Selective Repeat ARQ protocols? | <p>This is what I know:</p>

<ul>
<li>GBN weakness is the fact that when the window size is too large, the number of packets in the pipeline grows and one packet error causes the retransmition of many packets unnecessarily. </li>
<li>Selective Repeat solves this by acknowleding just the suspicious packe... | computer networks communication protocols | 1 | Performance differences between Go-Back-N and Selective Repeat ARQ protocols? -- (computer networks communication protocols)
<p>This is what I know:</p>

<ul>
<li>GBN weakness is the fact that when the window size is too large, the number of packets in the pipeline grows and one packet error causes the retr... | habedi/stack-exchange-dataset |
11,718 | Generating 3SAT circuit for Integer factorization example | <p>I read somewhere that 3SAT can be used to solve Integer Factorization.</p>

<p>If that is true, could someone teach me a simple example of generating the 3SAT by using a small number? Let's say you are given the number 6, then the factors are 2 and 3.</p>
 | np hard factoring 3 sat | 1 | Generating 3SAT circuit for Integer factorization example -- (np hard factoring 3 sat)
<p>I read somewhere that 3SAT can be used to solve Integer Factorization.</p>

<p>If that is true, could someone teach me a simple example of generating the 3SAT by using a small number? Let's say you are given the number 6, ... | habedi/stack-exchange-dataset |
11,719 | Given the logical address, how to extract the page number? | <p>I am studying Computer Systems. I have th following question and its answer:</p>

<blockquote>
 <p>Given the logical address 0xAEF9 (in hexadecimal) with a page size of
 256 bytes, what is the page number?</p>
 
 <p>Answer: <strong>0xAE</strong> (I found this answer in the web, but I want... | operating systems memory management paging virtual memory | 1 | Given the logical address, how to extract the page number? -- (operating systems memory management paging virtual memory)
<p>I am studying Computer Systems. I have th following question and its answer:</p>

<blockquote>
 <p>Given the logical address 0xAEF9 (in hexadecimal) with a page size of
 256 byt... | habedi/stack-exchange-dataset |
11,726 | Random generator considerations in the design of randomized algorithms | <p>It is well known that the efficiency of randomized algorithms (at least those in BPP and RP) depends on the quality of the random generator used. Perfect random sources are unavailable in practice. Although it is proved that for all $0 < \delta \leq \frac{1}{2}$ the identities BPP = $\delta$-BPP and RP = $\delta$... | randomized algorithms randomness pseudo random generators | 1 | Random generator considerations in the design of randomized algorithms -- (randomized algorithms randomness pseudo random generators)
<p>It is well known that the efficiency of randomized algorithms (at least those in BPP and RP) depends on the quality of the random generator used. Perfect random sources are unavailabl... | habedi/stack-exchange-dataset |
11,729 | Determining grammar decidability | <p>Got a final coming up, so I gotta get this concept down.</p>

<p>Given $A= \{(G_1,G_2 \mid G_1$ and $G_2$ are two CFG's and $L(G_1)=L(G_2) \}$.
Is $A$ decidable?</p>

<p>Would it be sufficient to take an undecidable language such as $B= \{x \mid L(M_x)$ is a CFG $ \}$. Then reduce it to A with f... | undecidability | 1 | Determining grammar decidability -- (undecidability)
<p>Got a final coming up, so I gotta get this concept down.</p>

<p>Given $A= \{(G_1,G_2 \mid G_1$ and $G_2$ are two CFG's and $L(G_1)=L(G_2) \}$.
Is $A$ decidable?</p>

<p>Would it be sufficient to take an undecidable language such as $B= \{x \mi... | habedi/stack-exchange-dataset |
11,730 | Weak Precedence Grammar and Parsing | <p>I am studying parsing, i.e. bottom-up parsing. it is said that there some rules which are used by weak precedence grammar. What does weak precedence grammar mean? What about precedence relation?</p>

<p>Any help will be appreciated. If it is possible, could you give an example. Thanks</p>
 | formal languages terminology context free parsers | 1 | Weak Precedence Grammar and Parsing -- (formal languages terminology context free parsers)
<p>I am studying parsing, i.e. bottom-up parsing. it is said that there some rules which are used by weak precedence grammar. What does weak precedence grammar mean? What about precedence relation?</p>

