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 |
|---|---|---|---|---|---|---|
492 | Saving on array initialization | <p>I recently read that it is possible to have arrays which need not be initialized, i.e. it is possible to use them without having to spend any time trying to set each member to the default value. i.e. you can start using the array as if it has been initialized by the default value without having to initialize it. (So... | data structures arrays | 1 | Saving on array initialization -- (data structures arrays)
<p>I recently read that it is possible to have arrays which need not be initialized, i.e. it is possible to use them without having to spend any time trying to set each member to the default value. i.e. you can start using the array as if it has been initialize... | habedi/stack-exchange-dataset |
495 | Are generational garbage collectors inherently cache-friendly? | <p>A typical <a href="http://en.wikipedia.org/wiki/Garbage_collection_%28computer_science%29#Generational_GC_.28ephemeral_GC.29">generational garbage collector</a> keeps recently allocated data in a separate memory region. In typical programs, a lot of data is short-lived, so collecting young garbage (a minor GC cycle)... | programming languages computer architecture cpu cache garbage collection | 1 | Are generational garbage collectors inherently cache-friendly? -- (programming languages computer architecture cpu cache garbage collection)
<p>A typical <a href="http://en.wikipedia.org/wiki/Garbage_collection_%28computer_science%29#Generational_GC_.28ephemeral_GC.29">generational garbage collector</a> keeps recently ... | habedi/stack-exchange-dataset |
524 | Does there exist a priority queue with $O(1)$ extracts? | <p>There are a great many data structures that implement the priority-queue interface:</p>

<ul>
<li>Insert: insert an element into the structure</li>
<li>Get-Min: return the smallest element in the structure</li>
<li>Extract-Min: remove the smallest element in the structure</li>
</ul>

... | data structures amortized analysis priority queues | 1 | Does there exist a priority queue with $O(1)$ extracts? -- (data structures amortized analysis priority queues)
<p>There are a great many data structures that implement the priority-queue interface:</p>

<ul>
<li>Insert: insert an element into the structure</li>
<li>Get-Min: return the smallest element ... | habedi/stack-exchange-dataset |
525 | What is coinduction? | <p>I've heard of (structural) induction. It allows you to build up finite structures from smaller ones and gives you proof principles for reasoning about such structures. The idea is clear enough.</p>

<blockquote>
 <p>But what about coinduction? How does it work? How can one say anything conclusive about ... | terminology logic proof techniques formal methods coinduction | 1 | What is coinduction? -- (terminology logic proof techniques formal methods coinduction)
<p>I've heard of (structural) induction. It allows you to build up finite structures from smaller ones and gives you proof principles for reasoning about such structures. The idea is clear enough.</p>

<blockquote>
 <p>... | habedi/stack-exchange-dataset |
539 | Visual Programming languages | <p>Most of us learned programming using "textual" programming languages like Basic, C/C++, and Java. I believe it is more natural and efficient for humans to think visually. Visual programming allows developers to write programs by manipulating graphical elements. I guess using visual programming should improve the qua... | programming languages | 1 | Visual Programming languages -- (programming languages)
<p>Most of us learned programming using "textual" programming languages like Basic, C/C++, and Java. I believe it is more natural and efficient for humans to think visually. Visual programming allows developers to write programs by manipulating graphical elements.... | habedi/stack-exchange-dataset |
540 | Notions of efficient computation | <p>A polynomial-time Turing machine algorithm is considered efficient if its run-time, in the worst-case, is bounded by a polynomial function in the input size. I'm aware of the strong Church-Turing thesis:</p>

<blockquote>
 <p>Any reasonable model of computation can be efficiently simulated on Turing mac... | complexity theory efficiency computation models | 1 | Notions of efficient computation -- (complexity theory efficiency computation models)
<p>A polynomial-time Turing machine algorithm is considered efficient if its run-time, in the worst-case, is bounded by a polynomial function in the input size. I'm aware of the strong Church-Turing thesis:</p>

<blockquote>&#... | habedi/stack-exchange-dataset |
541 | When are two simulations not a bisimulation? | <p>Given a <a href="http://en.wikipedia.org/wiki/State_transition_system">labelled transition system</a> $(S,\Lambda,\to)$, where $S$ is a set of states, $\Lambda$ is a set of labels, and $\to\subseteq S\times\Lambda\times S$ is a ternary relation. As usual, write $p \stackrel\alpha\rightarrow q$ for $(p,\alpha,q)\in\t... | programming languages formal methods semantics process algebras | 1 | When are two simulations not a bisimulation? -- (programming languages formal methods semantics process algebras)
<p>Given a <a href="http://en.wikipedia.org/wiki/State_transition_system">labelled transition system</a> $(S,\Lambda,\to)$, where $S$ is a set of states, $\Lambda$ is a set of labels, and $\to\subseteq S\ti... | habedi/stack-exchange-dataset |
553 | How Do Common Pathfinding Algorithms Compare To Human Process | <p>This might border on computational cognitive science, but I am curious as to how the process followed by common pathfinding algorithms (such as <a href="http://en.wikipedia.org/wiki/A_star_search_algorithm">A*</a>) compares to the process humans use in different pathfinding situations (given the same information). A... | algorithms graphs artificial intelligence | 1 | How Do Common Pathfinding Algorithms Compare To Human Process -- (algorithms graphs artificial intelligence)
<p>This might border on computational cognitive science, but I am curious as to how the process followed by common pathfinding algorithms (such as <a href="http://en.wikipedia.org/wiki/A_star_search_algorithm">A... | habedi/stack-exchange-dataset |
555 | Given a string and a CFG, what characters can follow the string (in the sentential forms of the CFG)? | <p>Let $\Sigma$ be the set of terminal and $N$ the set of non-terminal symbols of some context-free grammar $G$.</p>

<p>Say I have a string $a \in (\Sigma \cup N)^+$ such that $x a y \in \mathcal{S}(G)$ where $x,y\in (\Sigma \cup N)^*$ and $\mathcal{S}(G)$ are the sentential forms of $G$.</p>

