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 |
|---|---|---|---|---|---|---|
62,393 | Machine Learning to predict the Halting Problem | <p>I seem to recall an academic paper from some years ago which used machine learning (possibly genetic or evolutionary programming) to predict whether a Turing Machine would halt.</p>

<p>By predict, I mean the standard notion in ML: minimize the error on some validation set. For simplicity, let's assume that ... | machine learning halting problem | 1 | Machine Learning to predict the Halting Problem -- (machine learning halting problem)
<p>I seem to recall an academic paper from some years ago which used machine learning (possibly genetic or evolutionary programming) to predict whether a Turing Machine would halt.</p>

<p>By predict, I mean the standard notio... | habedi/stack-exchange-dataset |
62,395 | Change in Training Accuracy | <p>I am solving a problem in the Kaggle learn section : <a href="https://www.kaggle.com/c/facial-keypoints-detection" rel="nofollow">https://www.kaggle.com/c/facial-keypoints-detection</a></p>

<p>The problem involves detecting facial keypoints in a 96x96 image, some 30 features are detected. It is a supervised... | machine learning neural networks | 1 | Change in Training Accuracy -- (machine learning neural networks)
<p>I am solving a problem in the Kaggle learn section : <a href="https://www.kaggle.com/c/facial-keypoints-detection" rel="nofollow">https://www.kaggle.com/c/facial-keypoints-detection</a></p>

<p>The problem involves detecting facial keypoints i... | habedi/stack-exchange-dataset |
62,396 | Why can PDAs only write one symbol to the stack according to this definition? | <p>This is in regards to the definition 2.13 of non-deterministic PDA given in Theory of Computation 3rd ed. by Michael Sipser.</p>

<p>The transition is defined as 
$$
\delta: Q\times \Sigma_\varepsilon \times \Gamma_\varepsilon \to P(Q\times \Gamma_\varepsilon)
$$
where $Q$ is the set of state... | automata pushdown automata | 1 | Why can PDAs only write one symbol to the stack according to this definition? -- (automata pushdown automata)
<p>This is in regards to the definition 2.13 of non-deterministic PDA given in Theory of Computation 3rd ed. by Michael Sipser.</p>

<p>The transition is defined as 
$$
\delta: Q\times \Sigma_\v... | habedi/stack-exchange-dataset |
62,401 | Is it possible to get Nth Fibonacci number in sublinear time? | <p>I was researching the topic of Fibonacci numbers and asymptotic complexity of generating them. Coming across a seemingly paradoxical conclusion, I've decided to check out if you agree with my explanation.</p>

<ol>
<li><p>The naive algorithms runs in $O(n)$, if we ignore the cost of addition.</p></li>&#x... | algorithm analysis time complexity asymptotics | 1 | Is it possible to get Nth Fibonacci number in sublinear time? -- (algorithm analysis time complexity asymptotics)
<p>I was researching the topic of Fibonacci numbers and asymptotic complexity of generating them. Coming across a seemingly paradoxical conclusion, I've decided to check out if you agree with my explanation... | habedi/stack-exchange-dataset |
62,420 | Collection of APX-hard problems | <p>Everyone knows "Garey & Johnson", which is my go-to reference whenever I need a problem to transform from for an NP-hardness proof. However I recently find myself in need of an APX-hardness proof, and I wonder if there is a similar (and more up to date..?) collection of problems that have been shown to be APX-ha... | complexity theory reference request time complexity complexity classes | 1 | Collection of APX-hard problems -- (complexity theory reference request time complexity complexity classes)
<p>Everyone knows "Garey & Johnson", which is my go-to reference whenever I need a problem to transform from for an NP-hardness proof. However I recently find myself in need of an APX-hardness proof, and I wo... | habedi/stack-exchange-dataset |
62,444 | Length of the solution calculation in Breadth-first | <p>I'm trying to figure out how to calculate the route cost on this graph (it's the missionaries and cannibals game)</p>

<p>I have my definition as:</p>

<pre><code>Mi = Missionary on the initial side, C = Cannibal on the initial side, B = Boat [I = Boat in the Initial Side, F = Boat on the Final Side]... | graphs algorithm analysis runtime analysis search algorithms graph traversal | 1 | Length of the solution calculation in Breadth-first -- (graphs algorithm analysis runtime analysis search algorithms graph traversal)
<p>I'm trying to figure out how to calculate the route cost on this graph (it's the missionaries and cannibals game)</p>

<p>I have my definition as:</p>

<pre><code>Mi =... | habedi/stack-exchange-dataset |
62,448 | When is ε-removal from a CFG idempotent? | <p>For which context-free grammars is it idempotent to remove $\varepsilon$-productions? Given that there are multiple rewriting algorithms which preserve language and leave the grammar without $\varepsilon$-productions (apart from $S \to \varepsilon$ iff $\varepsilon \in L(G)$), is this sensitive to the choice of alg... | algorithms context free formal grammars normal forms | 1 | When is ε-removal from a CFG idempotent? -- (algorithms context free formal grammars normal forms)
<p>For which context-free grammars is it idempotent to remove $\varepsilon$-productions? Given that there are multiple rewriting algorithms which preserve language and leave the grammar without $\varepsilon$-productions ... | habedi/stack-exchange-dataset |
62,487 | Stabilization of lower approximation | <p>Let $f:\mathbb{N} \to \mathbb{R}$ be a lower semicomputable function, i.e. there exists a recursive function $g:\mathbb{N}\times \mathbb{N} \to \mathbb{Q}$ s.t.</p>

<p>$$\forall x \in \mathbb{N} \quad \lim_{k \to \infty} g(k,x) = f(x) \qquad\qquad (1)$$
$$\forall x \in \mathbb{N} \quad g(k,x) \le g(k+1,... | computability approximation | 1 | Stabilization of lower approximation -- (computability approximation)
<p>Let $f:\mathbb{N} \to \mathbb{R}$ be a lower semicomputable function, i.e. there exists a recursive function $g:\mathbb{N}\times \mathbb{N} \to \mathbb{Q}$ s.t.</p>

<p>$$\forall x \in \mathbb{N} \quad \lim_{k \to \infty} g(k,x) = f(x) \qq... | habedi/stack-exchange-dataset |
62,490 | DFA's with more than one initial state | <p>( This may be related to <a href="https://cs.stackexchange.com/questions/24491/nfas-with-more-than-one-initial-state">NFAs with more than one initial state</a> )</p>

<p>Consider a dfa $M$ with alphabet $\Sigma$ and states $Q$, typically also characterized by a specific initial state $q_0\in Q$. As the above... | finite automata | 1 | DFA's with more than one initial state -- (finite automata)
<p>( This may be related to <a href="https://cs.stackexchange.com/questions/24491/nfas-with-more-than-one-initial-state">NFAs with more than one initial state</a> )</p>

<p>Consider a dfa $M$ with alphabet $\Sigma$ and states $Q$, typically also charac... | habedi/stack-exchange-dataset |
62,497 | Greedy algorithm for a variation of the $k$-center problem | <p>This is a variation of the well-known <a href="https://en.wikipedia.org/wiki/Facility_location_problem" rel="nofollow noreferrer"><span class="math-container">$k$</span>-center</a> problem with priorities given on the vertices.</p>
<blockquote>
<p><strong>Problem:</strong></p>
<p>Let <span class="math-co... | approximation greedy algorithms | 1 | Greedy algorithm for a variation of the $k$-center problem -- (approximation greedy algorithms)
<p>This is a variation of the well-known <a href="https://en.wikipedia.org/wiki/Facility_location_problem" rel="nofollow noreferrer"><span class="math-container">$k$</span>-center</a> problem with priorities given on the ver... | habedi/stack-exchange-dataset |
62,505 | Genetic Algorithms: Converge to best solution for one, few or many environments? | <p>Let's say we take someone's garden (A) as the environment. We want a robot to pick up a series of eggs that chickens have laid in the garden, while covering as little ground as possible (those heavy rover tracks damage the turf, you know). So we evolve a solution whereby the genes representing the robot's <em>behavi... | algorithms artificial intelligence genetic algorithms | 1 | Genetic Algorithms: Converge to best solution for one, few or many environments? -- (algorithms artificial intelligence genetic algorithms)
<p>Let's say we take someone's garden (A) as the environment. We want a robot to pick up a series of eggs that chickens have laid in the garden, while covering as little ground as ... | habedi/stack-exchange-dataset |
62,514 | Safe way to explicitly define new types instead of using Algebraic data types for my functional language | <p><strong>Question:</strong></p>

<p>As I'm working on a Hindley-Milner typed lambda calculus, in order to make it usable I need to add some types such as list and pairs. The way I currently do it is, I have an <code>unsafe</code> keyword that lets me explicitly set the type of a global function that tells the... | type theory functional programming type checking language design | 1 | Safe way to explicitly define new types instead of using Algebraic data types for my functional language -- (type theory functional programming type checking language design)
<p><strong>Question:</strong></p>