<p>Any help will b... | habedi/stack-exchange-dataset |
11,739 | reducing Max3SAT to Max2sat | <p>I want to reduce $MAX3SAT$ to $MAX2SAT$ ...<br>
MAX-n-SAT : given $\phi $ n-CNF formula and number k does $\phi$ has an assignment that satisfy k clauses? </p>
 | algorithms np complete reductions approximation | 1 | reducing Max3SAT to Max2sat -- (algorithms np complete reductions approximation)
<p>I want to reduce $MAX3SAT$ to $MAX2SAT$ ...<br>
MAX-n-SAT : given $\phi $ n-CNF formula and number k does $\phi$ has an assignment that satisfy k clauses? </p>
 | habedi/stack-exchange-dataset |
11,741 | Binary decision diagram for a six-figure Boolean function | <blockquote>
 <p>Let $p$ be the six-figure Boolean function with the following definition: </p>
 
 <p>$p(x_{0},x_{1},x_{2},x_{3},x_{4},x_{5})=\begin{cases}
 true & \text{if } x_{0}=x_{5} \text{ and } x_{1}=x_{4} \text{ and } x_{2}=x_{3}, \\
 false & \text{else.}
\end{cases}$</p>&#x... | formal methods | 1 | Binary decision diagram for a six-figure Boolean function -- (formal methods)
<blockquote>
 <p>Let $p$ be the six-figure Boolean function with the following definition: </p>
 
 <p>$p(x_{0},x_{1},x_{2},x_{3},x_{4},x_{5})=\begin{cases}
 true & \text{if } x_{0}=x_{5} \text{ and } x_{1}=x_{4} \text... | habedi/stack-exchange-dataset |
11,752 | Chazelle's discrepancy book: greedy method | <p>In Bernard Chazelle's book <em>The Discrepancy Method</em>, which is <a href="http://www.cs.princeton.edu/~chazelle/pubs/book.pdf" rel="nofollow">available free as a PDF from the author's website</a>, the very first statement requiring thought by the reader (on page 3, just before Theorem 1) is obtained by a simple ... | reference request combinatorics probability theory books | 1 | Chazelle's discrepancy book: greedy method -- (reference request combinatorics probability theory books)
<p>In Bernard Chazelle's book <em>The Discrepancy Method</em>, which is <a href="http://www.cs.princeton.edu/~chazelle/pubs/book.pdf" rel="nofollow">available free as a PDF from the author's website</a>, the very fi... | habedi/stack-exchange-dataset |
11,756 | Is there a binary search tree datastructure which can avoid becoming badly weight-balanced? | <p>This is a follow-up question of "<a href="https://cs.stackexchange.com/questions/342/not-all-red-black-trees-are-balanced">Not all Red-Black trees are balanced?</a>" and "<a href="https://cs.stackexchange.com/questions/421/avl-trees-are-not-weight-balanced">AVL trees are not weight-balanced?</a>".$\def\le{\leqslant}... | data structures search trees | 1 | Is there a binary search tree datastructure which can avoid becoming badly weight-balanced? -- (data structures search trees)
<p>This is a follow-up question of "<a href="https://cs.stackexchange.com/questions/342/not-all-red-black-trees-are-balanced">Not all Red-Black trees are balanced?</a>" and "<a href="https://cs.... | habedi/stack-exchange-dataset |
11,759 | Without using pumping lemma, can we determine if $A =\{ww \mid w \in \{0,1\}^* \}$ is non regular? | <p>Without using pumping lemma, can we prove $A =\{ww \mid w \in \{0,1\}^* \}$ is non regular?</p>

<p>Is $L= \{w \mid w \in \{0,1\}^* \}$ non regular? I'm thinking of using concatenation to prove the former isn't regular. If L is non regular then so is LL</p>
 | formal languages regular languages | 1 | Without using pumping lemma, can we determine if $A =\{ww \mid w \in \{0,1\}^* \}$ is non regular? -- (formal languages regular languages)
<p>Without using pumping lemma, can we prove $A =\{ww \mid w \in \{0,1\}^* \}$ is non regular?</p>

<p>Is $L= \{w \mid w \in \{0,1\}^* \}$ non regular? I'm thinking of using... | habedi/stack-exchange-dataset |
11,761 | NP complete problems that are solvable in polynomial time if the input (e.g. number of variables) is fixed? | <p>I have seen some problems that are NP-hard but polynomially solvable in fixed dimension.</p>

