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 |
|---|---|---|---|---|---|---|
41,975 | How exactly does a two stack pushdown automaton work? | <p>I have to explain how a 2-PDA works and then write a program (in Delphi) which simulates a 2-PDA step by step for the language $L = \{w\$w\ |\ w ∈ \{0,1\}^n\ with\ n>0\}$. So far, so good.</p>

<p>Now I know that a 2-PDA works with two stacks and is equivalent to a Turing Machine. It reads from an input t... | turing machines automata pushdown automata | 1 | How exactly does a two stack pushdown automaton work? -- (turing machines automata pushdown automata)
<p>I have to explain how a 2-PDA works and then write a program (in Delphi) which simulates a 2-PDA step by step for the language $L = \{w\$w\ |\ w ∈ \{0,1\}^n\ with\ n>0\}$. So far, so good.</p>

<p>Now I k... | habedi/stack-exchange-dataset |
41,976 | How to use frame based speech features for learning using a neural network classifier? | <p>I am doing supervised learning on speech audio files using neural networks. For this purpose, I'll have to extract features from the audio file. But since an audio file is a time varying signal, it is generally divided into multiple frames and then features like MFCC etc are extracted from each frame. So how should ... | machine learning speech recognition features | 1 | How to use frame based speech features for learning using a neural network classifier? -- (machine learning speech recognition features)
<p>I am doing supervised learning on speech audio files using neural networks. For this purpose, I'll have to extract features from the audio file. But since an audio file is a time v... | habedi/stack-exchange-dataset |
41,977 | Transitions needed for dividing two fixed integers | <p>Let $Q$ be the set of states of the Turing Machine, $\Sigma$ be the alphabet, and $\{L,R,S\}$ be the left shift, right shift, and stay respectively.</p>

<p>A transition is an element of $Q \times \Sigma \times Q \times \Sigma \times \{L,R,S\}$ which can be read as current state, current symbol, next state, ... | algorithm analysis turing machines | 1 | Transitions needed for dividing two fixed integers -- (algorithm analysis turing machines)
<p>Let $Q$ be the set of states of the Turing Machine, $\Sigma$ be the alphabet, and $\{L,R,S\}$ be the left shift, right shift, and stay respectively.</p>

<p>A transition is an element of $Q \times \Sigma \times Q \time... | habedi/stack-exchange-dataset |
41,978 | How to understand equivalence of indexes of a family of types that are not definitionally equal | <p>So I've been reading things about HoTT and trying to get solid on the foundations before getting too much further into the book. I am confused by a certain point; maybe I just haven't read far enough yet however. I don't think my question is specific to HoTT but just dependent type theory in general.</p>

<p... | programming languages type theory dependent types inductive datatypes homotopy type theory | 1 | How to understand equivalence of indexes of a family of types that are not definitionally equal -- (programming languages type theory dependent types inductive datatypes homotopy type theory)
<p>So I've been reading things about HoTT and trying to get solid on the foundations before getting too much further into the bo... | habedi/stack-exchange-dataset |
41,982 | Why is automated theorem proving impossible? | <p>As far I know, in general case there is no Turing machine which could get any theorem on its input and produce its proof on its output.</p>

<p>Why is it so?</p>
 | turing machines logic automated theorem proving | 1 | Why is automated theorem proving impossible? -- (turing machines logic automated theorem proving)
<p>As far I know, in general case there is no Turing machine which could get any theorem on its input and produce its proof on its output.</p>

<p>Why is it so?</p>
 | habedi/stack-exchange-dataset |
41,992 | Time complexity of linear program? | <p>I have built a heuristic algorithm for approximately solving an NP complete graph problem by recursive linear relaxations. In each recursion, the algorithm returns a reduced graph, with number of nodes $N_{k+1} \leq 0.5N_{k}$.</p>

<p>I think this means that the overall complexity should be order $\log N \ti... | time complexity recursion linear programming | 1 | Time complexity of linear program? -- (time complexity recursion linear programming)
<p>I have built a heuristic algorithm for approximately solving an NP complete graph problem by recursive linear relaxations. In each recursion, the algorithm returns a reduced graph, with number of nodes $N_{k+1} \leq 0.5N_{k}$.</p>&#... | habedi/stack-exchange-dataset |
41,997 | Calculating DFT of a specific polynomial | <p>This seems like a simple problem but I'm getting the impression I'm missing something.</p>

<p><strong>The problem</strong></p>

<p>Given the values $v_1, v_2, \ldots, v_n$ such that $DFT_n(P(x)) = (v_1, v_2, \ldots, v_n) $ for $ P(x) = \sum\limits_{i=0}^k a_ix^i$ , $k < n$ - find $ DFT_{2n}(P(x^2... | algorithms fourier transform | 1 | Calculating DFT of a specific polynomial -- (algorithms fourier transform)
<p>This seems like a simple problem but I'm getting the impression I'm missing something.</p>

<p><strong>The problem</strong></p>

<p>Given the values $v_1, v_2, \ldots, v_n$ such that $DFT_n(P(x)) = (v_1, v_2, \ldots, v_n) $ fo... | habedi/stack-exchange-dataset |
42,001 | Is the Euclidean TSP weakly NP-hard? | <p>So the Euclidean TSP decision problem is NP-complete (see <a href="http://dx.doi.org/10.1016/0304-3975(77)90012-3" rel="nofollow">http://dx.doi.org/10.1016/0304-3975(77)90012-3</a> ) so the TSP optimization problem should be NP-hard.</p>

<p>On the other hand there is a PTAS for the Euclidean TSP (see <a hre... | np hard traveling salesman | 1 | Is the Euclidean TSP weakly NP-hard? -- (np hard traveling salesman)
<p>So the Euclidean TSP decision problem is NP-complete (see <a href="http://dx.doi.org/10.1016/0304-3975(77)90012-3" rel="nofollow">http://dx.doi.org/10.1016/0304-3975(77)90012-3</a> ) so the TSP optimization problem should be NP-hard.</p>

<... | habedi/stack-exchange-dataset |
42,010 | Proving the set of finite languages is countable without using the union of countable sets | <p>The list of finite languages over a finite alphabet is countable.</p>

<p>I could prove it by saying that the list of languages of size 1 is countable, the language of size 2 is countable, and so on. Then I can prove that the infinite union of countable set is countable.</p>

<p>However, I am sure th... | turing machines | 1 | Proving the set of finite languages is countable without using the union of countable sets -- (turing machines)
<p>The list of finite languages over a finite alphabet is countable.</p>

<p>I could prove it by saying that the list of languages of size 1 is countable, the language of size 2 is countable, and so o... | habedi/stack-exchange-dataset |
42,013 | How to replace one symbol with two on Turing machine's tape | <p>I want to implement following algorithm on Turing machine: </p>

<blockquote>
 <p>rewrite binary numbers to their unary counterparts. For example: 101
 will be rewritten to a string of 5 consecutive bars</p>
</blockquote>

<p>(<a href="http://en.wikipedia.org/wiki/Markov_algorithm#Anoth... | turing machines | 1 | How to replace one symbol with two on Turing machine's tape -- (turing machines)
<p>I want to implement following algorithm on Turing machine: </p>

<blockquote>
 <p>rewrite binary numbers to their unary counterparts. For example: 101
 will be rewritten to a string of 5 consecutive bars</p>
</bloc... | habedi/stack-exchange-dataset |
42,025 | Minimize Deterministic Finite Automata with no accepting states | <p>I have a finite automaton with no final/accepting states, so F is empty.
How do I minimize it?</p>

<p>I got this on a test and I didn't know how to approach the problem because the automaton had no accepting states.
Is a single initial state with all the transitions into itself the correct answer?</... | automata finite automata | 1 | Minimize Deterministic Finite Automata with no accepting states -- (automata finite automata)
<p>I have a finite automaton with no final/accepting states, so F is empty.
How do I minimize it?</p>

<p>I got this on a test and I didn't know how to approach the problem because the automaton had no accepting st... | habedi/stack-exchange-dataset |
42,027 | What does every root is at the same level mean | <p>My textbook says a "complete binary tree" is a "full binary tree" where every root is at the same level. </p>

<p>My conceptual understanding:</p>

<p>All this time, I was led by my textbook to believe a root is the "top-most vertex" in which all the other vertex are led away from it. So basically I ... | graphs binary trees | 1 | What does every root is at the same level mean -- (graphs binary trees)
<p>My textbook says a "complete binary tree" is a "full binary tree" where every root is at the same level. </p>

<p>My conceptual understanding:</p>

<p>All this time, I was led by my textbook to believe a root is the "top-most ver... | habedi/stack-exchange-dataset |
42,029 | Where to learn about Short-circuit evaluation? | <p>I would like to implement short circuit evaluation logic in my code. And I want to know about the full details how it works?</p>
<p><strong>Ex:</strong></p>
<p>function a() {return true;}</p>
<p>function b() {return false;}</p>
<p>function c() {return true;}</p>
<p><strong>Expression</strong></p>... | optimization programming languages evaluation strategies termination | 1 | Where to learn about Short-circuit evaluation? -- (optimization programming languages evaluation strategies termination)
<p>I would like to implement short circuit evaluation logic in my code. And I want to know about the full details how it works?</p>
<p><strong>Ex:</strong></p>
<p>function a() {return true;}<... | habedi/stack-exchange-dataset |
42,044 | Difference between time complexity and computational complexity | <p>For measuring the complexity of an algorithm, is it time complexity, or computational complexity? What is the difference between them?</p>