<p>As I'm working on a Hindley-Milner typed lambda calculus, in order to make it usable I need to add ... | habedi/stack-exchange-dataset |
62,526 | Complexity of finding a perfect matching in directed graphs | <p>To the best of my knowledge, finding a perfect matching in an undirected graph is NP-hard. But is this also the case for directed and possibly cyclic graphs?</p>

<p>I guess there are two possibilities to define whether two edges are incident to each other, which would also result in two possibilities to def... | complexity theory np complete np hard | 1 | Complexity of finding a perfect matching in directed graphs -- (complexity theory np complete np hard)
<p>To the best of my knowledge, finding a perfect matching in an undirected graph is NP-hard. But is this also the case for directed and possibly cyclic graphs?</p>

<p>I guess there are two possibilities to d... | habedi/stack-exchange-dataset |
62,527 | Streaming parsing algorithms | <p>A <em>parser</em> is a procedure which decides if an input belongs to a certain language and produces a witness in the form of a parse tree.</p>

<p>Let a <em>streaming parser</em> be a parser which for any prefix $u$ can produce a <em>partial</em> parse tree corresponding to the productions that <em>must</e... | algorithms reference request parsers streaming algorithm | 1 | Streaming parsing algorithms -- (algorithms reference request parsers streaming algorithm)
<p>A <em>parser</em> is a procedure which decides if an input belongs to a certain language and produces a witness in the form of a parse tree.</p>

<p>Let a <em>streaming parser</em> be a parser which for any prefix $u$ ... | habedi/stack-exchange-dataset |
62,544 | Question about the definition of strings that GNFA's accept | <p>In Sipser's "Introduction to the Theory of Computation" it states "A GNFA accepts a string $w$ in $Σ^{*}$ if $w = w_1 w_2 · · · w_k$ , where each $w_i$ is in $Σ^{*}$". </p>

<p>However, wouldn't a more precise definition be "A GNFA accepts a string $w$ in $Σ^{*}$ if $w = w_1 w_2 · · · w_k$ , where each $w_i$... | automata finite automata | 1 | Question about the definition of strings that GNFA's accept -- (automata finite automata)
<p>In Sipser's "Introduction to the Theory of Computation" it states "A GNFA accepts a string $w$ in $Σ^{*}$ if $w = w_1 w_2 · · · w_k$ , where each $w_i$ is in $Σ^{*}$". </p>

<p>However, wouldn't a more precise definitio... | habedi/stack-exchange-dataset |
62,550 | constructing a DFA and a regular expression for a given regular language | <p>This is the question 1.12 from Introduction to the Theory of Computation 3rd Edition by Michael Sipser. The questions says,</p>

<blockquote>
 <p>Let $D=\{w\mid w$ contains an even number of $\texttt{a}$'s and an odd
 number of $\texttt{b}$'s and does not contain the substring
 $\texttt{ab}$}.... | regular languages finite automata regular expressions | 1 | constructing a DFA and a regular expression for a given regular language -- (regular languages finite automata regular expressions)
<p>This is the question 1.12 from Introduction to the Theory of Computation 3rd Edition by Michael Sipser. The questions says,</p>

<blockquote>
 <p>Let $D=\{w\mid w$ contains... | habedi/stack-exchange-dataset |
62,552 | Is it possible to simplify $O(A \times B \times C + A^B)$ into $O(A^B)$ | <p>I am wondering if it is possible to simplify $O(A \times B \times C + A^B)$ into $O(A^B)$, i.e. omit the left part. $A$, $B$, and $C$ are all independent from each other.</p>

<p>Personally, I think that the simplification is possible. $O(A \times B \times C)$ is a polynomial growth, and (I think) it can be ... | asymptotics landau notation | 1 | Is it possible to simplify $O(A \times B \times C + A^B)$ into $O(A^B)$ -- (asymptotics landau notation)
<p>I am wondering if it is possible to simplify $O(A \times B \times C + A^B)$ into $O(A^B)$, i.e. omit the left part. $A$, $B$, and $C$ are all independent from each other.</p>

<p>Personally, I think that ... | habedi/stack-exchange-dataset |
62,559 | Computer vision: object detection with labels that are single coordinates | <p>Are there papers in the literature that address the following object detection task ?</p>

<p>The task can be described as follows:</p>

<ul>
<li><p>Given a set of images, the labels are just coordinates (x,y) that represent the object locations that we wish to detect. A coordinate is not necessa... | machine learning image processing computer vision data mining | 1 | Computer vision: object detection with labels that are single coordinates -- (machine learning image processing computer vision data mining)
<p>Are there papers in the literature that address the following object detection task ?</p>

<p>The task can be described as follows:</p>

<ul>
<li><p>Given a... | habedi/stack-exchange-dataset |
62,560 | Simplified Maximum Diversity Problem | <p>The Maximum Diversity Problem calls for choosing $m$ items from a list of $n$ items, such that the diversity defined as some metric distance between items is maximized.</p>

<p>I have a simpler problem, which I was hoping I could solve in a simpler manner. In my case I have a list of $n$ items each with a ce... | algorithms optimization | 1 | Simplified Maximum Diversity Problem -- (algorithms optimization)
<p>The Maximum Diversity Problem calls for choosing $m$ items from a list of $n$ items, such that the diversity defined as some metric distance between items is maximized.</p>

<p>I have a simpler problem, which I was hoping I could solve in a si... | habedi/stack-exchange-dataset |
62,561 | Using persistence on a constant database | <p>I'm quite new to understanding persistent data structures, so bear with me.</p>

<p>Consider some database with data of the form $(\text{id}, d_1, d_2)$. The last two could e.g. mean production data and sales date, respectively. The database is constant, i.e. we will not be adding or removing data points.</... | data structures persistent data structure | 1 | Using persistence on a constant database -- (data structures persistent data structure)
<p>I'm quite new to understanding persistent data structures, so bear with me.</p>

<p>Consider some database with data of the form $(\text{id}, d_1, d_2)$. The last two could e.g. mean production data and sales date, respec... | habedi/stack-exchange-dataset |
62,569 | Is there a paradigm for composing "incremental update" functions in a pure dataflow style? | <p>I don't know the correct terminology for asking this question, so I'll describe it with lots of words instead, bear with me.</p>

<p><strong>Background</strong>, just so we're on the same page: Programs often contain caches - a time/memory tradeoff. A common programmer's mistake is to forget to update a cach... | terminology reference request functional programming programming paradigms | 1 | Is there a paradigm for composing "incremental update" functions in a pure dataflow style? -- (terminology reference request functional programming programming paradigms)
<p>I don't know the correct terminology for asking this question, so I'll describe it with lots of words instead, bear with me.</p>

<p><stro... | habedi/stack-exchange-dataset |
62,583 | Comparing the sizes of two search spaces by comparing their numbers of possibilities | <p>I am trying to solve an optimisation problem and come up with two Integer Linear Programming models. For each model, I am able to find a function that calculate the number of possibilities based on different variables, e.g. problem sizes.</p>

<p>I cannot directly conclude that one model has a smaller search... | complexity theory linear programming integer programming | 1 | Comparing the sizes of two search spaces by comparing their numbers of possibilities -- (complexity theory linear programming integer programming)
<p>I am trying to solve an optimisation problem and come up with two Integer Linear Programming models. For each model, I am able to find a function that calculate the numbe... | habedi/stack-exchange-dataset |
62,591 | Bounded bin covering problem | <p>This all seems fairly related to the knapsack problem, bin packing and the subset sum problem, but I can't find the appropriate problem name.</p>

<p>I have a multiset $S$ of $n$ (not necessarily unique) integers in the range $\{1,2,\dots,k-1\}$.</p>

<p>The problem is to partition this multiset in s... | complexity theory partitions | 1 | Bounded bin covering problem -- (complexity theory partitions)
<p>This all seems fairly related to the knapsack problem, bin packing and the subset sum problem, but I can't find the appropriate problem name.</p>

<p>I have a multiset $S$ of $n$ (not necessarily unique) integers in the range $\{1,2,\dots,k-1\}$.... | habedi/stack-exchange-dataset |
62,594 | Why we cannot prove that a computable function is total? | <p>We know that we cannot find an algorithm that would prove that a computable function "f" is total if it IS total. How come?</p>

<p>When a function is total, it must have a proof (derived from soundness and correctness of logic). And proof is a finite sequence of symbols, so why does simple enumeration throu... | computability undecidability decision problem | 1 | Why we cannot prove that a computable function is total? -- (computability undecidability decision problem)
<p>We know that we cannot find an algorithm that would prove that a computable function "f" is total if it IS total. How come?</p>

<p>When a function is total, it must have a proof (derived from soundnes... | habedi/stack-exchange-dataset |
62,600 | Deciding which logical proposition is stronger | <p>I am studying propositional logic and I am trying to solve some exercise related to the following definition:</p>

<p>Given two logical propositions $\alpha$ and $\beta$, we say that $\alpha$ is stronger than $\beta$ if and only if $(\alpha \implies \beta)$ is a tautology. Determine which of the two proposit... | logic propositional logic | 1 | Deciding which logical proposition is stronger -- (logic propositional logic)
<p>I am studying propositional logic and I am trying to solve some exercise related to the following definition:</p>