<p>Examples, I think, are Knapsack that is polynomial time solvable if the number of items is fixed and Integer Linear Programming with fixed number of variables or constraints by Lenstras result.</p>

<p>Qu... | np complete optimization decision problem linear programming parameterized complexity | 1 | NP complete problems that are solvable in polynomial time if the input (e.g. number of variables) is fixed? -- (np complete optimization decision problem linear programming parameterized complexity)
<p>I have seen some problems that are NP-hard but polynomially solvable in fixed dimension.</p>

<p>Examples, I t... | habedi/stack-exchange-dataset |
11,766 | Hardness of approximation of the 3 colorability problem | <p>If we have polynomial algorithm that $c$-approximation, $c<\frac{4}{3}$ for graphs that their chromatic number $\geq k$ then $NP=P$, how to prove such statements?</p>

<p>I also have some sort of explanation of this statement: It's NP-hard to separate between graphs that have chromatic number $k$ and chro... | algorithms np hard approximation | 1 | Hardness of approximation of the 3 colorability problem -- (algorithms np hard approximation)
<p>If we have polynomial algorithm that $c$-approximation, $c<\frac{4}{3}$ for graphs that their chromatic number $\geq k$ then $NP=P$, how to prove such statements?</p>

<p>I also have some sort of explanation of t... | habedi/stack-exchange-dataset |
11,772 | Is there a binary tree structure with fast access to recently accessed elements and worst $O \left( \log n \right )$ complexity? | <p>The idea of <a href="http://en.wikipedia.org/wiki/Splay_tree">splay trees</a> is very nice as they move frequently accessed elements to the top, which can gain a considerable speed up in many applications. The drawback is that in the worst case an operation can have $O(n)$ complexity. 
(Although amortized bounds... | data structures binary trees search trees splay trees | 1 | Is there a binary tree structure with fast access to recently accessed elements and worst $O \left( \log n \right )$ complexity? -- (data structures binary trees search trees splay trees)
<p>The idea of <a href="http://en.wikipedia.org/wiki/Splay_tree">splay trees</a> is very nice as they move frequently accessed eleme... | habedi/stack-exchange-dataset |
11,777 | Sublinear query time for the $i$th element of an array after some additions? | <p>We are given an array $A[1..n]$ of integers, and an array of 3-tuples known as queries. The query tuples $(i,j,v)$ denote additions of an integer $v$ to the subarray of $A[i..j]$. I'm interested in the query time of $A[k]$ for $1 \leq k \leq n$ between the queries.</p>

<p>For example, let $A = [1,2,3,4]$, a... | algorithms arrays | 1 | Sublinear query time for the $i$th element of an array after some additions? -- (algorithms arrays)
<p>We are given an array $A[1..n]$ of integers, and an array of 3-tuples known as queries. The query tuples $(i,j,v)$ denote additions of an integer $v$ to the subarray of $A[i..j]$. I'm interested in the query time of $... | habedi/stack-exchange-dataset |
11,781 | Algorithm analysis question in growth of functions | <p>How would I solve the following.</p>

<p>An algorithm that is $O(n^2)$ takes 10 seconds to execute on a particular computer when n=100, how long would you expect to take it when n=500?</p>

<p>Can anyone help me answer dis. </p>
 | algorithms time complexity asymptotics | 1 | Algorithm analysis question in growth of functions -- (algorithms time complexity asymptotics)
<p>How would I solve the following.</p>

<p>An algorithm that is $O(n^2)$ takes 10 seconds to execute on a particular computer when n=100, how long would you expect to take it when n=500?</p>

<p>Can anyone he... | habedi/stack-exchange-dataset |
11,785 | Proving that language is regular or not regular | <blockquote>
 <p>Let $L$ be a regular language. Prove that:</p>
 
 <ol>
 <li><p>$L_{+--}=\left\{w: \exists_u |u|=2|w| \wedge wu\in L\right\}$ </p></li>
 <li><p>$L_{++-}=\left\{w: \exists_u 2|u|=|w| \wedge wu\in L \right\}$</p></li>
 <li><p>$L_{-+-}=\left\{w:\exists_{u,v} |u|=|w|=|v| \wedge... | regular languages | 1 | Proving that language is regular or not regular -- (regular languages)
<blockquote>
 <p>Let $L$ be a regular language. Prove that:</p>
 