<p>I used to calculate the maximum (worst) count of basic (most costing) operation in the algorithm.</p>
 | complexity theory terminology algorithm analysis time complexity | 1 | Difference between time complexity and computational complexity -- (complexity theory terminology algorithm analysis time complexity)
<p>For measuring the complexity of an algorithm, is it time complexity, or computational complexity? What is the difference between them?</p>

<p>I used to calculate the maximum ... | habedi/stack-exchange-dataset |
42,048 | Heap-like data structure allowing peek at largest & smallest | <p>For the purpose of implementing an optimization algorithm (finding the minimum of a multivariate function) I want to create a data structure that supports the following operations:</p>

<ul>
<li>load from array</li>
<li>Peek at maximum element (but don't destroy it)</li>
<li>Peek at next-to-maxim... | algorithms data structures heaps priority queues | 1 | Heap-like data structure allowing peek at largest & smallest -- (algorithms data structures heaps priority queues)
<p>For the purpose of implementing an optimization algorithm (finding the minimum of a multivariate function) I want to create a data structure that supports the following operations:</p>

<ul>
... | habedi/stack-exchange-dataset |
42,058 | What's the difference between a reorder buffer and an instruction window? | <p>In an out-of-order processor, what is the difference between a reorder buffer and an instruction window? </p>

<p>Wikipedia says:<br>
"In particular, in a conventional design, the instruction window consists of all instructions which are in the Reorder Buffer (ROB)." </p>

<p>Does this mean tha... | computer architecture | 1 | What's the difference between a reorder buffer and an instruction window? -- (computer architecture)
<p>In an out-of-order processor, what is the difference between a reorder buffer and an instruction window? </p>

<p>Wikipedia says:<br>
"In particular, in a conventional design, the instruction window cons... | habedi/stack-exchange-dataset |
42,065 | Find a CFG for the language $\{ x\$y \mid x,y\in\{a,b\}^* \wedge |x| \ne |y| \}$? | <p>Consider the language below, on the alphabet $\Sigma = \{a,b,\$\}$:
$$L = \left\{ x$y \mid x,y\in\{a,b\}^* \land \left|x\right| \ne \left|y\right| \right\}$$</p>

<p>I need to define a CFG for this language. I've tried couple of CFGs but they all failed in one way or another.</p>

<p>I'd be glad ... | formal languages context free | 1 | Find a CFG for the language $\{ x\$y \mid x,y\in\{a,b\}^* \wedge |x| \ne |y| \}$? -- (formal languages context free)
<p>Consider the language below, on the alphabet $\Sigma = \{a,b,\$\}$:
$$L = \left\{ x$y \mid x,y\in\{a,b\}^* \land \left|x\right| \ne \left|y\right| \right\}$$</p>

<p>I need to define a CFG... | habedi/stack-exchange-dataset |
42,067 | Verification wanted: Show the language $L=\{0^m1^n \enspace | \enspace m \neq n\}$ is not regular | <p>$$L=\{0^m1^n \enspace | \enspace m \neq n\}$$</p>

<p>I saw that this exact question exists <a href="https://math.stackexchange.com/questions/480430/show-0m1n-m-neq-n-is-not-regular">elsewhere</a>, but I couldn't understand what was being said there. My question does not mandate the use of the Pumping Lemma ... | formal languages regular languages pumping lemma | 1 | Verification wanted: Show the language $L=\{0^m1^n \enspace | \enspace m \neq n\}$ is not regular -- (formal languages regular languages pumping lemma)
<p>$$L=\{0^m1^n \enspace | \enspace m \neq n\}$$</p>

<p>I saw that this exact question exists <a href="https://math.stackexchange.com/questions/480430/show-0m1... | habedi/stack-exchange-dataset |
42,069 | Understanding definition of NP | <p>In my lecture notes, the definition of the class NP is given as:</p>

<p>A language $L$ is in the class NP, if there exists a turing machine $M$ and polynomials $T$ and $p$ such that:</p>

<ul>
<li>For every input $x$, $M$ terminates after at most $T(|x|)$ steps</li>
<li>If $x\in L$, then the... | complexity theory turing machines np | 1 | Understanding definition of NP -- (complexity theory turing machines np)
<p>In my lecture notes, the definition of the class NP is given as:</p>

<p>A language $L$ is in the class NP, if there exists a turing machine $M$ and polynomials $T$ and $p$ such that:</p>

<ul>
<li>For every input $x$, $M$ t... | habedi/stack-exchange-dataset |
42,073 | Can one use the PCP theorem to prove correctness of deternimistic algorithms? | <p>I am thinking of the equality "PCP(O(log(n)),0) = P"</p>

<p>Say I have a deterministic polynomial time algorithm $A$ whose correctness I can't prove immediately. But say I create a probabilistic version of this algorithm say $A_P$ such that it uses log(n) random bits. Now if I prove somekind of (exactly wh... | complexity theory probability theory randomized algorithms information theory | 1 | Can one use the PCP theorem to prove correctness of deternimistic algorithms? -- (complexity theory probability theory randomized algorithms information theory)
<p>I am thinking of the equality "PCP(O(log(n)),0) = P"</p>

<p>Say I have a deterministic polynomial time algorithm $A$ whose correctness I can't prov... | habedi/stack-exchange-dataset |
42,074 | this automata is NFA or DFA? | <p><img src="https://i.stack.imgur.com/cVdCK.png" alt="automata">
That's my question, since it has two symbols but go to a single state, is DFA or NFA?</p>
 | automata | 1 | this automata is NFA or DFA? -- (automata)
<p><img src="https://i.stack.imgur.com/cVdCK.png" alt="automata">
That's my question, since it has two symbols but go to a single state, is DFA or NFA?</p>
 | habedi/stack-exchange-dataset |
42,093 | What's the difference between all these terms? | <p>What's the difference between them - Physically based simulation, Physically based animation, Physical simulation for computer animation, Physically based animation for Computer graphics, Physically based modelling for interactive simulation and games and Cognitive modelling ?</p>
 | terminology graphics | 1 | What's the difference between all these terms? -- (terminology graphics)
<p>What's the difference between them - Physically based simulation, Physically based animation, Physical simulation for computer animation, Physically based animation for Computer graphics, Physically based modelling for interactive simulation an... | habedi/stack-exchange-dataset |
42,095 | Flags register in an out-of-order processor | <pre><code>LW R2, 0(R1)
CMP R3, R2
CMP R7, R5
</code></pre>

<p>the LW instruction stalls the first CMP so the second one will execute first. Wouldn't this cause the flags register to contain the wrong value since it expects the second CMP to be the last one that updates the flags register?</p>
... | computer architecture | 1 | Flags register in an out-of-order processor -- (computer architecture)
<pre><code>LW R2, 0(R1)
CMP R3, R2
CMP R7, R5
</code></pre>

<p>the LW instruction stalls the first CMP so the second one will execute first. Wouldn't this cause the flags register to contain the wrong value since it expects the ... | habedi/stack-exchange-dataset |
42,098 | Limiting memory usage while keeping score | <p>For an assignment we are asked the following(simplified) :</p>
<blockquote>
<p>A function F(a) has a non-negative integer as a result. This result is reused in the function itself. Like this, and where the first a is given:</p>
<p>new_a = (c1 * (previous_a or first_a) + c2) mod c3</p>
<p>Write, in C#... | efficiency | 1 | Limiting memory usage while keeping score -- (efficiency)
<p>For an assignment we are asked the following(simplified) :</p>
<blockquote>
<p>A function F(a) has a non-negative integer as a result. This result is reused in the function itself. Like this, and where the first a is given:</p>
<p>new_a = (c1 * (p... | habedi/stack-exchange-dataset |
42,099 | What is the use of finding minimum number of straight lines to cover a set of points? | <p>There is that popular problem <a href="http://link.springer.com/article/10.1007%2FBF02187791#page-1">[1]</a> <a href="http://eurocg.org/06/delaunay.tem.uoc.gr/~mkaravel/ewcg06/papers/35.pdf">[2]</a> in the computer science that is finding minimum number of straight lines that covers a given set of points in 2D.</p>&... | reference request computational geometry applied theory | 1 | What is the use of finding minimum number of straight lines to cover a set of points? -- (reference request computational geometry applied theory)
<p>There is that popular problem <a href="http://link.springer.com/article/10.1007%2FBF02187791#page-1">[1]</a> <a href="http://eurocg.org/06/delaunay.tem.uoc.gr/~mkaravel/e... | habedi/stack-exchange-dataset |
42,105 | Splicing squares on a Turing Machine finite tape | <p>Trying to explain a problem, I thought of a variant of Turing
Machines. It is unlikely to be new, but I do not recall ever seing it
before, and I wonder whether it has been used or has a name. The idea
is that the TM uses a "linked list" rather than a tape, so that the
head can splice a new symbol po... | terminology turing machines reference request computation models | 1 | Splicing squares on a Turing Machine finite tape -- (terminology turing machines reference request computation models)
<p>Trying to explain a problem, I thought of a variant of Turing
Machines. It is unlikely to be new, but I do not recall ever seing it
before, and I wonder whether it has been used or has a nam... | habedi/stack-exchange-dataset |
42,112 | O(2^n) runs in P... Is this true? | <p>My professor doesn't always know what's actually correct or wrong - he always has to think about it for a very long time and get back to the book and read the book for a long time to answer any of our questions. </p>