<p>Given two logical propositions $\alpha$ and $\beta$, we say that $\alpha$ is stronger than $\beta$ if and only if... | habedi/stack-exchange-dataset |
62,606 | Role of network layer in Routers | <p>I just started reading communication networks.<br>
Now, routers contain the network layer, data link control layer and physical layer. <br>
That being true I am confused as to why the network layer is required or to be more specific what is its function.<br>
In "Computer Networks A top-down approach", it... | computer networks | 1 | Role of network layer in Routers -- (computer networks)
<p>I just started reading communication networks.<br>
Now, routers contain the network layer, data link control layer and physical layer. <br>
That being true I am confused as to why the network layer is required or to be more specific what is its function... | habedi/stack-exchange-dataset |
62,617 | What will be the time complexity of this function (C++) and why? | <p>The function:</p>

<pre><code>double sum1(std::vector& v)
{ 
 if (v.empty()) {
 return 0.0;
 }
 for(size_t i = 0; i < v.size() - 1; ++i) {
 std::sort(v.begin()+i, v.end());
 v[i+1] += v[i];
 }
 return v.back();
}
</code... | complexity theory time complexity | 1 | What will be the time complexity of this function (C++) and why? -- (complexity theory time complexity)
<p>The function:</p>

<pre><code>double sum1(std::vector& v)
{ 
 if (v.empty()) {
 return 0.0;
 }
 for(size_t i = 0; i < v.size() - 1; ++i) {
 std::sor... | habedi/stack-exchange-dataset |
62,625 | Proof Knuth S algortihm correctness | <p>In the programming pearls book by Jon Bentley, there is a section about the problem of finding a random set of m integers from range 0 to n-1 integers. To do so they use Knuth's algorithm given by the following code (see also <a href="http://rosettacode.org/wiki/Knuth%27s_algorithm_S" rel="nofollow">here</a>). How c... | algorithms correctness proof randomness sampling | 1 | Proof Knuth S algortihm correctness -- (algorithms correctness proof randomness sampling)
<p>In the programming pearls book by Jon Bentley, there is a section about the problem of finding a random set of m integers from range 0 to n-1 integers. To do so they use Knuth's algorithm given by the following code (see also <... | habedi/stack-exchange-dataset |
62,626 | Why is this not a valid Red-Black tree? | <p>I'm having some difficulty understanding the rules for valid red-black tree. 
If my understanding is correct there are 4 rules that a tree has to follow to be a red-black tree.</p>

<ol>
<li>Every node has a color either red or black.</li>
<li>Root of tree is always black.</li>
<li>There are ... | data structures binary trees search trees balanced search trees | 1 | Why is this not a valid Red-Black tree? -- (data structures binary trees search trees balanced search trees)
<p>I'm having some difficulty understanding the rules for valid red-black tree. 
If my understanding is correct there are 4 rules that a tree has to follow to be a red-black tree.</p>

<ol>
<li>E... | habedi/stack-exchange-dataset |
62,627 | An integer linear program | <p>I have the following problem: </p>

<blockquote>
 <p>Given positive integers $a, b, c, d, n$, compute the maximum possible value (which is garuanteed to be less than $10^9$) of the function $$f(x,y) = cx + dy$$ where the only pairs $(x, y)$ that are considered for which $x$ and $y$ are positive integers... | optimization linear programming integer programming | 1 | An integer linear program -- (optimization linear programming integer programming)
<p>I have the following problem: </p>

<blockquote>
 <p>Given positive integers $a, b, c, d, n$, compute the maximum possible value (which is garuanteed to be less than $10^9$) of the function $$f(x,y) = cx + dy$$ where the ... | habedi/stack-exchange-dataset |
62,642 | Prove that PP is closed under complement | <p>I found <a href="https://en.wikipedia.org/wiki/PP_(complexity)#Proof_that_PP_is_closed_under_complement" rel="nofollow">this proof</a> in Wikipedia, but one of the most important steps in it doesn't make any sense to me. I'll explain:</p>

<blockquote>
 <p>By the definition of PP there is a polynomial-... | complexity theory closure properties complexity classes probabilistic algorithms | 1 | Prove that PP is closed under complement -- (complexity theory closure properties complexity classes probabilistic algorithms)
<p>I found <a href="https://en.wikipedia.org/wiki/PP_(complexity)#Proof_that_PP_is_closed_under_complement" rel="nofollow">this proof</a> in Wikipedia, but one of the most important steps in it... | habedi/stack-exchange-dataset |
62,647 | Link utilization of sliding window protocol | <p>Before I ask my doubt I would like to state that problem which led me to my doubt. It can also serve as a good example scenario.</p>

<blockquote>
 <p>A $20\ Kbps$ satellite link has a propagation delay of $400\ ms$. The transmitter employs the "Sliding Window protocol" scheme with Window Size set to $1... | computer networks communication protocols | 1 | Link utilization of sliding window protocol -- (computer networks communication protocols)
<p>Before I ask my doubt I would like to state that problem which led me to my doubt. It can also serve as a good example scenario.</p>

<blockquote>
 <p>A $20\ Kbps$ satellite link has a propagation delay of $400\ m... | habedi/stack-exchange-dataset |
62,650 | AI: Heuristic function A* search | <p>I have an assignment in my university where I have to implement Uniform Cost Search and A* Search.</p>

<p>We have an input which includes a map and queries.</p>

<p>The map is weighted, directed graph, represented by an adjacency matrix. The queries include Uniform Cost Search and A* Search queries ... | algorithms graphs search algorithms shortest path heuristics | 1 | AI: Heuristic function A* search -- (algorithms graphs search algorithms shortest path heuristics)
<p>I have an assignment in my university where I have to implement Uniform Cost Search and A* Search.</p>

<p>We have an input which includes a map and queries.</p>

<p>The map is weighted, directed graph,... | habedi/stack-exchange-dataset |
62,655 | Are there parallel matrix exponentiation algorithms that are more efficient than sequential multiplication? | <p>One is required to find power (positive integer) of matrix of real numbers. There are lots of efficient matrix multiplication algorithms (e.g. some parallel algorithms are <a href="http://parallelcomp.uw.hu/ch08lev1sec2.html" rel="noreferrer">Cannon's, DNS</a>) but are there algorithms that are intended exactly for ... | algorithms parallel computing efficiency matrices numerical algorithms | 1 | Are there parallel matrix exponentiation algorithms that are more efficient than sequential multiplication? -- (algorithms parallel computing efficiency matrices numerical algorithms)
<p>One is required to find power (positive integer) of matrix of real numbers. There are lots of efficient matrix multiplication algorit... | habedi/stack-exchange-dataset |
62,658 | Partitioning an undirected, unweighted, square planar graph paths that join certain pairs of nodes | <p>I am trying to find a way to efficiently solve a puzzle that I play a lot by turning it into a graph partitioning problem (which is basically is in its actual form). I know that generally, graph partitioning problems are considered NP-hard or even NP-complete, but considering the unique constraints of the input grap... | algorithms graphs search problem partitions planar graphs | 1 | Partitioning an undirected, unweighted, square planar graph paths that join certain pairs of nodes -- (algorithms graphs search problem partitions planar graphs)
<p>I am trying to find a way to efficiently solve a puzzle that I play a lot by turning it into a graph partitioning problem (which is basically is in its act... | habedi/stack-exchange-dataset |
62,666 | Finding minimal and complete test sets for circuits | <p>I have been playing around with analysis of circuits and am trying to generate test vectors. In order to exercise the circuit in the manner I require, I need a vector that includes every change in the circuit's inputs where only 1 input toggles, but in order to be efficient, it must include each change only once and... | optimization circuits software testing | 1 | Finding minimal and complete test sets for circuits -- (optimization circuits software testing)
<p>I have been playing around with analysis of circuits and am trying to generate test vectors. In order to exercise the circuit in the manner I require, I need a vector that includes every change in the circuit's inputs whe... | habedi/stack-exchange-dataset |
62,668 | Are turing machines and formal languages the same mathematical object? | <p>Turing's objective while building his concept was to formalise how humans do abstract reasoning.</p>

<p>Now correct me if I am wrong but that reasoning seems just an exercise where you manipulate a set of formal statements i.e. strings with no semantics attached to it.</p>

<p>So if Turing machines ... | formal languages turing machines | 1 | Are turing machines and formal languages the same mathematical object? -- (formal languages turing machines)
<p>Turing's objective while building his concept was to formalise how humans do abstract reasoning.</p>

<p>Now correct me if I am wrong but that reasoning seems just an exercise where you manipulate a s... | habedi/stack-exchange-dataset |
62,674 | Does NP = coNP imply the collapse of PH to level 1? | <p>It was already asked <a href="https://cs.stackexchange.com/questions/19389/does-np-conp-imply-p-np">here</a> whether NP=coNP implies P=NP. I'd like to approach that question from the perspective of the Polynomial-Time Hierarchy.</p>