 <ol>
 <li><p>$L_{+--}=\left\{w: \exists_u |u|=2|w| \wedge wu\in L\right\}$ </p></li>
 <li><p>$L_{++-}=\left\{w: \exists_u 2|u|=|w| \wedge wu\in L \right\}$</... | habedi/stack-exchange-dataset |
11,787 | Regular expression for the strings without a particular substring | <p>How can we design a regular expressions without particular substrings.
The goal of this is to create language <code>L</code> which won't contain a particular substring (i.e. 110)</p>

<p>for the case of a regular expression without substring $110$, I Was thinking of: $\require{cancel}\cancel{(101)^*+}(01... | regular languages finite automata regular expressions | 1 | Regular expression for the strings without a particular substring -- (regular languages finite automata regular expressions)
<p>How can we design a regular expressions without particular substrings.
The goal of this is to create language <code>L</code> which won't contain a particular substring (i.e. 110)</p>
&... | habedi/stack-exchange-dataset |
11,802 | Optimal upper bound on the number of states in the complement of an NFA | <p>I have my own version of <code>lex</code> and I would like to add the complement operation. Derived from that I can then add the intersection and difference also. My version also supports the generation of NFAs (Non-deterministic Finite Automaton) and of course I try to keep the automatons as small as possible.</p>&... | finite automata | 1 | Optimal upper bound on the number of states in the complement of an NFA -- (finite automata)
<p>I have my own version of <code>lex</code> and I would like to add the complement operation. Derived from that I can then add the intersection and difference also. My version also supports the generation of NFAs (Non-determin... | habedi/stack-exchange-dataset |
11,805 | Which theoretical parallel model is closest to CUDA? | <p>Which theoretical parallel model is closest to CUDA/OpenCL programming model?</p>

<p>For example, it fits at some degree to the generic Parallel Random Access Machine (PRAM) model. However, that is too generic, since it makes abstraction of various memory access latencies and synchronization issues.</p>
... | parallel computing machine models | 1 | Which theoretical parallel model is closest to CUDA? -- (parallel computing machine models)
<p>Which theoretical parallel model is closest to CUDA/OpenCL programming model?</p>

<p>For example, it fits at some degree to the generic Parallel Random Access Machine (PRAM) model. However, that is too generic, since... | habedi/stack-exchange-dataset |
11,807 | Prove that inserting $n$ sorted values in to an AVL using AVL insertion is $\Theta\left (n \log \left ( n \right ) \right )$ | <p>We're asked to prove the above mentioned lemma but I having a hard time proving this rigorously.</p>

<p>We did prove that given $n$ values AVL's height is $\Theta\left (\log \left ( n \right ) \right )$ So I thought that after inserting a $\frac{n}{2}$ values the height of the tree will be at least $\Theta\... | algorithms data structures binary trees search trees | 1 | Prove that inserting $n$ sorted values in to an AVL using AVL insertion is $\Theta\left (n \log \left ( n \right ) \right )$ -- (algorithms data structures binary trees search trees)
<p>We're asked to prove the above mentioned lemma but I having a hard time proving this rigorously.</p>

<p>We did prove that giv... | habedi/stack-exchange-dataset |
11,810 | Easiest way to write a grammar? | <p>When I see a problem like "Write a grammar for a language $L$ if $L = \{..\}$" for me is a matter of "instinct" the way that one can define productions. For example given the following exercise:</p>

<blockquote>
 <p>Let $L$ a language which alphabet is $\{x,y,z\}$ and accepts strings
 $w$ where th... | context free formal grammars | 1 | Easiest way to write a grammar? -- (context free formal grammars)
<p>When I see a problem like "Write a grammar for a language $L$ if $L = \{..\}$" for me is a matter of "instinct" the way that one can define productions. For example given the following exercise:</p>