<p>He says that</p>

<p><strong>I tell you that an algorithm runs in $O(2^n)$ but y... | asymptotics landau notation | 1 | O(2^n) runs in P... Is this true? -- (asymptotics landau notation)
<p>My professor doesn't always know what's actually correct or wrong - he always has to think about it for a very long time and get back to the book and read the book for a long time to answer any of our questions. </p>

<p>He says that</p>
... | habedi/stack-exchange-dataset |
42,120 | Sensitivity versus degree | <p>Given boolean function $f$, let $F$ denote the unique multiaffine real polynomial representing $f$.</p>

<p>Sensitivity of $f$ at input $x$ is $$S_x(f) = |\{i:f(x)\neq f(x^i)\}|$$ where $x^i=x\oplus\Bbb 1_i$ where $\oplus$ is $XOR$ operation.</p>

<p>Sensitivity of $f$ is $$S(f)=\max_xS_x(f)$$</p>&#x... | complexity theory | 1 | Sensitivity versus degree -- (complexity theory)
<p>Given boolean function $f$, let $F$ denote the unique multiaffine real polynomial representing $f$.</p>

<p>Sensitivity of $f$ at input $x$ is $$S_x(f) = |\{i:f(x)\neq f(x^i)\}|$$ where $x^i=x\oplus\Bbb 1_i$ where $\oplus$ is $XOR$ operation.</p>

<p>S... | habedi/stack-exchange-dataset |
42,125 | Is the language of all $a^n$ for which $n$ has an even number of digits in 10-base system regular? | <p>Is the language $ L = \{a^n ~| ~n \text{ has even number of digits in 10-base system}\} $ regular?</p>

<p>My approach: let the $ p $ be from the Pumping Lemma. Chose the smallest $ n $ which has even number of digits in 10-base system, but bigger or equal to $ p $, that is $ n = 10^{2m - 1} $ for appropriat... | formal languages regular languages pumping lemma | 1 | Is the language of all $a^n$ for which $n$ has an even number of digits in 10-base system regular? -- (formal languages regular languages pumping lemma)
<p>Is the language $ L = \{a^n ~| ~n \text{ has even number of digits in 10-base system}\} $ regular?</p>

<p>My approach: let the $ p $ be from the Pumping Le... | habedi/stack-exchange-dataset |
42,127 | Interval scheduling scheduling problem with minimal workers | <p>I am writing a greedy algorithm for a variation of the interval scheduling problem that I haven't seen before.</p>

<p>I have a set of jobs, each with start and finish time. All jobs in set must be assigned to a worker, workers cannot have overlapping jobs. My greedy algorithm should minimise workers - use t... | greedy algorithms intervals | 1 | Interval scheduling scheduling problem with minimal workers -- (greedy algorithms intervals)
<p>I am writing a greedy algorithm for a variation of the interval scheduling problem that I haven't seen before.</p>

<p>I have a set of jobs, each with start and finish time. All jobs in set must be assigned to a work... | habedi/stack-exchange-dataset |
42,136 | Can you write a program that alters another program semantically? | <p>It is definitely possible to write a program that takes another program as an input and changes it <em>syntactically</em>, but does not alter the meaning.</p>

<p>But is it possible to write a general program $alter$ that alters the output of a given program $P$ for <em>some</em> input, i.e. $\exists x: P(x)... | computability | 1 | Can you write a program that alters another program semantically? -- (computability)
<p>It is definitely possible to write a program that takes another program as an input and changes it <em>syntactically</em>, but does not alter the meaning.</p>

<p>But is it possible to write a general program $alter$ that al... | habedi/stack-exchange-dataset |
42,143 | Difference between time complexity and computational complexity | <p>For measuring the complexity of an algorithm, is it time complexity, or computational complexity? What is the difference between them?
I used to calculate the maximum (worst) count of basic (most costing) operation in the algorithm.</p>
 | time complexity complexity theory | 1 | Difference between time complexity and computational complexity -- (time complexity complexity theory)
<p>For measuring the complexity of an algorithm, is it time complexity, or computational complexity? What is the difference between them?
I used to calculate the maximum (worst) count of basic (most costing) opera... | habedi/stack-exchange-dataset |
42,147 | TSP genetic algorithm: what mutation function for adjacency representation? | <p>When implementing TSP GA I decided for adjacency representation (i.e. $j$ value in $i$-th index means that node $j$ goes right after node $i$), as it enables interesting heuristical crossover operation (see <a href="http://www.cs.indiana.edu/~vgucht/Genetic_Algorithms_for_the_Travelling_Salesman+Problem.pdf" rel="no... | traveling salesman genetic algorithms | 1 | TSP genetic algorithm: what mutation function for adjacency representation? -- (traveling salesman genetic algorithms)
<p>When implementing TSP GA I decided for adjacency representation (i.e. $j$ value in $i$-th index means that node $j$ goes right after node $i$), as it enables interesting heuristical crossover operat... | habedi/stack-exchange-dataset |
42,161 | Is set cover still NP-complete if you have a given k? | <p><a href="http://en.wikipedia.org/wiki/Set_cover_problem" rel="nofollow">Set cover</a> is NP-complete given an arbitrary set $U$, a set $S$ of subsets of $U$, and an integer $k$. However, what if $k$ is always a constant 3? Is that problem still NP-complete? </p>
 | np complete | 1 | Is set cover still NP-complete if you have a given k? -- (np complete)
<p><a href="http://en.wikipedia.org/wiki/Set_cover_problem" rel="nofollow">Set cover</a> is NP-complete given an arbitrary set $U$, a set $S$ of subsets of $U$, and an integer $k$. However, what if $k$ is always a constant 3? Is that problem still N... | habedi/stack-exchange-dataset |
42,170 | Why do these recurrences determine the number of ways of tiling a 3xN rectangle with 2x1 dominoes? | <p><a href="http://www.algorithmist.com/index.php/UVa_10918" rel="nofollow">http://www.algorithmist.com/index.php/UVa_10918</a></p>

<p>The above link is a solution to UVa 10918 Problem. The problem is based on Dynamic Programming. I am not able to understand this approach to the problem. I have coded the solut... | recurrence relation dynamic programming correctness proof | 1 | Why do these recurrences determine the number of ways of tiling a 3xN rectangle with 2x1 dominoes? -- (recurrence relation dynamic programming correctness proof)
<p><a href="http://www.algorithmist.com/index.php/UVa_10918" rel="nofollow">http://www.algorithmist.com/index.php/UVa_10918</a></p>

<p>The above link... | habedi/stack-exchange-dataset |
42,173 | Lower bound for maxima on 2D plane | <blockquote>
 <p>Given $n$ points $(x_1, y_1), \ldots, (x_n, y_n)$ on a 2-dimensional plane.<br>
 A point $(x_1, y_1)$ <em>dominates</em> $(x_2, y_2)$ if $x_1 > x_2 \land y_1 > y_2$.<br>
 A point is called a <em>maxima</em> if no other points dominate it.</p>
</blockquote>

<p>I can com... | complexity theory reference request computational geometry lower bounds | 1 | Lower bound for maxima on 2D plane -- (complexity theory reference request computational geometry lower bounds)
<blockquote>
 <p>Given $n$ points $(x_1, y_1), \ldots, (x_n, y_n)$ on a 2-dimensional plane.<br>
 A point $(x_1, y_1)$ <em>dominates</em> $(x_2, y_2)$ if $x_1 > x_2 \land y_1 > y_2$.<br>
 ... | habedi/stack-exchange-dataset |
42,175 | Is multiprocessing possible on a turing machine? | <p>I recently created a parallel implementation of the Merge Sort, in which the sorting of several groups was accomplished by different processes, and was wondering if this was theoretically possible on Turing Machine?</p>
 | turing machines parallel computing | 1 | Is multiprocessing possible on a turing machine? -- (turing machines parallel computing)
<p>I recently created a parallel implementation of the Merge Sort, in which the sorting of several groups was accomplished by different processes, and was wondering if this was theoretically possible on Turing Machine?</p>
 | habedi/stack-exchange-dataset |
42,176 | Convert RE to DFA | <p>I've been trying to convert a regular expression to a non-deterministic finite automata (NFA) first using Thompson's construction, giving:</p>

<p><img src="https://i.stack.imgur.com/Pby82.jpg" alt="enter image description here"></p>