<p>Here is a theorem from Oded Goldreich's "Computational Complexity" (Prop... | complexity theory time complexity complexity classes | 1 | Does NP = coNP imply the collapse of PH to level 1? -- (complexity theory time complexity complexity classes)
<p>It was already asked <a href="https://cs.stackexchange.com/questions/19389/does-np-conp-imply-p-np">here</a> whether NP=coNP implies P=NP. I'd like to approach that question from the perspective of the Polyn... | habedi/stack-exchange-dataset |
62,679 | What is this fraction-like "discrete mathematics"–style notation used for formal rules? | <p>In the paper <a href="http://arxiv.org/abs/1608.03960" rel="nofollow noreferrer">"A Conflict-Free Replicated JSON Datatype"</a>, I encountered this notation for formally defining "rules":</p>

<p><img src="https://i.stack.imgur.com/WuNO1.png" alt="Some of the "rules" shown in the paper][1"></p>
... | semantics notation formal methods operational semantics | 1 | What is this fraction-like "discrete mathematics"–style notation used for formal rules? -- (semantics notation formal methods operational semantics)
<p>In the paper <a href="http://arxiv.org/abs/1608.03960" rel="nofollow noreferrer">"A Conflict-Free Replicated JSON Datatype"</a>, I encountered this notation for formall... | habedi/stack-exchange-dataset |
62,697 | Can random suitless $52$ playing card data be compressed to approach, match, or even beat entropy encoding storage? If so, how? | <p>I have real data I am using for a simulated card game. I am only interested in the ranks of the cards, not the suits. However it is a standard $52$ card deck so there are only $4$ of each rank possible in the deck. The deck is shuffled well for each hand, and then I output the entire deck to a file. So there are... | data compression | 1 | Can random suitless $52$ playing card data be compressed to approach, match, or even beat entropy encoding storage? If so, how? -- (data compression)
<p>I have real data I am using for a simulated card game. I am only interested in the ranks of the cards, not the suits. However it is a standard $52$ card deck so ther... | habedi/stack-exchange-dataset |
62,698 | Does a simple calculator require an operating system? | <p>I don't mean a TI-84 type calculator, and I also do not mean a simple calculator app on your phone.</p>

<p>Does a basic scientific calculator require an operating system?</p>
 | operating systems | 1 | Does a simple calculator require an operating system? -- (operating systems)
<p>I don't mean a TI-84 type calculator, and I also do not mean a simple calculator app on your phone.</p>

<p>Does a basic scientific calculator require an operating system?</p>
 | habedi/stack-exchange-dataset |
62,714 | Examples of NP Complete key exchange algorithms | <p>There's a number of questions on the internet (this site and others; e.g. <a href="https://cs.stackexchange.com/questions/356/why-hasnt-there-been-an-encryption-algorithm-that-is-based-on-the-known-np-hard">Why hasn't there been an encryption algorithm that is based on the known NP-Hard problems?</a> ) discussin... | complexity theory np complete cryptography | 1 | Examples of NP Complete key exchange algorithms -- (complexity theory np complete cryptography)
<p>There's a number of questions on the internet (this site and others; e.g. <a href="https://cs.stackexchange.com/questions/356/why-hasnt-there-been-an-encryption-algorithm-that-is-based-on-the-known-np-hard">Why hasn't... | habedi/stack-exchange-dataset |
62,725 | Many-one reducibility: why $A = \{1\}$ is not a counterexample to $\forall A : A \leq_m A \cup \{0\}$? | <p>I'm looking at a textbook exercise that asks to prove or give a counterexample that $\forall A : A \leq_m A \cup \{0\}$.</p>

<p>$A \leq_m B$ <a href="https://books.google.com/books?id=wAstOUE36kcC&lpg=PP1&pg=PA158" rel="nofollow">is defined</a> as:</p>

<p>$\exists f$ total, computable s.t. ... | computability reductions sets | 1 | Many-one reducibility: why $A = \{1\}$ is not a counterexample to $\forall A : A \leq_m A \cup \{0\}$? -- (computability reductions sets)
<p>I'm looking at a textbook exercise that asks to prove or give a counterexample that $\forall A : A \leq_m A \cup \{0\}$.</p>

<p>$A \leq_m B$ <a href="https://books.google... | habedi/stack-exchange-dataset |
62,732 | When do the gradients exist in a Reinforcement Learning setting? | <p>I am getting properly stuck into reinforcement learning and <a href="http://www.ias.tu-darmstadt.de/uploads/Publications/Kober_IJRR_2013.pdf" rel="nofollow">I am currently reading the review paper by Kober et al. (2013)</a>.</p>

<p>And there is one constant feature that I cannot get my head around, but whic... | reinforcement learning | 1 | When do the gradients exist in a Reinforcement Learning setting? -- (reinforcement learning)
<p>I am getting properly stuck into reinforcement learning and <a href="http://www.ias.tu-darmstadt.de/uploads/Publications/Kober_IJRR_2013.pdf" rel="nofollow">I am currently reading the review paper by Kober et al. (2013)</a>.... | habedi/stack-exchange-dataset |
62,739 | Reference request: Introduction to reinforcement learning with hand calculation examples | <p>For me, the most difficulty when it comes to learning about reinforcement learning is that there is not much to learn in the sense that without running some algorithm, it is very difficult to get a sense of how abstract RL framework is done in practice. </p>

<p>This is in contrast to a lot of the stuff you ... | optimization reference request machine learning mathematical analysis reinforcement learning | 1 | Reference request: Introduction to reinforcement learning with hand calculation examples -- (optimization reference request machine learning mathematical analysis reinforcement learning)
<p>For me, the most difficulty when it comes to learning about reinforcement learning is that there is not much to learn in the sense... | habedi/stack-exchange-dataset |
62,740 | What is the space complexity of function $f(x) = \sum_{i=1}^x g(i)$ where g(n) is O(n)? | <p>What is the space complexity of function $f(x) = \sum_{i=1}^x g(i)$ where g(n) is O(n)?</p>

<p>Is it O(n) because the maximum stack size is n, or is it O($n^2$) because there are $n(n+1)/2$ memory references?</p>
 | algorithms space complexity | 1 | What is the space complexity of function $f(x) = \sum_{i=1}^x g(i)$ where g(n) is O(n)? -- (algorithms space complexity)
<p>What is the space complexity of function $f(x) = \sum_{i=1}^x g(i)$ where g(n) is O(n)?</p>

<p>Is it O(n) because the maximum stack size is n, or is it O($n^2$) because there are $n(n+1)/... | habedi/stack-exchange-dataset |
62,746 | Can Tree Transducers Self-Interpret? | <p>Is it possible for MSO graph/tree transducers to reflect themselves, namely to create an interpreter of tree/graph transducers using tree/graph transducers? If yes, I'll be happy for some design guidelines.</p>
 | programming languages interpreters transducers | 1 | Can Tree Transducers Self-Interpret? -- (programming languages interpreters transducers)
<p>Is it possible for MSO graph/tree transducers to reflect themselves, namely to create an interpreter of tree/graph transducers using tree/graph transducers? If yes, I'll be happy for some design guidelines.</p>
 | habedi/stack-exchange-dataset |
62,748 | Finite automaton - language acceptance | <p>In the book "The New Turing Omnibus", an excercise reads as the follows: </p>

<blockquote>
 <p>"Show that no finite automaton can accept the language consisting of
 all words of the form $a^n b^n, n=1,2,3,...$ The formula represents
 $n$ a's followed by $n$ b's."</p>
</blockquote>
&#x... | formal languages automata finite automata | 1 | Finite automaton - language acceptance -- (formal languages automata finite automata)
<p>In the book "The New Turing Omnibus", an excercise reads as the follows: </p>

<blockquote>
 <p>"Show that no finite automaton can accept the language consisting of
 all words of the form $a^n b^n, n=1,2,3,...$ Th... | habedi/stack-exchange-dataset |
62,759 | Check if a given polynomial is primitive | <p>I try to estimate error detection capabilities of arbitrary CRC polynomials. One important criteria is if a given polynomial is primitive. So I need an algorithm to check that. My goal is to write a C or C++ routine.</p>

<p>Unfortunately I only found analytical solutions for the problem on the web. </p>
... | numerical algorithms polynomials crc | 1 | Check if a given polynomial is primitive -- (numerical algorithms polynomials crc)
<p>I try to estimate error detection capabilities of arbitrary CRC polynomials. One important criteria is if a given polynomial is primitive. So I need an algorithm to check that. My goal is to write a C or C++ routine.</p>

<p>U... | habedi/stack-exchange-dataset |
62,765 | Relation between "syntax" and "grammar" in CS | <p>I do sure that "grammar" and "syntax" is two different thing in CS, e.g</p>

<blockquote>
 <p>Syntax of Java language is defined by a context-free grammar.</p>
</blockquote>

<p>My question are</p>

<p>What is different in definitions of "grammar" and "syntax" in CS?</p>

<p>... | terminology context free formal grammars programming languages syntax | 1 | Relation between "syntax" and "grammar" in CS -- (terminology context free formal grammars programming languages syntax)
<p>I do sure that "grammar" and "syntax" is two different thing in CS, e.g</p>