<p>Given... | algorithms context free formal grammars compilers | 1 | Given a string and a CFG, what characters can follow the string (in the sentential forms of the CFG)? -- (algorithms context free formal grammars compilers)
<p>Let $\Sigma$ be the set of terminal and $N$ the set of non-terminal symbols of some context-free grammar $G$.</p>

<p>Say I have a string $a \in (\Sigma... | habedi/stack-exchange-dataset |
559 | Creating a Self Ordering Binary Tree | <p>I have an assignment where I need to make use a binary search tree and alter it to self order itself such that items that are accessed the most (have a higher priority) are at the top of the tree, the root being the most accessed node.</p>

<p>The professor gave me the BST and node struct to work with, but t... | algorithms data structures binary trees search trees | 1 | Creating a Self Ordering Binary Tree -- (algorithms data structures binary trees search trees)
<p>I have an assignment where I need to make use a binary search tree and alter it to self order itself such that items that are accessed the most (have a higher priority) are at the top of the tree, the root being the most a... | habedi/stack-exchange-dataset |
561 | Why has research on genetic algorithms slowed? | <p>While discussing some intro level topics today, including the use of genetic algorithms; I was told that research has really slowed in this field. The reason given was that most people are focusing on machine learning and data mining. <br>
<strong>Update:</strong> Is this accurate? And if so, what advantages doe... | machine learning data mining evolutionary computing history | 1 | Why has research on genetic algorithms slowed? -- (machine learning data mining evolutionary computing history)
<p>While discussing some intro level topics today, including the use of genetic algorithms; I was told that research has really slowed in this field. The reason given was that most people are focusing on mach... | habedi/stack-exchange-dataset |
578 | What is the complexity of these tree-based algorithms? | <p>Suppose we have a balanced binary tree, which represents a recursive partitioning of a set of $N$ points into nested subsets. Each node of the tree represents a subset, with the following properties: subsets represented by two children nodes of the same parent are disjoint, and their union is equal to the subset re... | algorithms time complexity binary trees | 1 | What is the complexity of these tree-based algorithms? -- (algorithms time complexity binary trees)
<p>Suppose we have a balanced binary tree, which represents a recursive partitioning of a set of $N$ points into nested subsets. Each node of the tree represents a subset, with the following properties: subsets represen... | habedi/stack-exchange-dataset |
580 | What combination of data structures efficiently stores discrete Bayesian networks? | <p>I understand the theory behind Bayesian networks, and am wondering what it takes to build one in practice. Let's say for this example, that I have a Bayesian (directed) network of 100 discrete random variables; each variable can take one of up to 10 values.</p>

<p>Do I store all the nodes in a DAG, and for ... | data structures machine learning | 1 | What combination of data structures efficiently stores discrete Bayesian networks? -- (data structures machine learning)
<p>I understand the theory behind Bayesian networks, and am wondering what it takes to build one in practice. Let's say for this example, that I have a Bayesian (directed) network of 100 discrete ran... | habedi/stack-exchange-dataset |
581 | Algorithmic intuition for logarithmic complexity | <p>I believe I have a reasonable grasp of complexities like <span class="math-container">$\mathcal{O}(1)$</span>, <span class="math-container">$\Theta(n)$</span> and <span class="math-container">$\Theta(n^2)$</span>.</p>

<p>In terms of a list, <span class="math-container">$\mathcal{O}(1)$</span> is a constant ... | algorithms complexity theory time complexity intuition | 1 | Algorithmic intuition for logarithmic complexity -- (algorithms complexity theory time complexity intuition)
<p>I believe I have a reasonable grasp of complexities like <span class="math-container">$\mathcal{O}(1)$</span>, <span class="math-container">$\Theta(n)$</span> and <span class="math-container">$\Theta(n^2)$</s... | habedi/stack-exchange-dataset |
586 | Could quantum computing eventually be used to make modern day hashing trivial to break? | <p>Simply put, if one were to build a quantum computing device with the power of, say, 20 qubits, could such a computer be used to make any kind of modern hashing algorithm useless?</p>

<p>Would it even be possible to harness the power of quantum computing in a traditional computing application?</p>
 | cryptography quantum computing hash | 1 | Could quantum computing eventually be used to make modern day hashing trivial to break? -- (cryptography quantum computing hash)
<p>Simply put, if one were to build a quantum computing device with the power of, say, 20 qubits, could such a computer be used to make any kind of modern hashing algorithm useless?</p>
... | habedi/stack-exchange-dataset |
588 | Can every linear grammar be converted to Greibach form? | <p>Can every <a href="http://en.wikipedia.org/wiki/Linear_grammar" rel="nofollow">linear grammar</a> be converted to a linear <a href="http://en.wikipedia.org/wiki/Greibach_normal_form" rel="nofollow">Greibach normal form</a>, a form in which all productions look like $A \rightarrow ax$ where $a \in T$ and $x \in V \cu... | formal languages formal grammars | 1 | Can every linear grammar be converted to Greibach form? -- (formal languages formal grammars)
<p>Can every <a href="http://en.wikipedia.org/wiki/Linear_grammar" rel="nofollow">linear grammar</a> be converted to a linear <a href="http://en.wikipedia.org/wiki/Greibach_normal_form" rel="nofollow">Greibach normal form</a>,... | habedi/stack-exchange-dataset |
594 | CPU frequency per year | <p>I know that since ~2004, Moore's law stopped working for CPU clock speed.
I'm looking for a graph showing this, but am unable to find it: most charts out there show the transistor count or the capacity per year.</p>

<p>Where can I find some data showing the CPU frequency of computers (anything is fine, ... | computer architecture empirical research data sets | 1 | CPU frequency per year -- (computer architecture empirical research data sets)
<p>I know that since ~2004, Moore's law stopped working for CPU clock speed.
I'm looking for a graph showing this, but am unable to find it: most charts out there show the transistor count or the capacity per year.</p>