<blockquote>
 <p>Let $L$ a language wh... | habedi/stack-exchange-dataset |
11,820 | Disk scheduling and process scheduling | <p>Whats the diffrence between Disk scheduling and process scheduling? I mean i know the roles of disks and processes, but it seems to me they both have the same aim. to reduce monopolies, they even both share similar algorithms like first come first serve. Am i right?</p>
 | operating systems process scheduling | 1 | Disk scheduling and process scheduling -- (operating systems process scheduling)
<p>Whats the diffrence between Disk scheduling and process scheduling? I mean i know the roles of disks and processes, but it seems to me they both have the same aim. to reduce monopolies, they even both share similar algorithms like first... | habedi/stack-exchange-dataset |
11,825 | change the info part of each node in binary tree | <p>i have a binary tree.</p>

<pre><code> 2
 / \
 3 4
 / \ \
 5 1 8
 \ /
 6 9
</code></pre>

<p>I want to change the info part of each node such that the</p>

<pre><code>nodeinfo = nodeinfo + nextInorderNode... | data structures | 1 | change the info part of each node in binary tree -- (data structures)
<p>i have a binary tree.</p>

<pre><code> 2
 / \
 3 4
 / \ \
 5 1 8
 \ /
 6 9
</code></pre>

<p>I want to change the info part of each node such ... | habedi/stack-exchange-dataset |
11,832 | Changing AVL's balance factor to some other $s>2 \in \mathbb{N}$ | <p>Given we change the rule to: </p>

<blockquote>
 <p>$-s \ \ \leq$ height(left-subtree) - height(right-subtree) $\leq \ \ s$</p>
</blockquote>

<p>I was wandering whether it's possible and how would it affect the trees' height, would it still be logarithmic? </p>

<p>Would the exact s... | algorithms data structures binary trees trees | 1 | Changing AVL's balance factor to some other $s>2 \in \mathbb{N}$ -- (algorithms data structures binary trees trees)
<p>Given we change the rule to: </p>

<blockquote>
 <p>$-s \ \ \leq$ height(left-subtree) - height(right-subtree) $\leq \ \ s$</p>
</blockquote>

<p>I was wandering whether it's p... | habedi/stack-exchange-dataset |
11,836 | How to measure "sortedness" | <p>I'm wondering if there is a standard way of measuring the "sortedness" of an array? Would an array which has the median number of possible inversions be considered maximally unsorted? By that I mean it's basically as far as possible from being either sorted or reverse sorted.</p>
 | algorithms algorithm analysis sorting arrays | 1 | How to measure "sortedness" -- (algorithms algorithm analysis sorting arrays)
<p>I'm wondering if there is a standard way of measuring the "sortedness" of an array? Would an array which has the median number of possible inversions be considered maximally unsorted? By that I mean it's basically as far as possible from... | habedi/stack-exchange-dataset |
11,838 | Clique in P when the input graph's connected components have at most $3\log|V|$ vertices? | <p>What's the time complexity of the clique problem for input graphs where each connected component has size at most $3\log|V|$? Is it in P?</p>
 | algorithms graphs | 1 | Clique in P when the input graph's connected components have at most $3\log|V|$ vertices? -- (algorithms graphs)
<p>What's the time complexity of the clique problem for input graphs where each connected component has size at most $3\log|V|$? Is it in P?</p>
 | habedi/stack-exchange-dataset |
11,841 | Classes of NFAs which allow efficient subset testing or unambiguity conversions | <p>I'm doing some research regarding NFAs and inclusion problems with them. I know that in general, the inclusion problems, and converting to an unambiguous NFA, are both PSPACE-complete.</p>

<p>I'm wondering, are there any sub-classes of NFA for which these can be decided efficiently? In particular, the NFAs ... | complexity theory formal languages automata finite automata nondeterminism | 1 | Classes of NFAs which allow efficient subset testing or unambiguity conversions -- (complexity theory formal languages automata finite automata nondeterminism)
<p>I'm doing some research regarding NFAs and inclusion problems with them. I know that in general, the inclusion problems, and converting to an unambiguous NFA... | habedi/stack-exchange-dataset |
11,850 | Computability of Kolmogorov Complexity | <p>Fix a universal Turing machine $M$.</p>

<p>Let $A^*=\{0,1\}^n$ be the set of all binary string of length $n$.</p>

<p>Determine the Kolmorogov complexity $K(x)$ of each $x\in A$, w.r.t. $M$.</p>

<p>Just for a matter of simplicity assume that $K(x)'=\min(|x|,K(x))$.</p>

<p>Let $B^*=... | computability kolmogorov complexity | 1 | Computability of Kolmogorov Complexity -- (computability kolmogorov complexity)
<p>Fix a universal Turing machine $M$.</p>