<p>, which looks correct.</p>

<p>I am then using subset c... | regular languages automata finite automata compilers regular expressions | 1 | Convert RE to DFA -- (regular languages automata finite automata compilers regular expressions)
<p>I've been trying to convert a regular expression to a non-deterministic finite automata (NFA) first using Thompson's construction, giving:</p>

<p><img src="https://i.stack.imgur.com/Pby82.jpg" alt="enter image de... | habedi/stack-exchange-dataset |
42,179 | What is the difference between the Mogensen-Scott and the Boehm-Berarducci encoding for ADTs on the Lambda Calculus? | <p>On the Lambda Calculus, there are several different ways to represent a list. For example, one can encode it as its right fold:</p>

<pre><code>list = (λ (cons nil) (cons 1 (cons 2 (cons 3 nil))))
</code></pre>

<p>One can, instead, use <code>pair</code>, <code>false</code>, <code>fst</code> and ... | functional programming lambda calculus | 1 | What is the difference between the Mogensen-Scott and the Boehm-Berarducci encoding for ADTs on the Lambda Calculus? -- (functional programming lambda calculus)
<p>On the Lambda Calculus, there are several different ways to represent a list. For example, one can encode it as its right fold:</p>

<pre><code>list... | habedi/stack-exchange-dataset |
42,198 | Is Deciding Decidability Decidable? | <p>I am wondering if deciding the decidability of problem is a decidable problem. I am guessing not, but after initial searches I cannot find any literature on this problem.</p>
 | computability undecidability decision problem | 1 | Is Deciding Decidability Decidable? -- (computability undecidability decision problem)
<p>I am wondering if deciding the decidability of problem is a decidable problem. I am guessing not, but after initial searches I cannot find any literature on this problem.</p>
 | habedi/stack-exchange-dataset |
42,204 | Requiring at least one alldiff constraint to be satisfied converted to SAT | <p>For generating certain hard puzzles, I am trying to model a problem (ultimately) in SAT. I don't know how to do that, so I am starting with CSP because it's more expressive. In CSP, there is a global <a href="http://en.wikipedia.org/wiki/Local_consistency#Specialized_constraints" rel="nofollow">alldiff constraint</a... | modelling constraint programming constraint satisfaction | 1 | Requiring at least one alldiff constraint to be satisfied converted to SAT -- (modelling constraint programming constraint satisfaction)
<p>For generating certain hard puzzles, I am trying to model a problem (ultimately) in SAT. I don't know how to do that, so I am starting with CSP because it's more expressive. In CSP... | habedi/stack-exchange-dataset |
42,206 | Big Theta Proof: May I chose any constant? | <p>I have the following assignment:</p>

<blockquote>
 <p>Prove that $\sum^n_{i=1} i2^i \in \Theta(n2^n)$</p>
</blockquote>

<p>My current approach thus far is the following:</p>

<p>Since we need to prove $k_1 \cdot n2^n \le \sum^n_{i=1} i2^i \le k_2 n2^n$ I chose $k_1 = 1$ and $k_2 = ... | asymptotics landau notation | 1 | Big Theta Proof: May I chose any constant? -- (asymptotics landau notation)
<p>I have the following assignment:</p>

<blockquote>
 <p>Prove that $\sum^n_{i=1} i2^i \in \Theta(n2^n)$</p>
</blockquote>

<p>My current approach thus far is the following:</p>

<p>Since we need to prove $k_1 ... | habedi/stack-exchange-dataset |
42,208 | NFA-style representation of regexps which includes AND | <p>I'm looking for a regexp matching strategy that supports conjunction and which is based on an NFA-style machine. I know how to handle conjunctions using a DFA, or using Brzozowski's approach, but for various reasons, I can't use Brzozowski's technique and bump into state explosion when using a DFA.</p>

<p>... | finite automata regular expressions matching | 1 | NFA-style representation of regexps which includes AND -- (finite automata regular expressions matching)
<p>I'm looking for a regexp matching strategy that supports conjunction and which is based on an NFA-style machine. I know how to handle conjunctions using a DFA, or using Brzozowski's approach, but for various rea... | habedi/stack-exchange-dataset |
42,219 | Tackling overlearning neural network issue | <p>I'm trying to train a neural network using this sort of data (for a homework):
Number of Features : 42,
Target data : 0 or 1,
Number of Samples : 111 Individuals ( 69 Cases + 42 Controls )</p>

<p>However i'm facing an over-learning issue (the learning curve approaches the goal set, however the v... | neural networks | 1 | Tackling overlearning neural network issue -- (neural networks)
<p>I'm trying to train a neural network using this sort of data (for a homework):
Number of Features : 42,
Target data : 0 or 1,
Number of Samples : 111 Individuals ( 69 Cases + 42 Controls )</p>

<p>However i'm facing an over-learning ... | habedi/stack-exchange-dataset |
42,224 | People crossing a bridge (a proof for a greedy algorithm) | <p><strong>The problem</strong></p>

<p>Some people are crossing a bridge. Each one takes a different time to pass.</p>

<p>Assume the people are sorted by their passing time increasingly.</p>

<p>These are the conditions of crossing the bridge:</p>

<ol>
<li>only 1 or 2 people can c... | proof techniques correctness proof greedy algorithms | 1 | People crossing a bridge (a proof for a greedy algorithm) -- (proof techniques correctness proof greedy algorithms)
<p><strong>The problem</strong></p>

<p>Some people are crossing a bridge. Each one takes a different time to pass.</p>

<p>Assume the people are sorted by their passing time increasingly.... | habedi/stack-exchange-dataset |
42,226 | the convention for declaring arrays in pseudocode | <p>I have a very simple question. 
What is the right standard convention to use for declaring arrays?</p>

<p>I understand that for a simple declaration of a variable as an integer, this is the convention:</p>

<pre><code>DECLARE myVar : INTEGER
</code></pre>

<p>What about for an intege... | arrays | 1 | the convention for declaring arrays in pseudocode -- (arrays)
<p>I have a very simple question. 
What is the right standard convention to use for declaring arrays?</p>

<p>I understand that for a simple declaration of a variable as an integer, this is the convention:</p>

<pre><code>DECLARE myVar : ... | habedi/stack-exchange-dataset |
42,233 | Are there BBP formulas for all computable numbers? | <p>A BBP algorithm is a formula with the following form where $b \in \mathbb Z$, $b \ge 2$, and $p(k)$ and $q(k)$ are polynomials in $k$
$$\sum_{k=0}^{\infty}\frac{1}{b^k}\frac{p(k)}{q(k)}$$
There are known BBP formulas for many computable numbers and it is easy to prove that any number with a BBP formula is co... | computability | 1 | Are there BBP formulas for all computable numbers? -- (computability)
<p>A BBP algorithm is a formula with the following form where $b \in \mathbb Z$, $b \ge 2$, and $p(k)$ and $q(k)$ are polynomials in $k$
$$\sum_{k=0}^{\infty}\frac{1}{b^k}\frac{p(k)}{q(k)}$$
There are known BBP formulas for many computable nu... | habedi/stack-exchange-dataset |
42,235 | Doubts about infinite language decided by a turing machine | <p>Assume you have an infinite language $L$ over alphabet $\Sigma=\{a,b\}$
For example, $L=\{ax \mid x \in \Sigma^*\}$</p>

<p>Can a Turing Machine, $M$ decide this language?</p>

<p>(Generalizing, are all the recursive languages finite?)</p>

<p>In my opinion, it can, since I can enumerate ... | turing machines | 1 | Doubts about infinite language decided by a turing machine -- (turing machines)
<p>Assume you have an infinite language $L$ over alphabet $\Sigma=\{a,b\}$
For example, $L=\{ax \mid x \in \Sigma^*\}$</p>

<p>Can a Turing Machine, $M$ decide this language?</p>

<p>(Generalizing, are all the recursive ... | habedi/stack-exchange-dataset |
42,246 | comparison in speed between the processor and the hard disk | <p>I'm reading through William Stalling's operating system intrnals and design principles book. Talking about interrupts, it gives the following examples when comparing the speed of a processor and a hard disk:</p>

<blockquote>
 <p>To give a specific example, consider a PC that operates at 1 GHz, which wo... | computer architecture operating systems comparison | 1 | comparison in speed between the processor and the hard disk -- (computer architecture operating systems comparison)
<p>I'm reading through William Stalling's operating system intrnals and design principles book. Talking about interrupts, it gives the following examples when comparing the speed of a processor and a hard... | habedi/stack-exchange-dataset |
42,247 | Given n distinct numbers show that the second smallest element can be found in n + lg n - 2 comparisons in the worst case | <p>This is a question from Introduction to Algorithms by CLRS (Exercise 9-1-1).</p>

<p>The approach I thought of is </p>

<ul>
<li>compare the first two numbers, assign the lower number min and the bigger one to next_min</li>
<li>loop through numbers 3 - n,
if the number is lower than min, ... | algorithms algorithm analysis | 1 | Given n distinct numbers show that the second smallest element can be found in n + lg n - 2 comparisons in the worst case -- (algorithms algorithm analysis)
<p>This is a question from Introduction to Algorithms by CLRS (Exercise 9-1-1).</p>