<blockquote>
 <p>Syntax of Java language is defined by a context-free grammar.</p>
</blockquote>
&... | habedi/stack-exchange-dataset |
62,769 | Find ellipsoid that contains intersection of an ellipsoid and a hyperplane | <p>I have an $n$-dimensional ellipsoid $E$ and a hyperplane $H$. This hyperplane cuts $E$ into two parts: $E_1$ and $E_2$ (whose disjoint union is $E$). I want to find another ellipsoid $E'$ that has minimal hyper-volume and contains $E_1$. Is there an efficient algorithm to do this?</p>

<p>My first thought w... | optimization computational geometry approximation | 1 | Find ellipsoid that contains intersection of an ellipsoid and a hyperplane -- (optimization computational geometry approximation)
<p>I have an $n$-dimensional ellipsoid $E$ and a hyperplane $H$. This hyperplane cuts $E$ into two parts: $E_1$ and $E_2$ (whose disjoint union is $E$). I want to find another ellipsoid $E'$... | habedi/stack-exchange-dataset |
62,779 | Formal way to model or describe distributed systems architecture | <p>I've been tasked to create the systems architecture for a distributed system.</p>

<p>One approach to designing this system is to pick systems architecture patterns, and then evaluate different technologies that implement those architectural patterns.</p>

<p>For example, a particular architecture mi... | distributed systems | 1 | Formal way to model or describe distributed systems architecture -- (distributed systems)
<p>I've been tasked to create the systems architecture for a distributed system.</p>

<p>One approach to designing this system is to pick systems architecture patterns, and then evaluate different technologies that impleme... | habedi/stack-exchange-dataset |
62,782 | Sum of size of distinct set of descendants $d$ distance from a node $u$, over all $u$ and $d$ is $\mathcal{O}(n\sqrt{n})$ | <p>Let's consider a rooted tree $T$ of $n$ nodes. For any node $u$ of the tree, define $L(u,d)$ to be the list of descendants of $u$ that are distance $d$ away from $u$. Let $|L(u,d)|$ denote the number of nodes that are present in the list $L(u,d)$.</p>

<p>Prove that the sum of $|L(u,d)|$ over all distinct li... | trees upper bound | 1 | Sum of size of distinct set of descendants $d$ distance from a node $u$, over all $u$ and $d$ is $\mathcal{O}(n\sqrt{n})$ -- (trees upper bound)
<p>Let's consider a rooted tree $T$ of $n$ nodes. For any node $u$ of the tree, define $L(u,d)$ to be the list of descendants of $u$ that are distance $d$ away from $u$. Let $... | habedi/stack-exchange-dataset |
62,787 | Relationship between PP and PH | <p>Toda's theorem says that $PH \subset P^{PP}$. Does this imply any relationship between $PH$ and $PP$ that does not involve oracles? Does it imply either that $PH \subset PP$ or that $PP \subset PH$? Is it known or conjectured whether either of those hold?</p>
 | complexity theory complexity classes | 1 | Relationship between PP and PH -- (complexity theory complexity classes)
<p>Toda's theorem says that $PH \subset P^{PP}$. Does this imply any relationship between $PH$ and $PP$ that does not involve oracles? Does it imply either that $PH \subset PP$ or that $PP \subset PH$? Is it known or conjectured whether either ... | habedi/stack-exchange-dataset |
62,789 | Query regarding the structure of Graph over All (known/unknown) NPC Problems? | <p>Let us consider the set of all NPComplete problems. Since every problem in the set is Reducible to/from at least one known NPComplete problem, lets create a directed Graph with the following conventions:</p>

<ol>
<li>If a problem B is Reducible from Problem A, create an edge from A to B. We assume an or... | complexity theory | 1 | Query regarding the structure of Graph over All (known/unknown) NPC Problems? -- (complexity theory)
<p>Let us consider the set of all NPComplete problems. Since every problem in the set is Reducible to/from at least one known NPComplete problem, lets create a directed Graph with the following conventions:</p>

... | habedi/stack-exchange-dataset |
62,801 | Are vector clocks useful in centralized systems? | <p>Vectors clocks seem to be a common way to synchronize the partial ordering of events in a distributed, peer-to-peer, system across all clients.</p>

<p>Is there any benefit to using them in a centralized system, where one node in the system has the power to order all events anyway, to order events? If one co... | distributed systems clocks | 1 | Are vector clocks useful in centralized systems? -- (distributed systems clocks)
<p>Vectors clocks seem to be a common way to synchronize the partial ordering of events in a distributed, peer-to-peer, system across all clients.</p>

<p>Is there any benefit to using them in a centralized system, where one node i... | habedi/stack-exchange-dataset |
62,812 | Path in directed, weighted, cyclic graph with total distance closest to D? | <p><strong>Input</strong>: Directed, weighted, cyclic graph <em>G</em>. Two distinct vertices in that graph, <em>A</em> and <em>B</em>, where there exists a path from <em>A</em> to <em>B</em>. A distance <em>d</em>.</p>

<p><strong>Output</strong>: A path between <em>A</em> and <em>B</em> with distance closest ... | graphs optimization weighted graphs hamiltonian path | 1 | Path in directed, weighted, cyclic graph with total distance closest to D? -- (graphs optimization weighted graphs hamiltonian path)
<p><strong>Input</strong>: Directed, weighted, cyclic graph <em>G</em>. Two distinct vertices in that graph, <em>A</em> and <em>B</em>, where there exists a path from <em>A</em> to <em>B<... | habedi/stack-exchange-dataset |
62,814 | Auction where each bidder bids on a bundle of items | <p>Is there some optimal solution in an auction where each bidder bids on a bundle of items?</p>
 | algorithms optimization bipartite matching | 1 | Auction where each bidder bids on a bundle of items -- (algorithms optimization bipartite matching)
<p>Is there some optimal solution in an auction where each bidder bids on a bundle of items?</p>
 | habedi/stack-exchange-dataset |
62,820 | Why do Tarjan's and Kosaraju's algorithms for finding strongly connected components have the same running-time complexity? | <p>I followed an explanation of <a href="http://www.geeksforgeeks.org/strongly-connected-components/" rel="nofollow">Kosaraju's</a> and <a href="http://www.geeksforgeeks.org/tarjan-algorithm-find-strongly-connected-components/" rel="nofollow">Tarjan's</a> strongly-connected components algorithms, and they say that both... | algorithm analysis asymptotics runtime analysis | 1 | Why do Tarjan's and Kosaraju's algorithms for finding strongly connected components have the same running-time complexity? -- (algorithm analysis asymptotics runtime analysis)
<p>I followed an explanation of <a href="http://www.geeksforgeeks.org/strongly-connected-components/" rel="nofollow">Kosaraju's</a> and <a href=... | habedi/stack-exchange-dataset |
62,827 | How to Determine Existence of Turing Reducible Languages? | <p>Are <em>finite</em> and <em>recursive</em> instances of $L$ possible with the following constraints?</p>

<p>$\text{L $\subseteq$ {0,1}*}$ and $L \leq HALT \leq \overline L$ where $\overline L = \{\text{ x $\in$ {0,1}* : x $\notin$ L }\}$. </p>

<p><strong>NOTE:</strong> Raphael and Yuval kindly poi... | computability reductions | 1 | How to Determine Existence of Turing Reducible Languages? -- (computability reductions)
<p>Are <em>finite</em> and <em>recursive</em> instances of $L$ possible with the following constraints?</p>

<p>$\text{L $\subseteq$ {0,1}*}$ and $L \leq HALT \leq \overline L$ where $\overline L = \{\text{ x $\in$ {0,1}* : ... | habedi/stack-exchange-dataset |
62,847 | Draw a 5 × 5 grid graph. How many edges does the n × n grid graph have? | <p>just confuse with this problem. What is n × n grid graph and how many edges it has?</p>
 | graphs square grid | 1 | Draw a 5 × 5 grid graph. How many edges does the n × n grid graph have? -- (graphs square grid)
<p>just confuse with this problem. What is n × n grid graph and how many edges it has?</p>
 | habedi/stack-exchange-dataset |
62,850 | Find a string that covers many sets of binary strings with don't-cares | <p>Consider $N$ sets $S_1,S_2,....,S_{N}$ of binary strings with don't-cares ($X$) with $|S_i| = n$ and the length of all strings is $m$.<br>
In my application, $N=1000$, $n=100$ and $m=500$.</p>

<p>I have to find atleast one binary string with all set bits (either $1$ or $0$) that is compatible with at le... | algorithms strings heuristics enumeration | 1 | Find a string that covers many sets of binary strings with don't-cares -- (algorithms strings heuristics enumeration)
<p>Consider $N$ sets $S_1,S_2,....,S_{N}$ of binary strings with don't-cares ($X$) with $|S_i| = n$ and the length of all strings is $m$.<br>
In my application, $N=1000$, $n=100$ and $m=500$.</p>&#x... | habedi/stack-exchange-dataset |
62,871 | Compression of a text that contains only the 5 first letters of the alphabet? | <p>So the question is: "Imagine the compression of a text written only with the first 5 characters of the alphabet (a, b, c, d, e). Knowing that their apparition's frequency is 1)e, 2)a, 3)c, 4)d, 5)b, code the letters on the minimum bits possible."</p>