<p>Where ... | habedi/stack-exchange-dataset |
602 | Measuring one way network latency | <p>This is a puzzle about measuring network latency that I created. I believe the solution is that it's impossible, but friends disagree. I'm looking for convincing explanations either way. (Though it is posed as a puzzle I think it fits on this web site because of its applicability to the design and experience of comm... | computer networks protocols distributed systems | 1 | Measuring one way network latency -- (computer networks protocols distributed systems)
<p>This is a puzzle about measuring network latency that I created. I believe the solution is that it's impossible, but friends disagree. I'm looking for convincing explanations either way. (Though it is posed as a puzzle I think it ... | habedi/stack-exchange-dataset |
614 | Late and Early Bisimulation | <p>This is a follow up to my earlier questions on <a href="https://cs.stackexchange.com/q/525/31">coinduction</a> and <a href="https://cs.stackexchange.com/q/541/31">bisimulation</a>.</p>

<p>A relation $R \subseteq S \times S$ on the states of an LTS is a <em>bisimulation</em> iff $\forall (p,q)\in R,$ 
$... | semantics formal methods process algebras pi calculus | 1 | Late and Early Bisimulation -- (semantics formal methods process algebras pi calculus)
<p>This is a follow up to my earlier questions on <a href="https://cs.stackexchange.com/q/525/31">coinduction</a> and <a href="https://cs.stackexchange.com/q/541/31">bisimulation</a>.</p>

<p>A relation $R \subseteq S \times... | habedi/stack-exchange-dataset |
625 | Find shortest paths in a weighed unipathic graph | <p>A directed graph is said to be <em>unipathic</em> if for any two vertices $u$ and $v$ in
the graph $G=(V,E)$, there is at most one simple path from $u$ to $v$. </p>

<p>Suppose I am given a unipathic graph $G$ such that each edge has a positive or negative weight, but contains no negative weight cycles.<... | algorithms graphs | 1 | Find shortest paths in a weighed unipathic graph -- (algorithms graphs)
<p>A directed graph is said to be <em>unipathic</em> if for any two vertices $u$ and $v$ in
the graph $G=(V,E)$, there is at most one simple path from $u$ to $v$. </p>

<p>Suppose I am given a unipathic graph $G$ such that each edge has... | habedi/stack-exchange-dataset |
627 | Decidablity of Languages of Grammars and Automata | <p><em>Note this is a question related to study in a CS course at a university, it is NOT homework and can be found <a href="http://www.cs.ucf.edu/%7Edmarino/ucf/transparency/cot4210/exam/" rel="noreferrer">here</a> under Fall 2011 exam2.</em></p>
<p>Here are the two questions I'm looking at from a past exam. They... | formal languages computability context free regular languages turing machines | 1 | Decidablity of Languages of Grammars and Automata -- (formal languages computability context free regular languages turing machines)
<p><em>Note this is a question related to study in a CS course at a university, it is NOT homework and can be found <a href="http://www.cs.ucf.edu/%7Edmarino/ucf/transparency/cot4210/exam... | habedi/stack-exchange-dataset |
634 | What is beta equivalence? | <p>In the script I am currently reading on the lambda calculus, beta equivalence is defined as this:</p>

<blockquote>
 <p>The $\beta$-equivalence $\equiv_\beta$ is the smallest equivalence that contains $\rightarrow_\beta$.</p>
</blockquote>

<p>I have no idea what that means. Can someone expl... | logic terminology lambda calculus type theory | 1 | What is beta equivalence? -- (logic terminology lambda calculus type theory)
<p>In the script I am currently reading on the lambda calculus, beta equivalence is defined as this:</p>

<blockquote>
 <p>The $\beta$-equivalence $\equiv_\beta$ is the smallest equivalence that contains $\rightarrow_\beta$.</p>&#... | habedi/stack-exchange-dataset |
636 | A Question relating to a Turing Machine with a useless state | <p>OK, so here is a question from a past test in my Theory of Computation class:</p>

<blockquote>
 <p>A useless state in a TM is one that is never entered on any input string. Let $$\mathrm{USELESS}_{\mathrm{TM}} = \{\langle M, q \rangle \mid q \text{ is a useless state in }M\}.$$
 Prove that $\mat... | computability undecidability formal methods turing machines | 1 | A Question relating to a Turing Machine with a useless state -- (computability undecidability formal methods turing machines)
<p>OK, so here is a question from a past test in my Theory of Computation class:</p>

<blockquote>
 <p>A useless state in a TM is one that is never entered on any input string. Let... | habedi/stack-exchange-dataset |
640 | Language of the values of an affine function | <p>Write $\bar n$ for the decimal expansion of $n$ (with no leading <code>0</code>). Let $a$ and $b$ be integers, with $a > 0$. Consider the language of the decimal expansions of the multiples of $a$ plus a constant:</p>

<p>$$M = \{ \overline{a\,x+b} \mid x\in\mathbb{N} \}$$</p>

<p>Is $M$ regular? ... | formal languages context free regular languages integers | 1 | Language of the values of an affine function -- (formal languages context free regular languages integers)
<p>Write $\bar n$ for the decimal expansion of $n$ (with no leading <code>0</code>). Let $a$ and $b$ be integers, with $a > 0$. Consider the language of the decimal expansions of the multiples of $a$ plus a con... | habedi/stack-exchange-dataset |
641 | Language of the graph of an affine function | <p>Write $\bar n$ for the decimal expansion of $n$ (with no leading <code>0</code>). Let <code>:</code> be a symbol distinct from any digit. Let $a$ and $b$ be integers, with $a > 0$. Consider the language of solutions of the Diophantine equation $y=ax+b$:</p>

<p>$$L = \{ \bar{x} \mathtt: \bar{y} \mid y = a... | formal languages regular languages context free integers | 1 | Language of the graph of an affine function -- (formal languages regular languages context free integers)
<p>Write $\bar n$ for the decimal expansion of $n$ (with no leading <code>0</code>). Let <code>:</code> be a symbol distinct from any digit. Let $a$ and $b$ be integers, with $a > 0$. Consider the language of so... | habedi/stack-exchange-dataset |
645 | Deciding on Sub-Problems for Dynamic Programming | <p>I have used the technique of dynamic programming multiple times however today a friend asked me how I go about defining my sub-problems, I realized I had no way of providing an objective formal answer. How do you formally define a sub-problem for a problem that you would solve using dynamic programming?</p>
 | algorithms dynamic programming | 1 | Deciding on Sub-Problems for Dynamic Programming -- (algorithms dynamic programming)
<p>I have used the technique of dynamic programming multiple times however today a friend asked me how I go about defining my sub-problems, I realized I had no way of providing an objective formal answer. How do you formally define a s... | habedi/stack-exchange-dataset |
653 | Is there a difference between $\lambda xy.xy$ and $\lambda x.\lambda y.xy$? | <p>I am currently learning the lambda calculus and was wondering about the following two different kinds of writing a lambda term. </p>