<p>The approach I thought of is </p>

<ul>
<li>compare the... | habedi/stack-exchange-dataset |
42,249 | Why is NP not trivially equal to Co-NP? (a.k.a. what does Co-NP mean exactly?) | <p>I've been trying to wrap my head around Co-NP, and how it's different to NP, but I am having some trouble.</p>

<p>Co-NP is defined by <a href="http://en.wikipedia.org/wiki/Co-NP" rel="nofollow noreferrer">Wikipedia</a> as this: "A decision problem $\mathcal{X}$ is a member of <strong>co-NP</strong> if and o... | complexity theory complexity classes np co np | 1 | Why is NP not trivially equal to Co-NP? (a.k.a. what does Co-NP mean exactly?) -- (complexity theory complexity classes np co np)
<p>I've been trying to wrap my head around Co-NP, and how it's different to NP, but I am having some trouble.</p>

<p>Co-NP is defined by <a href="http://en.wikipedia.org/wiki/Co-NP"... | habedi/stack-exchange-dataset |
42,257 | Why is f(n) of class O(g(n)) in this graph? | <p>There is a lot of explanation about big O, but I'm really confused about this part.</p>

<p>Acoording to the definition of Big-O, in this function </p>

<p>$$f (n) \le c g(n), \quad \text{for } n \ge n_0$$
$f (n)$ is $O(g(n))$. </p>

<p>But a description of a function in terms of big O... | asymptotics landau notation | 1 | Why is f(n) of class O(g(n)) in this graph? -- (asymptotics landau notation)
<p>There is a lot of explanation about big O, but I'm really confused about this part.</p>

<p>Acoording to the definition of Big-O, in this function </p>

<p>$$f (n) \le c g(n), \quad \text{for } n \ge n_0$$
$f (n)$ is ... | habedi/stack-exchange-dataset |
42,261 | Why is it true that the relation R and its negation are not semi decidable? | <p>An example given for a relation R where its negation and itself are not semi-decidable was:</p>

<p>$R(x,y)$ holds iff $y = 0$ then $R_{HALT}(x)$ holds, otherwise $y = 1$ and $R_{HALT}(x)$ does not hold.</p>

<p>It's stated with the assumption that the proof is trivial (which for most it probably is)... | computability undecidability halting problem semi decidability | 1 | Why is it true that the relation R and its negation are not semi decidable? -- (computability undecidability halting problem semi decidability)
<p>An example given for a relation R where its negation and itself are not semi-decidable was:</p>

<p>$R(x,y)$ holds iff $y = 0$ then $R_{HALT}(x)$ holds, otherwise $y... | habedi/stack-exchange-dataset |
42,263 | Curry Howard correspondence and Church-Turing thesis | <p>Curry-Howard correspondence states the equivalence between logic/deduction and types/programs.</p>

<p>The Church-Turing thesis states the equivalence of some models of computation. Specifically, all computable functions can be written both on a Turing Machine and in Lambda Calculus.</p>

<p>Not all ... | computability logic functional programming church turing thesis curry howard | 1 | Curry Howard correspondence and Church-Turing thesis -- (computability logic functional programming church turing thesis curry howard)
<p>Curry-Howard correspondence states the equivalence between logic/deduction and types/programs.</p>

<p>The Church-Turing thesis states the equivalence of some models of compu... | habedi/stack-exchange-dataset |
42,266 | Nomenclature for deterministic algorithms that might fail | <p>What do you call an algorithm which is</p>

<ul>
<li>Deterministic</li>
<li>When an answer is returned, it is correct</li>
<li>For some input, the algorithm returns no answer (fails, in bounded time).</li>
</ul>

<p>Such algorithms crop up a lot in cryptographic attacks, for instance,... | algorithms terminology | 1 | Nomenclature for deterministic algorithms that might fail -- (algorithms terminology)
<p>What do you call an algorithm which is</p>

<ul>
<li>Deterministic</li>
<li>When an answer is returned, it is correct</li>
<li>For some input, the algorithm returns no answer (fails, in bounded time).</li>
<... | habedi/stack-exchange-dataset |
42,269 | Rational subsets of a monoid | <p>In "Rational Set of Commutative Monoid", S. Eilenberg and M.P. Schützenberger define the class of rational subsets of a monoid $M$ as the least class $F$ of subsets of $M$ such that satisfy the following properties: </p>

<ol>
<li><p>the empty set is in $F$;</p></li>
<li><p>Each single element set is... | formal languages regular languages | 1 | Rational subsets of a monoid -- (formal languages regular languages)
<p>In "Rational Set of Commutative Monoid", S. Eilenberg and M.P. Schützenberger define the class of rational subsets of a monoid $M$ as the least class $F$ of subsets of $M$ such that satisfy the following properties: </p>

<ol>
<li><p>th... | habedi/stack-exchange-dataset |
42,279 | Turing Machine construction | <p>How should I go about building a Turing machine for the following language:</p>

<p>$$L = \{ a^ib^j \in (a,b)^* \mid i \le j \le 2i \} $$</p>

<p>I know how to construct a Turing machine for $\{ a^nb^nc^n \mid n \in \mathbb N \}$ but don't really where to start for the one above.</p>
 | formal languages turing machines | 1 | Turing Machine construction -- (formal languages turing machines)
<p>How should I go about building a Turing machine for the following language:</p>

<p>$$L = \{ a^ib^j \in (a,b)^* \mid i \le j \le 2i \} $$</p>

<p>I know how to construct a Turing machine for $\{ a^nb^nc^n \mid n \in \mathbb N \}$ but... | habedi/stack-exchange-dataset |
42,281 | How to create this pushdown transducer? (formal languages and automata) | <p>Create a pushdown transducer that translates $a^m b^{2m}c^{m+n}$ into $b^{n-m}$, with $n\geq m \geq 0$.
How should I use the stack to remember or to compute how many characters of c to read? And how can I output $b^{n-m}$?</p>

<p>I have also tried to simplify the problem and firstly create a pushdown au... | formal languages automata pushdown automata | 1 | How to create this pushdown transducer? (formal languages and automata) -- (formal languages automata pushdown automata)
<p>Create a pushdown transducer that translates $a^m b^{2m}c^{m+n}$ into $b^{n-m}$, with $n\geq m \geq 0$.
How should I use the stack to remember or to compute how many characters of c to read? A... | habedi/stack-exchange-dataset |
42,282 | pumping lemma for $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ | <p>Using pumping lemma, how can I prove that $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ is not regular?.</p>

<p>If I choose $w= a^m b^m c^m$ and pump up with $i=2$, if have $a^m=1 b^m c^m$ but the string is still in the language. Any hint?</p>
 | regular languages pumping lemma | 1 | pumping lemma for $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ -- (regular languages pumping lemma)
<p>Using pumping lemma, how can I prove that $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ is not regular?.</p>

<p>If I choose $w= a^m b^m c^m$ and pump up with $i=2$, if have $a^m=1 b^m c^m$ but the string is stil... | habedi/stack-exchange-dataset |
42,283 | What is the decidable language in $P/poly$ but not in $P$? | <p>Except for the undecidable unaries I have no idea if there is anything in the gap between $P/poly$ and $P$</p>
 | complexity theory polynomial time circuits | 1 | What is the decidable language in $P/poly$ but not in $P$? -- (complexity theory polynomial time circuits)
<p>Except for the undecidable unaries I have no idea if there is anything in the gap between $P/poly$ and $P$</p>
 | habedi/stack-exchange-dataset |
42,296 | Compare vs Radix | <p>Is it better to use comparison or radix sort to sort a long sequences of java int array? </p>

<p>I know that I should probably use mergesort (NlogN) for comparison sort, since it is one of the fastest and compare that to LSD or MSD. I thought about how for extremely large N, the logarithm would be larger th... | sorting comparison radix sort | 1 | Compare vs Radix -- (sorting comparison radix sort)
<p>Is it better to use comparison or radix sort to sort a long sequences of java int array? </p>

<p>I know that I should probably use mergesort (NlogN) for comparison sort, since it is one of the fastest and compare that to LSD or MSD. I thought about how for... | habedi/stack-exchange-dataset |
42,302 | Can I find a clique with more than 2 nodes in a bipartite graph? | <p>As in the title, is it possible to find a clique with more than 2 nodes in a bipartite graph?</p>
 | graphs clique | 1 | Can I find a clique with more than 2 nodes in a bipartite graph? -- (graphs clique)
<p>As in the title, is it possible to find a clique with more than 2 nodes in a bipartite graph?</p>
 | habedi/stack-exchange-dataset |
42,304 | speed, cost and capacity tradoff | <p>I'm reading William Stalling's Operating System Design and internals. Talking about memory, the following tradeoff was introduced:</p>

<blockquote>
 <p>As might be expected, there is a tradeoff among the three key characteristics
 of memory: namely, capacity, access time, and cost. A variety of te... | computer architecture memory hardware | 1 | speed, cost and capacity tradoff -- (computer architecture memory hardware)
<p>I'm reading William Stalling's Operating System Design and internals. Talking about memory, the following tradeoff was introduced:</p>