<p>so here's how I did start: </p>

<p>We have 5 ... | data compression huffman coding | 1 | Compression of a text that contains only the 5 first letters of the alphabet? -- (data compression huffman coding)
<p>So the question is: "Imagine the compression of a text written only with the first 5 characters of the alphabet (a, b, c, d, e). Knowing that their apparition's frequency is 1)e, 2)a, 3)c, 4)d, 5)b, cod... | habedi/stack-exchange-dataset |
62,872 | Why can you push multiple symbols on a PDA stack at once? | <p>I'm really new to learning about PDA's and stuff, i understand that on a edge between 2 nodes you'll have something like this a,b->c. This means:</p>

<p>if a is in the beginning of your string and b is on top of your stack you can </p>

<ul>
<li>remove a from your string (the one you run through... | automata pushdown automata | 1 | Why can you push multiple symbols on a PDA stack at once? -- (automata pushdown automata)
<p>I'm really new to learning about PDA's and stuff, i understand that on a edge between 2 nodes you'll have something like this a,b->c. This means:</p>

<p>if a is in the beginning of your string and b is on top of your s... | habedi/stack-exchange-dataset |
62,886 | Is Turing Reduction always in context to decidable languages? | <p>According to Wikipedia's article on <a href="https://en.wikipedia.org/wiki/Turing_reduction" rel="nofollow">Turing Reduction</a></p>

<blockquote>
 <p>It can be understood as an algorithm that could be used to solve A if it had available to it a subroutine for solving B.</p>
</blockquote>

<... | computability reductions | 1 | Is Turing Reduction always in context to decidable languages? -- (computability reductions)
<p>According to Wikipedia's article on <a href="https://en.wikipedia.org/wiki/Turing_reduction" rel="nofollow">Turing Reduction</a></p>

<blockquote>
 <p>It can be understood as an algorithm that could be used to so... | habedi/stack-exchange-dataset |
62,895 | Checking for $3$-colorability by searching for $K_4$ as a minor | <p>Determining if a graph is $3$-colorable is NP-complete. But this is equivalent, by a resolved case of Hadwiger's Conjecture, to checking if the graph has $K_4$ as a minor.</p>

<p>Per <a href="https://en.wikipedia.org/wiki/Graph_minor#Algorithms" rel="nofollow">https://en.wikipedia.org/wiki/Graph_minor#Algor... | complexity theory graphs np complete | 1 | Checking for $3$-colorability by searching for $K_4$ as a minor -- (complexity theory graphs np complete)
<p>Determining if a graph is $3$-colorable is NP-complete. But this is equivalent, by a resolved case of Hadwiger's Conjecture, to checking if the graph has $K_4$ as a minor.</p>

<p>Per <a href="https://en... | habedi/stack-exchange-dataset |
62,899 | How hard is recovering a binary matrix from its check sums? | <p>I am interested in combinatorial (worst-case) one-way functions. I came across this problem which may be related to coding theory problems (I am not an expert in coding theory).</p>

<p><strong>INPUT</strong>: Two vectors $R_{n*1}$ and $C_{1*n}$. </p>

<p><strong>QUESTION</strong>: Is there a binary ... | complexity theory time complexity | 1 | How hard is recovering a binary matrix from its check sums? -- (complexity theory time complexity)
<p>I am interested in combinatorial (worst-case) one-way functions. I came across this problem which may be related to coding theory problems (I am not an expert in coding theory).</p>

<p><strong>INPUT</strong>: ... | habedi/stack-exchange-dataset |
62,910 | Why are these features missing in modern day general purpose computer languages? | <p>I often wondered why languages like c do not have simple syntactical allowances that would help readability. For example, large numbers such as 1073741823 can be hard to read so my opinion is modern day languages should allow delimiters such as , (comma) so you can write a statement such as x = 1,073,741,823. That... | programming languages | 1 | Why are these features missing in modern day general purpose computer languages? -- (programming languages)
<p>I often wondered why languages like c do not have simple syntactical allowances that would help readability. For example, large numbers such as 1073741823 can be hard to read so my opinion is modern day langu... | habedi/stack-exchange-dataset |
62,919 | Does local optimization in a genetic algorithm decrease diversity? | <p>I want to create a hybrid genetic algorithm for a project to solve really high dimensional problems (1000+) One of my ideas is to incorporate a local optimization method within GA so each individual will be optimized to its local optima before fitness evaluation. 
I've read some papers on hybrid GAs with hill cl... | algorithms optimization genetic algorithms evolutionary computing | 1 | Does local optimization in a genetic algorithm decrease diversity? -- (algorithms optimization genetic algorithms evolutionary computing)
<p>I want to create a hybrid genetic algorithm for a project to solve really high dimensional problems (1000+) One of my ideas is to incorporate a local optimization method within GA... | habedi/stack-exchange-dataset |
62,920 | Numerical ratio between the length of a string and the transited states | <p>If we have a finite automaton that accepts a string,</p>

<p>is there any numerical relationship that always is true like S ≥ |w| or something similar? </p>

<p>Where |w| the length of the string and S the number of transited states (counting multiplicities).</p>

<p>For example, if we have t... | automata finite automata | 1 | Numerical ratio between the length of a string and the transited states -- (automata finite automata)
<p>If we have a finite automaton that accepts a string,</p>

<p>is there any numerical relationship that always is true like S ≥ |w| or something similar? </p>

<p>Where |w| the length of the string and... | habedi/stack-exchange-dataset |
62,921 | Cyclic deterministic finite automata, exponential advantage over DFA | <p>Let's define Cyclic deterministic finite automata (CDFA) as a DFA that treats its input a bit differently -- namely, CDFA when given input $w$, firstly transforms its input into $w@$, where $@$ is a special character outside the alphabet that acts as a loop, gluing end of $w$ to the beginning of $w$. So, when CDFA r... | formal languages regular languages finite automata | 1 | Cyclic deterministic finite automata, exponential advantage over DFA -- (formal languages regular languages finite automata)
<p>Let's define Cyclic deterministic finite automata (CDFA) as a DFA that treats its input a bit differently -- namely, CDFA when given input $w$, firstly transforms its input into $w@$, where $@... | habedi/stack-exchange-dataset |
62,944 | Can POSIX BRE express all regular languages? | <p>It appears that "Basic Regular Expressions" as defined by <a href="http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap09.html#tag_09_03">POSIX.1-2008</a> do not support alternation, <code>a|b</code> (although some grep implementations recognize the escaped version, <code>\|</code>).</p>

<p>Sinc... | formal languages regular expressions | 1 | Can POSIX BRE express all regular languages? -- (formal languages regular expressions)
<p>It appears that "Basic Regular Expressions" as defined by <a href="http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/V1_chap09.html#tag_09_03">POSIX.1-2008</a> do not support alternation, <code>a|b</code> (although some gre... | habedi/stack-exchange-dataset |
62,947 | Is powerset construction deterministic? | <p><a href="https://en.wikipedia.org/wiki/Powerset_construction" rel="nofollow">Powerset construction</a> is used to convert a non-deterministic finite automaton (NFA) into a deterministic finite automaton (DFA). Is the method/algorithm used to do this deterministic itself and if so, why?</p>
 | automata finite automata | 1 | Is powerset construction deterministic? -- (automata finite automata)
<p><a href="https://en.wikipedia.org/wiki/Powerset_construction" rel="nofollow">Powerset construction</a> is used to convert a non-deterministic finite automaton (NFA) into a deterministic finite automaton (DFA). Is the method/algorithm used to do th... | habedi/stack-exchange-dataset |
62,961 | Computing counts of combinations (?) | <p>I'm not sure what terminology to use. Here is some input:</p>

<pre><code>John has items: A B D
Peter has items: A C D
</code></pre>

<p>And I want to produce such a table, that would count the # of people having these items (0-count is not required to be outputted):</p>

<pre><code>... | algorithms permutations counting | 1 | Computing counts of combinations (?) -- (algorithms permutations counting)
<p>I'm not sure what terminology to use. Here is some input:</p>

<pre><code>John has items: A B D
Peter has items: A C D
</code></pre>

<p>And I want to produce such a table, that would count the # of people having thes... | habedi/stack-exchange-dataset |
62,965 | Why is Church-Rosser so important for basing programming languages on lamdba-calculus? | <p>So, I know Church-Rosser has 2 thesis:</p>

<p>CR1: If $ E_1 \leftrightarrow E_2 $, then there exists an Expression E so $ E_1 \rightarrow E $ and $ E_2 \rightarrow E $</p>

<p>CR2: If $ E \rightarrow N $ (with N in normalform), then there exists a reduction row in normalorder (first reduce the left... | lambda calculus functional programming | 1 | Why is Church-Rosser so important for basing programming languages on lamdba-calculus? -- (lambda calculus functional programming)
<p>So, I know Church-Rosser has 2 thesis:</p>