<ol>
<li>$\lambda xy.xy$ </li>
<li>$\lambda x.\lambda y.xy$</li>
</ol>

<p>Is there any difference in meaning or the way you apply beta reduction, or are ... | logic lambda calculus | 1 | Is there a difference between $\lambda xy.xy$ and $\lambda x.\lambda y.xy$? -- (logic lambda calculus)
<p>I am currently learning the lambda calculus and was wondering about the following two different kinds of writing a lambda term. </p>

<ol>
<li>$\lambda xy.xy$ </li>
<li>$\lambda x.\lambda y.xy$</li... | habedi/stack-exchange-dataset |
654 | Logarithmic vs double logarithmic time complexity | <p>In real world applications is there a concrete benefit when using $\mathcal{O}(\log(\log(n))$ instead of $\mathcal{O}(\log(n))$ algorithms ?</p>

<p>This is the case when one use for instance van Emde Boas trees instead of more conventional binary search tree implementations. 
But for example, if we take... | algorithms complexity theory binary trees algorithm analysis search trees | 1 | Logarithmic vs double logarithmic time complexity -- (algorithms complexity theory binary trees algorithm analysis search trees)
<p>In real world applications is there a concrete benefit when using $\mathcal{O}(\log(\log(n))$ instead of $\mathcal{O}(\log(n))$ algorithms ?</p>

<p>This is the case when one use f... | habedi/stack-exchange-dataset |
669 | Are Turing machines more powerful than pushdown automata? | <p>I've came up with a result while reading some automata books, that Turing machines appear to be more powerful than pushdown automata. Since the tape of a Turing machine can always be made to behave like a stack, it'd seem that we can actually claim that TMs are more powerful. </p>

<p>Is this true?</p>
 | formal languages computability automata turing machines pushdown automata | 1 | Are Turing machines more powerful than pushdown automata? -- (formal languages computability automata turing machines pushdown automata)
<p>I've came up with a result while reading some automata books, that Turing machines appear to be more powerful than pushdown automata. Since the tape of a Turing machine can always ... | habedi/stack-exchange-dataset |
674 | Non-trivial tractable properties of triples | <p>Many intractable $NP$-complete problems can be modeled as deciding whether a set of triples, $F=${$t_1, t_2, ..., t_n$} where each triple $t_i$ is a subset of three elements over base set $U=${$a_1, a_2, ..., a_k$}, satisfy some non-trivial property. For example, 3-edge coloring of cubic graphs can be modeled as the... | complexity theory | 1 | Non-trivial tractable properties of triples -- (complexity theory)
<p>Many intractable $NP$-complete problems can be modeled as deciding whether a set of triples, $F=${$t_1, t_2, ..., t_n$} where each triple $t_i$ is a subset of three elements over base set $U=${$a_1, a_2, ..., a_k$}, satisfy some non-trivial property.... | habedi/stack-exchange-dataset |
680 | How many edges can a unipathic graph have? | <p>A unipathic graph is a directed graph such that there is at most one simple path from any one vertex to any other vertex.</p>

<p>Unipathic graphs can have cycles. For example, a doubly linked list (not a circular one!) is a unipathic graph; if the list has $n$ elements, the graph has $n-1$ cycles of length ... | graphs combinatorics | 1 | How many edges can a unipathic graph have? -- (graphs combinatorics)
<p>A unipathic graph is a directed graph such that there is at most one simple path from any one vertex to any other vertex.</p>

<p>Unipathic graphs can have cycles. For example, a doubly linked list (not a circular one!) is a unipathic graph... | habedi/stack-exchange-dataset |
684 | Turing Completeness + Dataflow Unification = Arbitrarily invertible (pure, nonrecursive) functions? | <p>Assume we are working in a Turing-complete, referentially-transparent, higher-order language that supports arbitrary dataflow unification. Shouldn't it then be possible to construct the following function (using Haskell-like syntax, because that's what I'm most familiar with)?</p>

<pre><code>-- Takes an ar... | programming languages | 1 | Turing Completeness + Dataflow Unification = Arbitrarily invertible (pure, nonrecursive) functions? -- (programming languages)
<p>Assume we are working in a Turing-complete, referentially-transparent, higher-order language that supports arbitrary dataflow unification. Shouldn't it then be possible to construct the fol... | habedi/stack-exchange-dataset |
689 | How to convert an NFA with overlapping cycles into a regular expression? | <p>If I understand correctly, NFA have the same expressive power as regular expressions. Often, reading off equivalent regular expressions from NFA is easy: you translate cycles to stars, junctions as alternatives and so on. But what to do in this case: </p>

<p><img src="https://i.stack.imgur.com/yCGnv.png" al... | algorithms formal languages finite automata regular expressions | 1 | How to convert an NFA with overlapping cycles into a regular expression? -- (algorithms formal languages finite automata regular expressions)
<p>If I understand correctly, NFA have the same expressive power as regular expressions. Often, reading off equivalent regular expressions from NFA is easy: you translate cycles ... | habedi/stack-exchange-dataset |
699 | How does a two-way pushdown automaton work? | <p>Note that by "two-way pushdown automaton", I mean a pushdown automaton that can move its reading head both ways on the input tape.</p>

<p>I recently had the question of determining the computational power of two-way PDAs in the Chomsky hierarchy. I don't entirely understand two-way PDAs, but I can see how w... | formal languages computability automata pushdown automata | 1 | How does a two-way pushdown automaton work? -- (formal languages computability automata pushdown automata)
<p>Note that by "two-way pushdown automaton", I mean a pushdown automaton that can move its reading head both ways on the input tape.</p>