<blockquote>
 <p>As might be expected, there is a tradeoff among the three key characteristi... | habedi/stack-exchange-dataset |
42,307 | prove that a language is context free given a regular language | <p>R is a regular language over $\Sigma=\{0,1\}$<br>
$Sub(R)=\{0^i1^j \mid \exists w\in R.|w|=i-j \}$<br>
I need to prove that Sub(R) is context free.</p>

<p>I know that the <a href="http://en.wikipedia.org/wiki/Right_quotient" rel="nofollow" title="Right quotient">quotient of a context free language w... | formal languages regular languages context free closure properties | 1 | prove that a language is context free given a regular language -- (formal languages regular languages context free closure properties)
<p>R is a regular language over $\Sigma=\{0,1\}$<br>
$Sub(R)=\{0^i1^j \mid \exists w\in R.|w|=i-j \}$<br>
I need to prove that Sub(R) is context free.</p>

<p>I know tha... | habedi/stack-exchange-dataset |
42,312 | Rearranging function in 'Theorems for free' | <p>I'm reading Wadler's '<a href="http://ttic.uchicago.edu/~dreyer/course/papers/wadler.pdf" rel="nofollow">Theorems for free</a>'. In section 3.5 he states that $m_{AA}(I_A)$ is a rearranging (i. e. injective) function. $I_A$ is the identity function on the type A.
$$m : \forall X.\forall Y. (X \rightarrow Y) \rig... | type theory | 1 | Rearranging function in 'Theorems for free' -- (type theory)
<p>I'm reading Wadler's '<a href="http://ttic.uchicago.edu/~dreyer/course/papers/wadler.pdf" rel="nofollow">Theorems for free</a>'. In section 3.5 he states that $m_{AA}(I_A)$ is a rearranging (i. e. injective) function. $I_A$ is the identity function on the ... | habedi/stack-exchange-dataset |
42,324 | Memory Hierarchy and storing data in caches | <p>Question: How many 32 bit integers can be stored in a 16 bit cache line.
Answer: 4</p>

<p>can somebody please explain for me why the answer is 4 i did not understand the reason and i think they should give us more given like the number of blocks in the cache..</p>
 | cpu cache | 1 | Memory Hierarchy and storing data in caches -- (cpu cache)
<p>Question: How many 32 bit integers can be stored in a 16 bit cache line.
Answer: 4</p>

<p>can somebody please explain for me why the answer is 4 i did not understand the reason and i think they should give us more given like the number of blocks... | habedi/stack-exchange-dataset |
42,330 | Occurrences notation in "Compiling Pattern Matching to Good Decision Trees" | <p>From <a href="http://moscova.inria.fr/~maranget/papers/ml05e-maranget.pdf" rel="nofollow">Compiling Pattern Matching to Good Decision Trees</a> (Luc Maranget, <em>Proceedings of ML '08</em>, pp. 35–46. ACM, 2008.)</p>

<blockquote>
 <p>We also consider the usual <em>occurrences</em>. Occ... | functional programming | 1 | Occurrences notation in "Compiling Pattern Matching to Good Decision Trees" -- (functional programming)
<p>From <a href="http://moscova.inria.fr/~maranget/papers/ml05e-maranget.pdf" rel="nofollow">Compiling Pattern Matching to Good Decision Trees</a> (Luc Maranget, <em>Proceedings of ML '08</em>, pp. 35&ndash... | habedi/stack-exchange-dataset |
42,332 | Are there two kinds of polynomial hierarchy collapses? | <p>It seems to me that there are two different situations which get called ``PH collapse", </p>

<p>(1) That $\exists i \geq 1$ s.t $\Sigma_i ^p = \Sigma_{i+1}^p$<br>
(2) That $\exists i \geq 1$ s.t $\Sigma_i^p = \Pi_i^p$</p>

<ul>
<li>Are these two different independent situations? </li>
</... | complexity theory logic | 1 | Are there two kinds of polynomial hierarchy collapses? -- (complexity theory logic)
<p>It seems to me that there are two different situations which get called ``PH collapse", </p>

<p>(1) That $\exists i \geq 1$ s.t $\Sigma_i ^p = \Sigma_{i+1}^p$<br>
(2) That $\exists i \geq 1$ s.t $\Sigma_i^p = \Pi_i^p$</p... | habedi/stack-exchange-dataset |
42,347 | Proving regular languages are closed under a form of interleaving | <p>I've got the following definitions:</p>

<p>$$\mathrm{Interleave}\,(x,y) = \{w_1\dots w_n\mid w_i\in\{x_i,y_i\} \text{ for }i=1, \dots, |x|\}$$</p>

<p>when $x$, $y$ and $w$ are words with $|x|=|y|$ and $w_i$ means the $i$-th letter in $w$.</p>

<p>$$\mathrm{Interleave}\,(L_1,L_2)\ \ = \!\!\... | regular languages finite automata closure properties | 1 | Proving regular languages are closed under a form of interleaving -- (regular languages finite automata closure properties)
<p>I've got the following definitions:</p>

<p>$$\mathrm{Interleave}\,(x,y) = \{w_1\dots w_n\mid w_i\in\{x_i,y_i\} \text{ for }i=1, \dots, |x|\}$$</p>

<p>when $x$, $y$ and $w$ are... | habedi/stack-exchange-dataset |
42,352 | Seemingly non sequitur in proof | <p>I'm trying to understand a small proof in an article about computing lumpability on Markov chains. There is a small detail that I cannot understand, i.e. I don't think it follows from the argument.</p>

<p>The article is <a href="http://link.springer.com/chapter/10.1007%2F978-3-642-12002-2_4" rel="nofollow">... | correctness proof weighted graphs markov chains | 1 | Seemingly non sequitur in proof -- (correctness proof weighted graphs markov chains)
<p>I'm trying to understand a small proof in an article about computing lumpability on Markov chains. There is a small detail that I cannot understand, i.e. I don't think it follows from the argument.</p>

<p>The article is <a ... | habedi/stack-exchange-dataset |
42,357 | What does "refuting random 3CNF" formulas mean? | <p>Intuitively, recall what 3CNF formulas mean:</p>

<p>Its a boolean formula with conjunctive normal form (i.e. formula of ANDs of clauses with ORs) with no more than three variables per conjunct.</p>

<p>I was reading a <a href="http://papers.nips.cc/paper/4905-more-data-speeds-up-training-time-in-lea... | complexity theory logic | 1 | What does "refuting random 3CNF" formulas mean? -- (complexity theory logic)
<p>Intuitively, recall what 3CNF formulas mean:</p>

<p>Its a boolean formula with conjunctive normal form (i.e. formula of ANDs of clauses with ORs) with no more than three variables per conjunct.</p>

<p>I was reading a <a hr... | habedi/stack-exchange-dataset |
42,358 | Are there any theorems/formulas that apply to the height of comparison trees? | <p>I have been drawing some binary comparison trees, which correspond to compares made to sort an array, and I was wondering if there is any formula to determine the height of a comparison tree for an array of N values, in Sedgewick's algorithms 4th ed. book for N = 3, the height of a comparison tree is 3. </p>
&#x... | complexity theory data structures sorting binary trees | 1 | Are there any theorems/formulas that apply to the height of comparison trees? -- (complexity theory data structures sorting binary trees)
<p>I have been drawing some binary comparison trees, which correspond to compares made to sort an array, and I was wondering if there is any formula to determine the height of a comp... | habedi/stack-exchange-dataset |
42,359 | set complement and superset | <p><code>If 'S is a set complement of S, then a set complement of a superset of S' is a subset of S.</code></p>

<p>Just want to verify that above is true just based on the definition of set complement and superset.</p>
 | sets | 1 | set complement and superset -- (sets)
<p><code>If 'S is a set complement of S, then a set complement of a superset of S' is a subset of S.</code></p>

<p>Just want to verify that above is true just based on the definition of set complement and superset.</p>
 | habedi/stack-exchange-dataset |
42,371 | Kruskal's and Prim's algorithm | <p>Does Kruskal's and Prim's algorithm work on directed graphs? I want the two algorithms to find a minimum spanning tree. For further enlightenment, I would like to know what other problems Kruskal's and Prim's can solve. So far, I only know they can solve minimum spanning trees. If it turns out there are an infinite ... | minimum spanning tree | 1 | Kruskal's and Prim's algorithm -- (minimum spanning tree)
<p>Does Kruskal's and Prim's algorithm work on directed graphs? I want the two algorithms to find a minimum spanning tree. For further enlightenment, I would like to know what other problems Kruskal's and Prim's can solve. So far, I only know they can solve mini... | habedi/stack-exchange-dataset |
42,376 | bounded length CoNP proof | <p><strong>Question:</strong> 
Let $A \subseteq $ {0,1}$^* $ be a language which satisfies $|A \cap ${0,1}$^n|=n^3 $ for all $n\ge 10$ Prove that $A \in NP$ implies $A \in coNP$.</p>