<p>Let $A^*=\{0,1\}^n$ be the set of all binary string of length $n$.</p>

<p>Determine the Kolmorogov complexity $K(x)$ of each $x\in A$, w.r.t. $M$.</p>

<p>Just for a ma... | habedi/stack-exchange-dataset |
11,854 | Can we understand SVM without knowledge of Machine Learning | <p>I was told by my adviser (future one) to look into <a href="http://www.csie.ntu.edu.tw/~cjlin/libsvm/" rel="nofollow">libsvm</a> library or any other and try to get familiar with it.. to work on a programming project (on Machine Learning) (will start in a month).</p>

<p>my background: Programming knowledge ... | reference request machine learning data mining | 1 | Can we understand SVM without knowledge of Machine Learning -- (reference request machine learning data mining)
<p>I was told by my adviser (future one) to look into <a href="http://www.csie.ntu.edu.tw/~cjlin/libsvm/" rel="nofollow">libsvm</a> library or any other and try to get familiar with it.. to work on a programm... | habedi/stack-exchange-dataset |
11,858 | Can we have a general function of any function this way? | <p>Lets say we need a function to add two numbers and another function to multiply two numbers.</p>

<p>To take a trivial example, consider the function $F(a, b, c, d) = a \cdot (c+d) + b \cdot (c\cdot d)$
If $a=1$ and $b=0$, then $F$ adds $c$ and $d$. If $a=0$ and $b=1$, then $F$ multiplies $c$ and $d$.</... | algorithms terminology | 1 | Can we have a general function of any function this way? -- (algorithms terminology)
<p>Lets say we need a function to add two numbers and another function to multiply two numbers.</p>

<p>To take a trivial example, consider the function $F(a, b, c, d) = a \cdot (c+d) + b \cdot (c\cdot d)$
If $a=1$ and $b=0... | habedi/stack-exchange-dataset |
11,860 | Vertex Cover problem modification | <p>Modification of vertex cover problem.<br>
Given a graph G,does G have a vertex cover with 10 vertices? Is this problem still in NP?<br>
Given a graph G and integer k, does G have a vertex cover with k vertices?<br>
Is there any important difference between this two problems? </p>
 | graphs np | 1 | Vertex Cover problem modification -- (graphs np)
<p>Modification of vertex cover problem.<br>
Given a graph G,does G have a vertex cover with 10 vertices? Is this problem still in NP?<br>
Given a graph G and integer k, does G have a vertex cover with k vertices?<br>
Is there any important difference between... | habedi/stack-exchange-dataset |
11,865 | What's the vertex cover of the null graph? | <p>Let $N(G)$ be the null graph. What's the number of vertex cover for this graph? I wanted to modify the reduction from SAT to vertex cover by adding vertices that are not connect to any vertices.</p>
 | algorithms approximation | 1 | What's the vertex cover of the null graph? -- (algorithms approximation)
<p>Let $N(G)$ be the null graph. What's the number of vertex cover for this graph? I wanted to modify the reduction from SAT to vertex cover by adding vertices that are not connect to any vertices.</p>
 | habedi/stack-exchange-dataset |
11,869 | Rearrange a sequence of real numbers to satisfy polynomial inequalities | <p>Assume we fix a degree $d$ polynomials $f$ of $k$ variables. (If it helps, let $t$ be the number of terms in $f$).
Consider a list of real numbers $a_1,\ldots,a_n$, does there exist a permutation $\pi$, such that for all $i\leq n-k$
$$ f(a_{\pi(i)},a_{\pi(i+1)},\ldots,a_{\pi(i+k-1)}) \geq 0$$</p>

<p... | complexity theory np complete permutations polynomials real numbers | 1 | Rearrange a sequence of real numbers to satisfy polynomial inequalities -- (complexity theory np complete permutations polynomials real numbers)
<p>Assume we fix a degree $d$ polynomials $f$ of $k$ variables. (If it helps, let $t$ be the number of terms in $f$).
Consider a list of real numbers $a_1,\ldots,a_n$, doe... | habedi/stack-exchange-dataset |
11,876 | How do I compute the luminance of a pixel? | <p>I have a color (say $R=100, G=150, B=130$). How do I compute its intensity?</p>