<p>I recently had the question of determining the computational po... | habedi/stack-exchange-dataset |
701 | Decidable restrictions of the Post Correspondence Problem | <p>The <a href="http://en.wikipedia.org/wiki/Post_correspondence_problem" rel="noreferrer">Post Correspondence Problem</a> (PCP) is undecidable.</p>

<p>The <em>bounded version of the PCP</em> is $\mathrm{NP}$-complete and the <em>marked version of the PCP</em> (the words of one of the two lists are required to... | complexity theory computability reference request | 1 | Decidable restrictions of the Post Correspondence Problem -- (complexity theory computability reference request)
<p>The <a href="http://en.wikipedia.org/wiki/Post_correspondence_problem" rel="noreferrer">Post Correspondence Problem</a> (PCP) is undecidable.</p>

<p>The <em>bounded version of the PCP</em> is $\m... | habedi/stack-exchange-dataset |
706 | Finding exact corner solutions to linear programming using interior point methods | <p>The simplex algorithm walks greedily on the corners of a polytope to find the optimal solution to the linear programming problem. As a result, the answer is always a corner of the polytope. Interior point methods walk the inside of the polytope. As a result, when a whole plane of the polytope is optimal (if the obje... | algorithms optimization linear programming | 1 | Finding exact corner solutions to linear programming using interior point methods -- (algorithms optimization linear programming)
<p>The simplex algorithm walks greedily on the corners of a polytope to find the optimal solution to the linear programming problem. As a result, the answer is always a corner of the polytop... | habedi/stack-exchange-dataset |
737 | Is Directed Graph a Graph? | <p>I came across an issue with the definition of a (directed) graph in Sipser's Introduction to the theory of computation, 2nd Ed.</p>

<p>On pp.10, An <strong>undirected graph</strong>, or simply a <strong>graph</strong>, is a set of points with lines connecting some of the points. The points are called nodes ... | graphs | 1 | Is Directed Graph a Graph? -- (graphs)
<p>I came across an issue with the definition of a (directed) graph in Sipser's Introduction to the theory of computation, 2nd Ed.</p>

<p>On pp.10, An <strong>undirected graph</strong>, or simply a <strong>graph</strong>, is a set of points with lines connecting some of t... | habedi/stack-exchange-dataset |
740 | Research on evaluating the performance of cache-obliviousness in practice | <p><a href="http://en.wikipedia.org/wiki/Cache-oblivious_algorithm">Cache-oblivious algorithms and data structures</a> are a rather new thing, introduced by Frigo et al. in <a href="http://userweb.cs.utexas.edu/~pingali/CS395T/2009fa/papers/coAlgorithms.pdf">Cache-oblivious algorithms, 1999</a>. Prokop's <a href="http:... | algorithms data structures computer architecture reference request cpu cache | 1 | Research on evaluating the performance of cache-obliviousness in practice -- (algorithms data structures computer architecture reference request cpu cache)
<p><a href="http://en.wikipedia.org/wiki/Cache-oblivious_algorithm">Cache-oblivious algorithms and data structures</a> are a rather new thing, introduced by Frigo e... | habedi/stack-exchange-dataset |
757 | Does every large enough string have repeats? | <p>Let $\Sigma$ be some finite set of characters of fixed size. Let $\alpha$ be some string over $\Sigma$. We say that a nonempty substring $\beta$ of $\alpha$ is a <em>repeat</em> if $\beta = \gamma \gamma$ for some string $\gamma$.</p>

<p>Now, my question is whether the following holds:</p>

<blockqu... | combinatorics strings word combinatorics | 1 | Does every large enough string have repeats? -- (combinatorics strings word combinatorics)
<p>Let $\Sigma$ be some finite set of characters of fixed size. Let $\alpha$ be some string over $\Sigma$. We say that a nonempty substring $\beta$ of $\alpha$ is a <em>repeat</em> if $\beta = \gamma \gamma$ for some string $\gam... | habedi/stack-exchange-dataset |
764 | Are two elements always in a relation within a partially ordered set? | <p>In a partially ordered set, am I always able to order two arbitrary elements out of the set? Or is it possible that two elements within the set have no order relation to each other?</p>

<p>For example if there are three elements $\{a, b, c\}$ and $a \leq b$ and $a \leq c$, does either $b \leq c$ or $c \leq ... | terminology discrete mathematics order theory | 1 | Are two elements always in a relation within a partially ordered set? -- (terminology discrete mathematics order theory)
<p>In a partially ordered set, am I always able to order two arbitrary elements out of the set? Or is it possible that two elements within the set have no order relation to each other?</p>

<... | habedi/stack-exchange-dataset |
772 | Error in the use of asymptotic notation | <p>I'm trying to understand what is wrong with the following proof of the following recurrence </p>

<p>$$
T(n) = 2\,T\!\left(\left\lfloor\frac{n}{2}\right\rfloor\right)+n 
$$
$$
T(n) \leq 2\left(c\left\lfloor\frac{n}{2}\right\rfloor\right)+n \leq cn+n = n(c+1) =O(n)
$$</... | algorithms landau notation asymptotics recurrence relation | 1 | Error in the use of asymptotic notation -- (algorithms landau notation asymptotics recurrence relation)
<p>I'm trying to understand what is wrong with the following proof of the following recurrence </p>

<p>$$
T(n) = 2\,T\!\left(\left\lfloor\frac{n}{2}\right\rfloor\right)+n 
$$
$$
&#x... | habedi/stack-exchange-dataset |
795 | Limitations of Stack Inspection | <p><em>This is a follow up to the <a href="https://cs.stackexchange.com/q/796/31">How does Stack Inspection work?</a> that explores the notion in more detail</em></p>

<p><a href="http://www.securingjava.com/chapter-three/chapter-three-6.html" rel="nofollow noreferrer">Stack inspection</a> is a mechanism for en... | security stack inspection | 1 | Limitations of Stack Inspection -- (security stack inspection)
<p><em>This is a follow up to the <a href="https://cs.stackexchange.com/q/796/31">How does Stack Inspection work?</a> that explores the notion in more detail</em></p>