<p><strong>Thoughts</strong>
I've been having difficulty with this problem. My idea is somehow showing that each set of ... | complexity theory time complexity | 1 | bounded length CoNP proof -- (complexity theory time complexity)
<p><strong>Question:</strong> 
Let $A \subseteq $ {0,1}$^* $ be a language which satisfies $|A \cap ${0,1}$^n|=n^3 $ for all $n\ge 10$ Prove that $A \in NP$ implies $A \in coNP$.</p>

<p><strong>Thoughts</strong>
I've been having difficult... | habedi/stack-exchange-dataset |
42,379 | Huffman tree generation if the frequency is same for all words | <p>Can a valid Huffman tree be generated if the frequency of words is same for all of them?</p>

<p>Example :</p>

<pre><code>Value | Frequency
--------------------
Google | 2
Yahoo | 2
Microsoft | 2
Amazon | 2 
</code></pre>
 | machine learning | 1 | Huffman tree generation if the frequency is same for all words -- (machine learning)
<p>Can a valid Huffman tree be generated if the frequency of words is same for all of them?</p>

<p>Example :</p>

<pre><code>Value | Frequency
--------------------
Google | 2
Yahoo | 2
Micros... | habedi/stack-exchange-dataset |
42,389 | Which optimization algorithm would you recommend for this small multidimensional problem? | <p>Which algorithm would be suitable for finding or estimating the vector 
$$\mathbf{s}_{opt}=\begin{bmatrix}
s_1 & \cdots & s_N
\end{bmatrix}=\arg\max_{\mathbf{s}}\sum_{n=1}^{N}p_{s_n,n}$$
under the constraint
$$\sum_{n=1}^{N}l_{s_n,n}\leq L_{max}$$
given known values for the integer $... | algorithms optimization discrete mathematics | 1 | Which optimization algorithm would you recommend for this small multidimensional problem? -- (algorithms optimization discrete mathematics)
<p>Which algorithm would be suitable for finding or estimating the vector 
$$\mathbf{s}_{opt}=\begin{bmatrix}
s_1 & \cdots & s_N
\end{bmatrix}=\arg\max_{\mathb... | habedi/stack-exchange-dataset |
42,396 | Language of walks in a grid – context-free? | <p>Consider the infinite two-dimensional grid with integer co-ordinates. A walk in the grid can be represented by a string over the alphabet $\{u,d,l,r\}$, where the letters stand for moving one square up, down, left and right, respectively. </p>

<p>Now consider the langauge of all strings representing closed ... | context free finite automata formal grammars | 1 | Language of walks in a grid – context-free? -- (context free finite automata formal grammars)
<p>Consider the infinite two-dimensional grid with integer co-ordinates. A walk in the grid can be represented by a string over the alphabet $\{u,d,l,r\}$, where the letters stand for moving one square up, down, left and right... | habedi/stack-exchange-dataset |
42,397 | How do you produce a CNF from a circular graph with colouring? | <p>If you had a circular graph e.g. A->B->C->D->E->A, and a legal coloring system with 3 colours (e.g. Red, Green Blue), where each node is assigned a colour and no node can be connected to another node of the same colour, what is the easiest way go about producing a Conjunctive Normal Form of node states (e.g. AR mean... | graphs boolean algebra colorings | 1 | How do you produce a CNF from a circular graph with colouring? -- (graphs boolean algebra colorings)
<p>If you had a circular graph e.g. A->B->C->D->E->A, and a legal coloring system with 3 colours (e.g. Red, Green Blue), where each node is assigned a colour and no node can be connected to another node of the same colo... | habedi/stack-exchange-dataset |
42,400 | Why is one traversal sufficient for the Kuhn's maximal matching problem algorithm? | <p>In Kuhn's algorithm for the maximum bipartite matching problem we iterate through the vertices of one partite set and try to build the increasing chain, starting with the current vertex. Once the traversal is completed, we claim that the maximal matching is found. But why don't we need to check again the vertices fo... | graphs bipartite matching | 1 | Why is one traversal sufficient for the Kuhn's maximal matching problem algorithm? -- (graphs bipartite matching)
<p>In Kuhn's algorithm for the maximum bipartite matching problem we iterate through the vertices of one partite set and try to build the increasing chain, starting with the current vertex. Once the travers... | habedi/stack-exchange-dataset |
42,403 | Proving a language to be Recursively Enumerable? | <p>I know to prove a language to be Recursively Enumerable, it is ideal to represent a Turing machine for it. Let L be set of strings which have alphabet {u,d,l,r}, where u is up 1, d is down 1, etc. L is representing paths on the Cartesian plane which can begin and end at any point so say begin at (1,3) and end back a... | graphs computability turing machines recursion theory | 1 | Proving a language to be Recursively Enumerable? -- (graphs computability turing machines recursion theory)
<p>I know to prove a language to be Recursively Enumerable, it is ideal to represent a Turing machine for it. Let L be set of strings which have alphabet {u,d,l,r}, where u is up 1, d is down 1, etc. L is represe... | habedi/stack-exchange-dataset |
42,429 | Simplying this regular expression | <p>I am trying to prove (without converting it into Automata, through just simplification) that the following two regular expressions are equal:</p>

<p>$ (\epsilon + 0^*1^+0)^* = \epsilon + (0+1)^*10 $</p>

<p>here is what I have got so far:</p>

<p>$$ (\epsilon + 0^*1^+0)^* = \\
 (0^*1^+0... | regular expressions | 1 | Simplying this regular expression -- (regular expressions)
<p>I am trying to prove (without converting it into Automata, through just simplification) that the following two regular expressions are equal:</p>

<p>$ (\epsilon + 0^*1^+0)^* = \epsilon + (0+1)^*10 $</p>

<p>here is what I have got so far:</p... | habedi/stack-exchange-dataset |
42,435 | Combinatorial optimization problem - What would you call this? | <p>I'm trying to solve an optimization problem which can be described as follows.</p>

<ul>
<li>There are four sets objects. For simplicity, let's call them :
<ol>
<li>Apples</li>
<li>Oranges</li>
<li>Pears</li>
<li>Lemons</li>
</ol></li>
<li>The sets can contain unequal numbers ... | algorithms optimization combinatorics | 1 | Combinatorial optimization problem - What would you call this? -- (algorithms optimization combinatorics)
<p>I'm trying to solve an optimization problem which can be described as follows.</p>

<ul>
<li>There are four sets objects. For simplicity, let's call them :
<ol>
<li>Apples</li>
<li>Orange... | habedi/stack-exchange-dataset |
42,436 | Basic question about backjumping in SAT solvers | <p>I am reading "Formalization and Implementation of Modern SAT Solvers", by Filip Marić.</p>

<p>My question is about how backjumping is defined. In an example [1], there is a conflict clause C equal to</p>

<p>[-1,-2,-3]</p>

<p>that has already been explained and learned. The decision trail i... | satisfiability sat solvers backtracking | 1 | Basic question about backjumping in SAT solvers -- (satisfiability sat solvers backtracking)
<p>I am reading "Formalization and Implementation of Modern SAT Solvers", by Filip Marić.</p>

<p>My question is about how backjumping is defined. In an example [1], there is a conflict clause C equal to</p>

<p... | habedi/stack-exchange-dataset |
42,438 | Can DFA with output (definition?) match expressiveness of NFA with unique output? | <p>For a deterministic finite automaton (DFA), some output tasks are easy when done in one direction, but difficult (or impossible?) when done in the reverse direction. Let's take a simple example of outputting a word lower-case, or upper-case, depending on a control sequence included in the input. So the task</p>
... | finite automata regular expressions | 1 | Can DFA with output (definition?) match expressiveness of NFA with unique output? -- (finite automata regular expressions)
<p>For a deterministic finite automaton (DFA), some output tasks are easy when done in one direction, but difficult (or impossible?) when done in the reverse direction. Let's take a simple example ... | habedi/stack-exchange-dataset |
42,439 | Undecidable definition of pure function? | <p>I am trying to come up with a formal definition for functional purity in a simple programming language (think JavaScript). What I've got so far is this:</p>

<blockquote>
 <p><strong>DEFINITION</strong>: A statement is <em>impure</em> if</p>
 
 <ul>
 <li>it is an assignment, unless it ass... | formal languages logic undecidability recursion | 1 | Undecidable definition of pure function? -- (formal languages logic undecidability recursion)
<p>I am trying to come up with a formal definition for functional purity in a simple programming language (think JavaScript). What I've got so far is this:</p>

<blockquote>
 <p><strong>DEFINITION</strong>: A stat... | habedi/stack-exchange-dataset |
42,440 | simulation of PDA with turing machine | <p>How to simulate a non-deterministic PDA with a turing machine? </p>
 | formal languages turing machines | 1 | simulation of PDA with turing machine -- (formal languages turing machines)
<p>How to simulate a non-deterministic PDA with a turing machine? </p>
 | habedi/stack-exchange-dataset |
42,443 | Relationship between formal system and formal languages | <p>In a course of computer science it is common to study the hierarchy of formal languages, grammars, automata and Turing machines. I wonder what is the relationship of these objects with formal systems.</p>