<p>Do I just sum up all three components? Or are the colors not evenly weighted?</p>
 | graphics | 1 | How do I compute the luminance of a pixel? -- (graphics)
<p>I have a color (say $R=100, G=150, B=130$). How do I compute its intensity?</p>

<p>Do I just sum up all three components? Or are the colors not evenly weighted?</p>
 | habedi/stack-exchange-dataset |
11,878 | Amdahl's Law and Computer Science | <p>I would like to learn more about Amdahl's Law and other similar topics. In what branch of computer science would one place Amdahl's law? Could someone point me to a textbook or further reading (aside from Wikipedia or other sites that are found on the first page of a Google search) that discusses it?</p>
 | reference request parallel computing | 1 | Amdahl's Law and Computer Science -- (reference request parallel computing)
<p>I would like to learn more about Amdahl's Law and other similar topics. In what branch of computer science would one place Amdahl's law? Could someone point me to a textbook or further reading (aside from Wikipedia or other sites that are ... | habedi/stack-exchange-dataset |
11,880 | Euclidean Steiner Tree Question in Approximation Algorithms | <p>Given $n$ points in $\mathbf{R}^2$, define the optimal Euclidean Steiner tree to be a minimum (Euclidean) length tree containing all $n$ points and any other subset of points from $\mathbf{R}^2$.
Prove that each of the additional points must have degree 3, with all three angles being $120^\circ$.</p>
 | algorithms algorithm analysis computational geometry approximation trees | 1 | Euclidean Steiner Tree Question in Approximation Algorithms -- (algorithms algorithm analysis computational geometry approximation trees)
<p>Given $n$ points in $\mathbf{R}^2$, define the optimal Euclidean Steiner tree to be a minimum (Euclidean) length tree containing all $n$ points and any other subset of points from... | habedi/stack-exchange-dataset |
11,883 | What is the fastest to find just smallest prime number to a given number N where N can be as large as 10^18? | <p>During a programming contest I was asked to find just smallest prime number to given number N.
As Sieve cannot be used and brute force also doesn't work.</p>

<p>So, I was wondering is there any other faster implementation.</p>

<p>Here N -> (2, 10^18).</p>
 | algorithms primes | 1 | What is the fastest to find just smallest prime number to a given number N where N can be as large as 10^18? -- (algorithms primes)
<p>During a programming contest I was asked to find just smallest prime number to given number N.
As Sieve cannot be used and brute force also doesn't work.</p>

<p>So, I was w... | habedi/stack-exchange-dataset |
11,889 | Can a language have $\Sigma^{*}$ as its syntactic monoid? | <p>As per the title I was wondering if it's possible for a language $L \subseteq \Sigma^{*}$ to have $\Sigma^{*}$ as its syntactic monoid and if so could one give an example of such a language? I first thought that this was probably an easy question with a simple answer but I haven't been able to make much progress wit... | formal languages | 1 | Can a language have $\Sigma^{*}$ as its syntactic monoid? -- (formal languages)
<p>As per the title I was wondering if it's possible for a language $L \subseteq \Sigma^{*}$ to have $\Sigma^{*}$ as its syntactic monoid and if so could one give an example of such a language? I first thought that this was probably an easy... | habedi/stack-exchange-dataset |
11,893 | What does 'true concurrency' mean? | <p>I often hear phrases like 'true concurrency semantics' and 'true concurrency equivalences' without any references. What does those terms mean and why are they important?</p>

<p>What are some examples of true concurrency equivalences and what is the need for them? E.g. in which cases they are more applicable... | terminology reference request concurrency | 1 | What does 'true concurrency' mean? -- (terminology reference request concurrency)
<p>I often hear phrases like 'true concurrency semantics' and 'true concurrency equivalences' without any references. What does those terms mean and why are they important?</p>

<p>What are some examples of true concurrency equiva... | habedi/stack-exchange-dataset |
11,897 | Efficiently finding key sets | <p>A few years ago I participated in German highschool computer science competition. One of the <a href="http://www.bundeswettbewerb-informatik.de/fileadmin/templates/bwinf/aufgaben/bwinf28/Aufgaben282.pdf" rel="nofollow">problems</a> was this (slightly abbreviated):</p>