<p><a href="http://www.securingjava.com/chapter-three/chapter-three-6.html" rel="... | habedi/stack-exchange-dataset |
796 | How does Stack Inspection work? | <p><em>This is precursor to my other, more advanced <a href="https://cs.stackexchange.com/q/795/31">question</a> about Stack Inspection.</em></p>

<p>Stack Inspection is a security mechanism introduced in the JVM to deal with running code originating from locations having different levels of trust. This is ques... | terminology security stack inspection | 1 | How does Stack Inspection work? -- (terminology security stack inspection)
<p><em>This is precursor to my other, more advanced <a href="https://cs.stackexchange.com/q/795/31">question</a> about Stack Inspection.</em></p>

<p>Stack Inspection is a security mechanism introduced in the JVM to deal with running cod... | habedi/stack-exchange-dataset |
802 | Are the Before and After sets for context-free grammars always context-free? | <p>Let $G$ be a context-free grammar. A string of terminals and nonterminals of $G$ is said to be a <em>sentential form</em> of $G$ if you can obtain it by applying productions of $G$ zero or more times to the start symbol of $S$. Let $\operatorname{SF}(G)$ be the set of sentential forms of $G$.</p>

<p>Let $\a... | formal languages context free formal grammars closure properties | 1 | Are the Before and After sets for context-free grammars always context-free? -- (formal languages context free formal grammars closure properties)
<p>Let $G$ be a context-free grammar. A string of terminals and nonterminals of $G$ is said to be a <em>sentential form</em> of $G$ if you can obtain it by applying producti... | habedi/stack-exchange-dataset |
805 | Proving a binary tree has at most $\lceil n/2 \rceil$ leaves | <p>I'm trying to prove that a <a href="http://en.wikipedia.org/wiki/Binary_tree" rel="nofollow noreferrer">binary tree</a> with $n$ nodes has at most $\left\lceil \frac{n}{2} \right\rceil$ leaves. How would I go about doing this with induction?</p>

<p><em>For people who were following in the original question ... | data structures binary trees combinatorics graphs proof techniques | 1 | Proving a binary tree has at most $\lceil n/2 \rceil$ leaves -- (data structures binary trees combinatorics graphs proof techniques)
<p>I'm trying to prove that a <a href="http://en.wikipedia.org/wiki/Binary_tree" rel="nofollow noreferrer">binary tree</a> with $n$ nodes has at most $\left\lceil \frac{n}{2} \right\rceil... | habedi/stack-exchange-dataset |
808 | NP completeness proof of a spanning tree problem | <p>I am looking for some hints in a question asked by my instructor.</p>

<p>So I just figured out this decision problem is $\sf{NP\text{-}complete}$:</p>

<p>In a graph $G$, is there a spanning tree in $G$ that contain an exact set of $S=\{x_1, x_2,\ldots, x_n\}$ as leafs. I figured out we can prove th... | complexity theory graphs np complete | 1 | NP completeness proof of a spanning tree problem -- (complexity theory graphs np complete)
<p>I am looking for some hints in a question asked by my instructor.</p>

<p>So I just figured out this decision problem is $\sf{NP\text{-}complete}$:</p>

<p>In a graph $G$, is there a spanning tree in $G$ that c... | habedi/stack-exchange-dataset |
809 | Logic gates from everyday materials | <p>Logic gates are an abstract device which can be implemented with electromagnetic relays, vacuum tubes, or transistors. These implemenations have been successful in computing in part because of various properties of chainability, durability, and size beyond their basic binary stability. They also work well because ... | computer architecture didactics | 1 | Logic gates from everyday materials -- (computer architecture didactics)
<p>Logic gates are an abstract device which can be implemented with electromagnetic relays, vacuum tubes, or transistors. These implemenations have been successful in computing in part because of various properties of chainability, durability, an... | habedi/stack-exchange-dataset |
811 | Proving that directed graph diagnosis is NP-hard | <p>I have a homework assignment that I've been bashing my head against for some time, and I'd appreciate any hints. It is about choosing a known problem, the NP-completeness of which is proven, and constructing a reduction from that problem to the following problem I'll call DGD (directed graph diagnosis).</p>
<h3>... | complexity theory np hard graphs | 1 | Proving that directed graph diagnosis is NP-hard -- (complexity theory np hard graphs)
<p>I have a homework assignment that I've been bashing my head against for some time, and I'd appreciate any hints. It is about choosing a known problem, the NP-completeness of which is proven, and constructing a reduction from that ... | habedi/stack-exchange-dataset |
813 | Are there other ways to describe formal languages other than grammars? | <p>I'm looking for mathematical theories that deal with describing formal languages (set of strings) in general and not just grammar hierarchies.</p>
 | formal languages formal grammars | 1 | Are there other ways to describe formal languages other than grammars? -- (formal languages formal grammars)
<p>I'm looking for mathematical theories that deal with describing formal languages (set of strings) in general and not just grammar hierarchies.</p>
 | habedi/stack-exchange-dataset |
818 | How To Best Learn About Algorithms In Depth | <p>I have been reading this site with a great deal of interest, but I find a lot of it goes over my head. This has made me wish to learn a lot more about algorithms and CS in general. As far as I can tell from my research, there are 2 main ways of doing this. </p>

<ol>
<li><p>I can by a nice thick heavy bo... | algorithms education | 1 | How To Best Learn About Algorithms In Depth -- (algorithms education)
<p>I have been reading this site with a great deal of interest, but I find a lot of it goes over my head. This has made me wish to learn a lot more about algorithms and CS in general. As far as I can tell from my research, there are 2 main ways of do... | habedi/stack-exchange-dataset |
820 | Learning Automated Theorem Proving | <p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories" rel="noreferrer">SMT solvers</a> / <a href="http://en.wikipedia.org/wiki/Proof_assistant" rel="noreferrer">Pro... | logic proof assistants automated theorem proving coq | 1 | Learning Automated Theorem Proving -- (logic proof assistants automated theorem proving coq)
<p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories" rel="noreferrer">... | habedi/stack-exchange-dataset |
824 | Sorting functions by asymptotic growth | <p>Assume I have a list of functions, for example </p>