<p>For example, lambda calculus is said to be a formal system. Would its grammar also be considered a ... | formal languages formal grammars | 1 | Relationship between formal system and formal languages -- (formal languages formal grammars)
<p>In a course of computer science it is common to study the hierarchy of formal languages, grammars, automata and Turing machines. I wonder what is the relationship of these objects with formal systems.</p>

<p>For ex... | habedi/stack-exchange-dataset |
42,451 | Cycles in hardness of ST-CON for the class NL | <p>It seems to me that the problem of $s$, $t$ connectivity in a DAG should still be NL-Complete.</p>

<p>I am aware that ST-CON without the DAG restriction is complete for NL, so obviously the DAG restriction is still in NL, but I believe hardness follows as well:</p>

<p>For a turing machine that runs... | algorithms complexity theory reductions | 1 | Cycles in hardness of ST-CON for the class NL -- (algorithms complexity theory reductions)
<p>It seems to me that the problem of $s$, $t$ connectivity in a DAG should still be NL-Complete.</p>

<p>I am aware that ST-CON without the DAG restriction is complete for NL, so obviously the DAG restriction is still in... | habedi/stack-exchange-dataset |
42,460 | What does least fix point and greatest fix point mean in Safety games | <p>In safety games there are these mathematical notation about greatest fix points and least fix points but I don't get it. How would we describe them plain English without mathematical symbols.</p>
 | terminology formal methods model checking mu calculus | 1 | What does least fix point and greatest fix point mean in Safety games -- (terminology formal methods model checking mu calculus)
<p>In safety games there are these mathematical notation about greatest fix points and least fix points but I don't get it. How would we describe them plain English without mathematical symbo... | habedi/stack-exchange-dataset |
42,464 | Are there any compression algorithms based on PI? | <p>What we know is that π is infinite and quite likely it <a href="https://math.stackexchange.com/q/216343/36904">contains every possible finite string of digits</a> (<a href="https://en.wikipedia.org/wiki/Disjunctive_sequence" rel="noreferrer">disjunctive sequence</a>).</p>

<p>I've seen recently some prototyp... | algorithms data compression mathematical programming | 1 | Are there any compression algorithms based on PI? -- (algorithms data compression mathematical programming)
<p>What we know is that π is infinite and quite likely it <a href="https://math.stackexchange.com/q/216343/36904">contains every possible finite string of digits</a> (<a href="https://en.wikipedia.org/wiki/Disjun... | habedi/stack-exchange-dataset |
42,474 | Converting a NFA to its equivalent regular expression | <p>I'm new to regular expressions and I'm currently working on some exercises on converting DFA's and NFA's into their equivalent regular expressions.</p>

<p>I have the following NFA:
<img src="https://i.stack.imgur.com/80G5U.png" alt="enter image description here"></p>

<p>I'm using the <strong>st... | formal languages automata regular expressions | 1 | Converting a NFA to its equivalent regular expression -- (formal languages automata regular expressions)
<p>I'm new to regular expressions and I'm currently working on some exercises on converting DFA's and NFA's into their equivalent regular expressions.</p>

<p>I have the following NFA:
<img src="https://... | habedi/stack-exchange-dataset |
42,475 | Prove Language Is Union of Fninitely Many Arithmetic Progressions | <p>So, you see in the image the question and its answer (proof below the black line).</p>

<p>I get the entire proof until the last formula. It basically says that if length of a string is larger than number of states then one or more states need to be re-visited (at least one more times). <br />
Formula fo... | formal languages regular languages | 1 | Prove Language Is Union of Fninitely Many Arithmetic Progressions -- (formal languages regular languages)
<p>So, you see in the image the question and its answer (proof below the black line).</p>

<p>I get the entire proof until the last formula. It basically says that if length of a string is larger than numbe... | habedi/stack-exchange-dataset |
42,486 | Probabilistic algorithm with two-sided error | <p>I am currently studying probabilistic algorithms and came across three major complexity classes:</p>

<ul>
<li>BPP: worst-case polynomial time, two-sided error</li>
<li>RP: worst-case polynomial time, one-sided error</li>
<li>ZPP: average-case polynomial time, no error</li>
</ul>

<p>... | complexity theory time complexity probability theory probabilistic algorithms | 1 | Probabilistic algorithm with two-sided error -- (complexity theory time complexity probability theory probabilistic algorithms)
<p>I am currently studying probabilistic algorithms and came across three major complexity classes:</p>

<ul>
<li>BPP: worst-case polynomial time, two-sided error</li>
<li>RP: ... | habedi/stack-exchange-dataset |
42,493 | Courses that give good insight on the nature of a Computer Science major? | <p>I'm a business informatics student so I am taking introduction to computer science and computer programming, and so far I hate everything that has to do with this major aside from these 2 courses which I am really enjoying so far, so I am considering changing to a computer science and engineering major, but I want t... | education | 1 | Courses that give good insight on the nature of a Computer Science major? -- (education)
<p>I'm a business informatics student so I am taking introduction to computer science and computer programming, and so far I hate everything that has to do with this major aside from these 2 courses which I am really enjoying so fa... | habedi/stack-exchange-dataset |
42,499 | Real world applications for Steiner Tree Problem? | <p>Are there real-world applications of the Steiner Tree Problem (STP)?</p>

<p>I understand that VSLI chip design is a good application of the STP. Are there any other examples of real world problems that people can suggest of that could be formulated in terms of the STP?</p>

<p>Background: I am begi... | graphs reference request optimization combinatorics applied theory | 1 | Real world applications for Steiner Tree Problem? -- (graphs reference request optimization combinatorics applied theory)
<p>Are there real-world applications of the Steiner Tree Problem (STP)?</p>

<p>I understand that VSLI chip design is a good application of the STP. Are there any other examples of real wor... | habedi/stack-exchange-dataset |
42,502 | Is 2-SAT with XOR-relations NP-complete? | <p>I'm wondering if there is a polynomial algorithm for "2-SAT with XOR-relations". Both 2-SAT and XOR-SAT are in P, but is its combination?</p>

<p>Example Input:</p>

<ul>
<li><p>2-SAT part: <code>(a or !b) and (b or c) and (b or d)</code></p></li>
<li><p>XOR part : <code>(a xor b xor c xor 1)... | np complete satisfiability xor 2 sat | 1 | Is 2-SAT with XOR-relations NP-complete? -- (np complete satisfiability xor 2 sat)
<p>I'm wondering if there is a polynomial algorithm for "2-SAT with XOR-relations". Both 2-SAT and XOR-SAT are in P, but is its combination?</p>

<p>Example Input:</p>

<ul>
<li><p>2-SAT part: <code>(a or !b) and (b o... | habedi/stack-exchange-dataset |
42,503 | Chandy/Misra dining philosophers solution | <p>So based on the Chandy/Misra section in this Wikipedia <a href="http://en.wikipedia.org/wiki/Dining_philosophers_problem#Chandy.2FMisra_solution" rel="nofollow noreferrer">article</a> we've got 5 philosophers numbered P1-P5.</p>
<p>Based on this quote:</p>
<blockquote>
<p>For every pair of philosophers c... | algorithms operating systems concurrency synchronization | 1 | Chandy/Misra dining philosophers solution -- (algorithms operating systems concurrency synchronization)
<p>So based on the Chandy/Misra section in this Wikipedia <a href="http://en.wikipedia.org/wiki/Dining_philosophers_problem#Chandy.2FMisra_solution" rel="nofollow noreferrer">article</a> we've got 5 philosophers numb... | habedi/stack-exchange-dataset |
42,506 | What is difference between Buffering and Spooling with respect to Operating System | <p>I have googled a lot to find the answer and found some links like <a href="https://techbask.wordpress.com/2012/03/05/spooling-buffering-caching-whats-the-difference/" rel="nofollow">this</a>, <a href="http://www.answers.com/Q/What_is_the_difference_between_spooling_and_buffering" rel="nofollow">this</a> and <a href=... | operating systems | 1 | What is difference between Buffering and Spooling with respect to Operating System -- (operating systems)
<p>I have googled a lot to find the answer and found some links like <a href="https://techbask.wordpress.com/2012/03/05/spooling-buffering-caching-whats-the-difference/" rel="nofollow">this</a>, <a href="http://www... | habedi/stack-exchange-dataset |
42,508 | Paxos: Responding to Reordered Prepare Requests | <p>In the paper, Paxos Made Simple, a proposer asks an acceptor to respond to a prepare request with:</p>

<blockquote>
 <p>A promise never to again accept a proposal numbered less than n, and the proposal with the highest number less than n that it has accepted.</p>
</blockquote>

<p>Therefore... | distributed systems | 1 | Paxos: Responding to Reordered Prepare Requests -- (distributed systems)
<p>In the paper, Paxos Made Simple, a proposer asks an acceptor to respond to a prepare request with:</p>

<blockquote>
 <p>A promise never to again accept a proposal numbered less than n, and the proposal with the highest number less... | habedi/stack-exchange-dataset |
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