<p>CR1: If $ E_1 \leftrightarrow E_2 $, then there exists an Expression E so $ E_1 \rightarrow E $ and $ E_2 \rightarrow E $</p>
... | habedi/stack-exchange-dataset |
62,978 | What method of collective recogintion to use for digits recognition? | <p><strong><em>The structure of the question is as follows:</em></strong> at first, I provide the concept of <em>collective recognition</em>, further I provide explanation of the various methods of group classification that I found, in the end I introduce you the question. Those who are experts in this field and may no... | machine learning artificial intelligence neural networks classification pattern recognition | 1 | What method of collective recogintion to use for digits recognition? -- (machine learning artificial intelligence neural networks classification pattern recognition)
<p><strong><em>The structure of the question is as follows:</em></strong> at first, I provide the concept of <em>collective recognition</em>, further I pr... | habedi/stack-exchange-dataset |
62,985 | Problems conjectured but not proven to be easy | <p>We have many problems, like factorization, that are strongly conjectured, but not proven, to be outside P. Are there any questions with the opposite property, namely, that they are strongly conjectured but not proven to be <em>inside</em> P?</p>
 | complexity theory polynomial time | 1 | Problems conjectured but not proven to be easy -- (complexity theory polynomial time)
<p>We have many problems, like factorization, that are strongly conjectured, but not proven, to be outside P. Are there any questions with the opposite property, namely, that they are strongly conjectured but not proven to be <em>insi... | habedi/stack-exchange-dataset |
62,994 | MLTT not being Turing Complete | <p>Where can I find a proof that <a href="https://en.wikipedia.org/wiki/Intuitionistic_type_theory" rel="nofollow">Martin-Löf Type Theory</a> isn't Turing Complete, if such proof exists?</p>
 | type theory | 1 | MLTT not being Turing Complete -- (type theory)
<p>Where can I find a proof that <a href="https://en.wikipedia.org/wiki/Intuitionistic_type_theory" rel="nofollow">Martin-Löf Type Theory</a> isn't Turing Complete, if such proof exists?</p>
 | habedi/stack-exchange-dataset |
63,000 | N-queens problem objective function | <p>I have read about the N-queens problem and I don't understand the following objective function:</p>

<p>$O(board)=N^2/2-L$</p>

<p>$N$ ... number of queens
$L$ ... number of pairs of queens that attack each other</p>

<p>Why they use $N^2/2$? They wrote that it is the number of pairs of q... | optimization board games | 1 | N-queens problem objective function -- (optimization board games)
<p>I have read about the N-queens problem and I don't understand the following objective function:</p>

<p>$O(board)=N^2/2-L$</p>

<p>$N$ ... number of queens
$L$ ... number of pairs of queens that attack each other</p>

<p>Wh... | habedi/stack-exchange-dataset |
63,001 | What all can be said when you say that the CPU is 32 bit? | <p>When someone tells a computer scientist that a CPU is, say, 32 bits, what all does he/she infer from this information?</p>

<p>I know that it means that the physical address has 32 bits. This meas that the physical memory can't hold more that 2^32 bytes of RAM. This also means that the word size is 32 bit or... | computer architecture | 1 | What all can be said when you say that the CPU is 32 bit? -- (computer architecture)
<p>When someone tells a computer scientist that a CPU is, say, 32 bits, what all does he/she infer from this information?</p>

<p>I know that it means that the physical address has 32 bits. This meas that the physical memory ca... | habedi/stack-exchange-dataset |
63,012 | Least squares fit of a 1D lattice of points to a 2D dataset | <p>Given a set of data points (shown in red), it is possible to fit a line $y = mx + c$ through the points using linear least squares regression.</p>

<p>I would like to modify this to fit a 1D lattice (grid) along the line such that $d$ is the offset of the the grid along the line and $i$ is the interval betwe... | optimization statistics clustering | 1 | Least squares fit of a 1D lattice of points to a 2D dataset -- (optimization statistics clustering)
<p>Given a set of data points (shown in red), it is possible to fit a line $y = mx + c$ through the points using linear least squares regression.</p>

<p>I would like to modify this to fit a 1D lattice (grid) alo... | habedi/stack-exchange-dataset |
63,013 | Positive Definiteness Constraint | <p>I want to add a constraint to a convex program, to guarantee some matrix $A$ to be positive semidefinite.
How should I do it?</p>

<p>The library I am working with can cope with linear/ quadratic inequalities only.</p>

<p>By definition, $A$ is positive semidefinite iff $\forall x \in \mathbb C^n... | optimization linear algebra | 1 | Positive Definiteness Constraint -- (optimization linear algebra)
<p>I want to add a constraint to a convex program, to guarantee some matrix $A$ to be positive semidefinite.
How should I do it?</p>

<p>The library I am working with can cope with linear/ quadratic inequalities only.</p>

<p>By defin... | habedi/stack-exchange-dataset |
63,018 | Visual programming tools, why don’t they work with the AST directly? | <p>I've found several open source visual programing tools like Blockly and friends, and other projects hosted at Github, but could't find any that work directly with the abstract syntax tree.</p>

<p><strong>Why is that?</strong></p>

<p>I'm asking because once I discovered that every compiler out there... | programming languages language design syntax trees | 1 | Visual programming tools, why don’t they work with the AST directly? -- (programming languages language design syntax trees)
<p>I've found several open source visual programing tools like Blockly and friends, and other projects hosted at Github, but could't find any that work directly with the abstract syntax tree.</p>... | habedi/stack-exchange-dataset |
63,031 | Why does many to one reduction imply Turing reducibility? | <p>So, $ A\leqslant_mB $ (many to one reduction) means that language $A$ can be reduced to language $B$ if there exists a Turing-calculable function $f$ so $ f(A) \subseteq B$ and $ f(\overline{A}) \subseteq \overline{B} $.</p>

<p>$ A\leqslant_TB $ (Turing reducibility) means that language $A$ can be Turing-re... | computability reductions | 1 | Why does many to one reduction imply Turing reducibility? -- (computability reductions)
<p>So, $ A\leqslant_mB $ (many to one reduction) means that language $A$ can be reduced to language $B$ if there exists a Turing-calculable function $f$ so $ f(A) \subseteq B$ and $ f(\overline{A}) \subseteq \overline{B} $.</p>
... | habedi/stack-exchange-dataset |
63,048 | What is the difference between radix trees and Patricia tries? | <p>I am learning about radix trees (aka compressed tries) and Patricia tries, but I am finding conflicting information on whether or not they are actually the same. A radix tree can be obtained from a normal (uncompressed) trie by merging nodes with their parents when the nodes are the only child. This also holds for P... | data structures trees | 1 | What is the difference between radix trees and Patricia tries? -- (data structures trees)
<p>I am learning about radix trees (aka compressed tries) and Patricia tries, but I am finding conflicting information on whether or not they are actually the same. A radix tree can be obtained from a normal (uncompressed) trie by... | habedi/stack-exchange-dataset |
63,054 | Representing non-contiguous memory regions as a standard vector with O(1) access | <p>What interesting alternatives are there for constructing an arbitrarily large static array from smaller scattered blocks of fixed-sized non-contiguous blocks of memory? </p>

<p>This is similar to the problem solved by hardware MMU pagetable mappings from virtual memory to physical memory, but in this partic... | data structures arrays virtual memory | 1 | Representing non-contiguous memory regions as a standard vector with O(1) access -- (data structures arrays virtual memory)
<p>What interesting alternatives are there for constructing an arbitrarily large static array from smaller scattered blocks of fixed-sized non-contiguous blocks of memory? </p>

<p>This is... | habedi/stack-exchange-dataset |
63,061 | Treewidth of k x k square grid graphs | <p>According to <a href="http://web.eecs.utk.edu/~cphillip/cs594_spring2015_projects/treewidth.pdf" rel="noreferrer">some slides</a> I found on google, the treewidth of any $k \times k$ <a href="http://mathworld.wolfram.com/GridGraph.html" rel="noreferrer">square grid graph</a> $G$ is $tw(G) = k$. I just started resear... | graphs planar graphs square grid | 1 | Treewidth of k x k square grid graphs -- (graphs planar graphs square grid)
<p>According to <a href="http://web.eecs.utk.edu/~cphillip/cs594_spring2015_projects/treewidth.pdf" rel="noreferrer">some slides</a> I found on google, the treewidth of any $k \times k$ <a href="http://mathworld.wolfram.com/GridGraph.html" rel=... | habedi/stack-exchange-dataset |
63,074 | Why isn't TQBF part of the polynomial hierarchy? | <p>TQBF consists of alternating quantifiers, so does $\Sigma^2_n$ for fixed $n$. So given a formula in TQBF, shouldn't there be a level of the polynomial hierarchy that solves it?</p>

<p>I think this is incorrect because TQBF consists of any number of quantifiers, but each level in the PH has fixed number of q... | complexity theory time complexity space complexity polynomial time | 1 | Why isn't TQBF part of the polynomial hierarchy? -- (complexity theory time complexity space complexity polynomial time)
<p>TQBF consists of alternating quantifiers, so does $\Sigma^2_n$ for fixed $n$. So given a formula in TQBF, shouldn't there be a level of the polynomial hierarchy that solves it?</p>