<p>$\qquad n^{\log \log(n)}, 2^n, n!, n^3, n \ln n, \dots$</p>

<p>How do I sort them asymptotically, i.e. after the relation defined by</p>

<p>$\qquad f \leq_O g \iff f \in O(g)$,</p>

<p>assuming they are indeed pairwise compara... | asymptotics landau notation reference question | 1 | Sorting functions by asymptotic growth -- (asymptotics landau notation reference question)
<p>Assume I have a list of functions, for example </p>

<p>$\qquad n^{\log \log(n)}, 2^n, n!, n^3, n \ln n, \dots$</p>

<p>How do I sort them asymptotically, i.e. after the relation defined by</p>

<p>$\q... | habedi/stack-exchange-dataset |
841 | Proving a binary heap has $\lceil n/2 \rceil$ leaves | <p>I'm trying to prove that a <a href="http://en.wikipedia.org/wiki/Binary_heap">binary heap</a> with $n$ nodes has exactly $\left\lceil \frac{n}{2} \right\rceil$ leaves, given that the heap is built in the following way:</p>

<p>Each new node is inserted via <a href="http://en.wikipedia.org/wiki/Binary_heap#In... | data structures binary trees | 1 | Proving a binary heap has $\lceil n/2 \rceil$ leaves -- (data structures binary trees)
<p>I'm trying to prove that a <a href="http://en.wikipedia.org/wiki/Binary_heap">binary heap</a> with $n$ nodes has exactly $\left\lceil \frac{n}{2} \right\rceil$ leaves, given that the heap is built in the following way:</p>
&#x... | habedi/stack-exchange-dataset |
850 | Is the shadow ray in a Whitted ray tracer occluded by transparent objects? | <p>In a Whitted ray tracer, each ray-object intersection spawns a transmitted ray (if the object was translucent), a reflected ray and a shadow ray. The shadow ray contributes the direct lighting component.</p>

<p>But what happens if the shadow ray intersects a transparent object? Is the direct lighting compon... | graphics | 1 | Is the shadow ray in a Whitted ray tracer occluded by transparent objects? -- (graphics)
<p>In a Whitted ray tracer, each ray-object intersection spawns a transmitted ray (if the object was translucent), a reflected ray and a shadow ray. The shadow ray contributes the direct lighting component.</p>

<p>But what... | habedi/stack-exchange-dataset |
851 | Polymorphism and Inductive datatypes | <p>I'm curious. I've been working on this datatype in <em>OCaml</em>:</p>

<pre><code>type 'a exptree =
 | Epsilon
 | Delta of 'a exptree * 'a exptree
 | Omicron of 'a
 | Iota of 'a exptree exptree
</code></pre>

<p>Which can be manipulated using explicitly typed recursive functi... | logic programming languages coq inductive datatypes | 1 | Polymorphism and Inductive datatypes -- (logic programming languages coq inductive datatypes)
<p>I'm curious. I've been working on this datatype in <em>OCaml</em>:</p>

<pre><code>type 'a exptree =
 | Epsilon
 | Delta of 'a exptree * 'a exptree
 | Omicron of 'a
 | Iota of 'a exptree exptree&... | habedi/stack-exchange-dataset |
857 | How to fool the plot inspection heuristic? | <p>Over <a href="https://cs.stackexchange.com/a/825/98">here</a>, Dave Clarke proposed that in order to compare asymptotic growth you should plot the functions at hand. As a theoretically inclined computer scientist, I call(ed) this vodoo as a plot is never proof. On second thought, I have to agree that this is a very ... | asymptotics didactics | 1 | How to fool the plot inspection heuristic? -- (asymptotics didactics)
<p>Over <a href="https://cs.stackexchange.com/a/825/98">here</a>, Dave Clarke proposed that in order to compare asymptotic growth you should plot the functions at hand. As a theoretically inclined computer scientist, I call(ed) this vodoo as a plot i... | habedi/stack-exchange-dataset |
864 | Reducing directed hamiltonian cycle to graph coloring | <p>The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time?</p>
 | complexity theory np complete reductions | 1 | Reducing directed hamiltonian cycle to graph coloring -- (complexity theory np complete reductions)
<p>The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time... | habedi/stack-exchange-dataset |
868 | Types of Automated Theorem Provers | <p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="nofollow noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories" rel="nofollow noreferrer">SMT solvers</a> / <a href="http://en.wikipedia.org/wiki/Proof_assistant" re... | logic automated theorem proving proof assistants | 1 | Types of Automated Theorem Provers -- (logic automated theorem proving proof assistants)
<p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="nofollow noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories" rel="nofollo... | habedi/stack-exchange-dataset |
878 | Issue in comparing classifiers for pattern recognition | <p>I have designed a classifier M which recognizes gestures and classifies it under any category always. A gesture is classified based on the hamming distance between the sample time series y and the training time series x. The result of the classifier are probabilistic values. There are 3 classes/categories with label... | machine learning pattern recognition | 1 | Issue in comparing classifiers for pattern recognition -- (machine learning pattern recognition)
<p>I have designed a classifier M which recognizes gestures and classifies it under any category always. A gesture is classified based on the hamming distance between the sample time series y and the training time series x.... | habedi/stack-exchange-dataset |
879 | Why do some inference engines need human assistance while others don't? | <p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="nofollow noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories" rel="nofollow noreferrer">SMT solvers</a> / <a href="http://en.wikipedia.org/wiki/Proof_assistant" re... | logic proof assistants automated theorem proving smt solvers | 1 | Why do some inference engines need human assistance while others don't? -- (logic proof assistants automated theorem proving smt solvers)
<p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="nofollow noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/... | habedi/stack-exchange-dataset |
880 | Priority queue with both decrease-key and increase-key operations | <p>A <a href="http://en.wikipedia.org/wiki/Fibonacci_heap#Summary_of_running_times">Fibonnaci Heap</a> supports the following operations:</p>