<blockquote>
 <p>A somewhat unusu... | algorithms | 1 | Efficiently finding key sets -- (algorithms)
<p>A few years ago I participated in German highschool computer science competition. One of the <a href="http://www.bundeswettbewerb-informatik.de/fileadmin/templates/bwinf/aufgaben/bwinf28/Aufgaben282.pdf" rel="nofollow">problems</a> was this (slightly abbreviated):</p>&#x... | habedi/stack-exchange-dataset |
11,902 | Can the heaviest edge ever be in an MST? | <p>Is it true that the heaviest edge in a directed graph can not be in the MST of that graph?</p>

<p>I don't think it is true because we might end up with a heaviest edge that is <em>not</em> part of a cycle. </p>

<p>Can anyone confirm?</p>
 | graphs minimum spanning tree | 1 | Can the heaviest edge ever be in an MST? -- (graphs minimum spanning tree)
<p>Is it true that the heaviest edge in a directed graph can not be in the MST of that graph?</p>

<p>I don't think it is true because we might end up with a heaviest edge that is <em>not</em> part of a cycle. </p>

<p>Can anyone... | habedi/stack-exchange-dataset |
11,904 | Reduction from Vertex Cover to an Independent Set problem | <p>Assume there exists some algorithm that solves vertex cover problem in time polynomial in terms of $n$ and exponential for $k$ with the run time that looks like this $O(k^2 55^k n^3)$. Can we claim that independent set can also be solved in time polynomial in terms of $n$ and exponential in terms of $k$ ? ($k$ here ... | graphs np complete np p vs np parameterized complexity | 1 | Reduction from Vertex Cover to an Independent Set problem -- (graphs np complete np p vs np parameterized complexity)
<p>Assume there exists some algorithm that solves vertex cover problem in time polynomial in terms of $n$ and exponential for $k$ with the run time that looks like this $O(k^2 55^k n^3)$. Can we claim t... | habedi/stack-exchange-dataset |
11,906 | How can Computer Science theories and inquiries be resolved? | <p>It's probably possible to prove that P ≠ NP, that one-way functions exist, and that parity games cannot be solved in polynomial time (yes, I've been reading through <a href="http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_computer_science" rel="nofollow noreferrer">this list</a>), but how would we go about... | epistemology | 1 | How can Computer Science theories and inquiries be resolved? -- (epistemology)
<p>It's probably possible to prove that P ≠ NP, that one-way functions exist, and that parity games cannot be solved in polynomial time (yes, I've been reading through <a href="http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_comput... | habedi/stack-exchange-dataset |
11,915 | Reducing from Hamiltonian Cycle problem to the Graph Wheel problem | <p>EDIT: This question is different from the other in a sense that unlike it this one goes into specifics and is intended to solve the problem. In the previous post, the only answer was a hint. In this post, the answer is a proper solution. </p>

<p>Is there a way to "polynomialy" reduce the problem of finding ... | graphs np complete | 1 | Reducing from Hamiltonian Cycle problem to the Graph Wheel problem -- (graphs np complete)
<p>EDIT: This question is different from the other in a sense that unlike it this one goes into specifics and is intended to solve the problem. In the previous post, the only answer was a hint. In this post, the answer is a prope... | habedi/stack-exchange-dataset |
11,920 | What does it mean to say that a language is "effectively closed" under an operation? | <p>I've been reading some formal language theory papers, and I've come across a term that I don't understand.</p>

<p>The paper will often refer to a set being "effectively closed under intersection" or other operations. What does "effectively" mean here? How does this differ from normal closure?</p>

<... | formal languages terminology computability automata closure properties | 1 | What does it mean to say that a language is "effectively closed" under an operation? -- (formal languages terminology computability automata closure properties)
<p>I've been reading some formal language theory papers, and I've come across a term that I don't understand.</p>

<p>The paper will often refer to a s... | habedi/stack-exchange-dataset |
11,925 | PDA with 2 stacks | <p>I urgently need a language which can be recognised by 2 PDA's but not with 1 PDA.</p>
 | formal languages pushdown automata | 1 | PDA with 2 stacks -- (formal languages pushdown automata)
<p>I urgently need a language which can be recognised by 2 PDA's but not with 1 PDA.</p>
 | habedi/stack-exchange-dataset |
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