<p>I t... | habedi/stack-exchange-dataset |
63,075 | Solving second-order ODEs with Taylor series approximation of second derivative and linear algebra | <p>I was told about an algorithm to solve ODEs which I thought was very clever. I am sure its not something new. It works by discarding the $\mathcal{O}(h^2)$-term from the usual formula for computing the second derivative:</p>

<p>$$f''_i = \frac{f_{i-1} + f_{i+1} - 2f_{i}}{h^2} + \mathcal{O}(h^2), \qquad i = ... | algorithms discrete mathematics numerical algorithms | 1 | Solving second-order ODEs with Taylor series approximation of second derivative and linear algebra -- (algorithms discrete mathematics numerical algorithms)
<p>I was told about an algorithm to solve ODEs which I thought was very clever. I am sure its not something new. It works by discarding the $\mathcal{O}(h^2)$-term... | habedi/stack-exchange-dataset |
63,083 | Space complexity of string indices: O(1) or O(log|S|)? | <p>Say you have a string <code>S</code> and wish to store indices of it, e.g. letter at index 3 of "toast" is 'a'. Seems that people generally consider an index as taking <code>O(1)</code> space to store*. But doesn't it take <code>O(log(|S|))</code> space?</p>

<p>If we use binary bits...</p>

<ul>
... | algorithm analysis strings space analysis | 1 | Space complexity of string indices: O(1) or O(log|S|)? -- (algorithm analysis strings space analysis)
<p>Say you have a string <code>S</code> and wish to store indices of it, e.g. letter at index 3 of "toast" is 'a'. Seems that people generally consider an index as taking <code>O(1)</code> space to store*. But doesn't ... | habedi/stack-exchange-dataset |
63,088 | what is the time complexity for an algorithm that operations to complete grows by 4 when doubling the input length? | <p>I'm working on an algorithm and I'm trying to figure out its time complexity given the operations it takes to complete a input set of specific length, I have been testing the algorithm with varying input lengths.</p>

<p>The results shows that every time I double the input length, it takes 4 times more opera... | algorithm analysis asymptotics runtime analysis | 1 | what is the time complexity for an algorithm that operations to complete grows by 4 when doubling the input length? -- (algorithm analysis asymptotics runtime analysis)
<p>I'm working on an algorithm and I'm trying to figure out its time complexity given the operations it takes to complete a input set of specific lengt... | habedi/stack-exchange-dataset |
63,091 | What defines a subproblem? | <p>In algorithm analysis what exactly defines a subproblem?</p>

<p>I know that one of the optimality conditions for greedy algorithms is that all subproblems of the solution are also optimal, but to me this begs the question. Are subproblems defined relative to a data set, a problem on that data set, or a solu... | algorithms terminology | 1 | What defines a subproblem? -- (algorithms terminology)
<p>In algorithm analysis what exactly defines a subproblem?</p>

<p>I know that one of the optimality conditions for greedy algorithms is that all subproblems of the solution are also optimal, but to me this begs the question. Are subproblems defined relati... | habedi/stack-exchange-dataset |
63,094 | Synchronous model: is taking steps simultaneously equivalent to having fixed upper bounds for communication/processing delays? | <p>I've just started reading about theory of distributed systems and am a bit confused. There seem to be two ways of defining a synchronous distributed system and I'm not sure whether they are equivalent.</p>
<p>Lynch, in her book <a href="https://rads.stackoverflow.com/amzn/click/com/1558603484" rel="nofollow nore... | computation models distributed systems | 1 | Synchronous model: is taking steps simultaneously equivalent to having fixed upper bounds for communication/processing delays? -- (computation models distributed systems)
<p>I've just started reading about theory of distributed systems and am a bit confused. There seem to be two ways of defining a synchronous distribut... | habedi/stack-exchange-dataset |
63,104 | Can a $k$-ary relation have polymorphisms of arity greater than $k$? | <p>To quote Hubie Chen's <a href="https://arxiv.org/pdf/cs/0611018v1.pdf" rel="nofollow">A Rendezvous of Logic, Complexity, and Algebra</a> (2009) on constraint satisfaction and complexity,</p>

<blockquote>
 <p>An operation $f : D^m \to D$ is a polymorphism of a relation $R \subseteq D^k$
 if, for an... | relational algebra constraint satisfaction polymorphisms | 1 | Can a $k$-ary relation have polymorphisms of arity greater than $k$? -- (relational algebra constraint satisfaction polymorphisms)
<p>To quote Hubie Chen's <a href="https://arxiv.org/pdf/cs/0611018v1.pdf" rel="nofollow">A Rendezvous of Logic, Complexity, and Algebra</a> (2009) on constraint satisfaction and complexity,... | habedi/stack-exchange-dataset |
63,133 | Solving T(n) = 3T(n/3)+n/2 using master method | <p>I thought I understood the Master Method quite well till I saw this question</p>

<p>$T(n) = 3T(\frac{n}{3})+\frac{n}{2}$ </p>

<p>My approach:
 $a = 3 ; b=3$ and $f(n) = \frac{n}{2}$</p>

<p>$n^{\log_b{a}}$ = $n^{log_3{3}} = n$</p>

<p>This looked like a classic solution of mast... | recurrence relation master theorem | 1 | Solving T(n) = 3T(n/3)+n/2 using master method -- (recurrence relation master theorem)
<p>I thought I understood the Master Method quite well till I saw this question</p>

<p>$T(n) = 3T(\frac{n}{3})+\frac{n}{2}$ </p>

<p>My approach:
 $a = 3 ; b=3$ and $f(n) = \frac{n}{2}$</p>

<p>$n^{\log_... | habedi/stack-exchange-dataset |
63,136 | Does the amount of symbols a turing machine has affect what computations it can perform? | <p>Do additonal symbols on a turing machine actually change what is computationally possible on a machine, or do they just make them easier to work with? For example is there anything a 3 symbol turing machine could compute that a 2 symbol turing machine could not? (Assuming each machine can have any number of states).... | turing machines computation models | 1 | Does the amount of symbols a turing machine has affect what computations it can perform? -- (turing machines computation models)
<p>Do additonal symbols on a turing machine actually change what is computationally possible on a machine, or do they just make them easier to work with? For example is there anything a 3 sym... | habedi/stack-exchange-dataset |
63,144 | Do problems in P have a minimum number of YES and NO instances? | <p>If a decision problem A belongs to the polynomial complexity class P, must there be at least one YES instance and one NO instance of the problem? I know that in the definition of a Turing machine an accept state and separate reject state are defined but I'm not sure if that applies to this case. Is it maybe possible... | complexity theory decision problem polynomial time | 1 | Do problems in P have a minimum number of YES and NO instances? -- (complexity theory decision problem polynomial time)
<p>If a decision problem A belongs to the polynomial complexity class P, must there be at least one YES instance and one NO instance of the problem? I know that in the definition of a Turing machine a... | habedi/stack-exchange-dataset |
63,146 | Is there a measure for connectedness? | <p>Is there a name for the "measure of connectedness", i.e. :
$$\text{MoC} = \frac{d(G)}{|G|-1}$$ with domain of function $D_\text{MoC} = [0,1]$, average degree of graph $d(G)$ and amount of nodes $|G|$? Meaning a quantitive measure for connectedness or meshedness of a graph? E.g. a complete graph would have a MoC ... | graphs terminology | 1 | Is there a measure for connectedness? -- (graphs terminology)
<p>Is there a name for the "measure of connectedness", i.e. :
$$\text{MoC} = \frac{d(G)}{|G|-1}$$ with domain of function $D_\text{MoC} = [0,1]$, average degree of graph $d(G)$ and amount of nodes $|G|$? Meaning a quantitive measure for connectedness or ... | habedi/stack-exchange-dataset |
63,164 | Reduction to longest path from longest chain of tiles | <p>We have some tiles that each tile has 2 number written on it. We can rotate each tile in order to swap the position of numbers. We want to find the longest chain of tiles starting with a certain tile so that adjacent tiles have the same number on their common endpoint. If the tiles were</p>

<pre><code> 7-4,... | complexity theory graphs np complete reductions np hard | 1 | Reduction to longest path from longest chain of tiles -- (complexity theory graphs np complete reductions np hard)
<p>We have some tiles that each tile has 2 number written on it. We can rotate each tile in order to swap the position of numbers. We want to find the longest chain of tiles starting with a certain tile so... | habedi/stack-exchange-dataset |
63,181 | Big-O complexity of sqrt(n) | <p>I'm trying to backfill missing CS knowledge and going through the MIT 6.006 course. </p>

<p>It asks me to rank functions by asymptotic complexity and I want to understand how they should be reduced rather than just guessing. The question is to reduce this to big-O notation, then rank it:</p>

<p>$$f... | asymptotics | 1 | Big-O complexity of sqrt(n) -- (asymptotics)
<p>I'm trying to backfill missing CS knowledge and going through the MIT 6.006 course. </p>

<p>It asks me to rank functions by asymptotic complexity and I want to understand how they should be reduced rather than just guessing. The question is to reduce this to big-... | habedi/stack-exchange-dataset |
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