<ul>
<li><code>insert(key, data)</code> : adds a new element to the data structure</li>
<li><code>find-min()</code> : returns a pointer to the element with minim... | data structures priority queues | 1 | Priority queue with both decrease-key and increase-key operations -- (data structures priority queues)
<p>A <a href="http://en.wikipedia.org/wiki/Fibonacci_heap#Summary_of_running_times">Fibonnaci Heap</a> supports the following operations:</p>

<ul>
<li><code>insert(key, data)</code> : adds a new element t... | habedi/stack-exchange-dataset |
882 | Why is unification so important to inference engines? | <p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiability_Modulo_Theories" rel="noreferrer">SMT solvers</a> / <a href="http://en.wikipedia.org/wiki/Proof_assistant" rel="noreferrer">Pro... | logic proof assistants automated theorem proving smt solvers unification | 1 | Why is unification so important to inference engines? -- (logic proof assistants automated theorem proving smt solvers unification)
<p><sup><em>I am learning <a href="http://en.wikipedia.org/wiki/Automated_theorem_proving" rel="noreferrer">Automated Theorem Proving</a> / <a href="http://en.wikipedia.org/wiki/Satisfiabi... | habedi/stack-exchange-dataset |
897 | Does spanning tree make sense for DAG? | <p>Why cannot I find any information about spanning tree for DAG ? I must be wrong somewhere.</p>
 | graphs spanning trees | 1 | Does spanning tree make sense for DAG? -- (graphs spanning trees)
<p>Why cannot I find any information about spanning tree for DAG ? I must be wrong somewhere.</p>
 | habedi/stack-exchange-dataset |
899 | Why is using a lexer/parser on binary data so wrong? | <p>I often work with <a href="http://en.wikipedia.org/wiki/Lexical_analysis">lexer</a>/<a href="http://en.wikipedia.org/wiki/Parsing">parsers</a>, as opposed to a parser combinator and see people who never took a class in parsing, ask about parsing binary data. Typically the data is not only binary but also context sen... | programming languages compilers parsers | 1 | Why is using a lexer/parser on binary data so wrong? -- (programming languages compilers parsers)
<p>I often work with <a href="http://en.wikipedia.org/wiki/Lexical_analysis">lexer</a>/<a href="http://en.wikipedia.org/wiki/Parsing">parsers</a>, as opposed to a parser combinator and see people who never took a class in ... | habedi/stack-exchange-dataset |
909 | Knapsack problem -- NP-complete despite dynamic programming solution? | <p>Knapsack problems are easily solved by dynamic programming. Dynamic programming runs in polynomial time; that is why we do it, right?</p>

<p>I have read it is actually an NP-complete problem, though, which would mean that solving the problem in polynomial problem is probably impossible.</p>

<p>Wher... | complexity theory np complete dynamic programming | 1 | Knapsack problem -- NP-complete despite dynamic programming solution? -- (complexity theory np complete dynamic programming)
<p>Knapsack problems are easily solved by dynamic programming. Dynamic programming runs in polynomial time; that is why we do it, right?</p>

<p>I have read it is actually an NP-complete ... | habedi/stack-exchange-dataset |
930 | Adding elements to a sorted array | <p>What would be the fastest way of doing this (from an algorithmic perspective, as well as a practical matter)?</p>

<p>I was thinking something along the following lines.</p>

<p>I could add to the end of an array and then use bubblesort as it has a best case (totally sorted array at start) that is cl... | algorithms efficiency arrays sorting | 1 | Adding elements to a sorted array -- (algorithms efficiency arrays sorting)
<p>What would be the fastest way of doing this (from an algorithmic perspective, as well as a practical matter)?</p>

<p>I was thinking something along the following lines.</p>

<p>I could add to the end of an array and then use... | habedi/stack-exchange-dataset |
934 | Computational power of nondeterministic type-1 min-heap automata with multiple heaps | <p>I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called <em>min-heap automata</em>; the original question, and links to others, can be found <a href="https://cs.stackexchange.com/q/110/69">here</a>.</p>

<p>This question concerns the power of type-... | formal languages automata | 1 | Computational power of nondeterministic type-1 min-heap automata with multiple heaps -- (formal languages automata)
<p>I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called <em>min-heap automata</em>; the original question, and links to others, can be found... | habedi/stack-exchange-dataset |
938 | From the LR(1) parsing table, can we deduce that it is also an LALR and SLR table? | <p>There is this question I read somewhere but could not answer myself.</p>

<p>Assume I have an LR(1) Parsing table. Is there any way that just by looking at it and its items, can I deduce that it is also a table for LALR and SLR?</p>
 | compilers parsers | 1 | From the LR(1) parsing table, can we deduce that it is also an LALR and SLR table? -- (compilers parsers)
<p>There is this question I read somewhere but could not answer myself.</p>

<p>Assume I have an LR(1) Parsing table. Is there any way that just by looking at it and its items, can I deduce that it is also ... | habedi/stack-exchange-dataset |
944 | Power of nondeterministic type-1 min-heap automaton with both a heap and a stack | <p>I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called min-heap automata; the original question, and links to others, can be found <a href="https://cs.stackexchange.com/q/110/69">here</a>.</p>

<p>Two of my last questions seem to have been quickly... | formal languages automata | 1 | Power of nondeterministic type-1 min-heap automaton with both a heap and a stack -- (formal languages automata)
<p>I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called min-heap automata; the original question, and links to others, can be found <a href="htt... | habedi/stack-exchange-dataset |
945 | Difference between "information" and "useful information" in algorithmic information theory | <p>According to <a href="http://en.wikipedia.org/wiki/Algorithmic_information_theory#Overview">Wikipedia</a>:</p>

<blockquote>
 <p>Informally, from the point of view of algorithmic information theory, the information content of a string is equivalent to the length of the shortest possible self-contained r... | information theory terminology kolmogorov complexity | 1 | Difference between "information" and "useful information" in algorithmic information theory -- (information theory terminology kolmogorov complexity)
<p>According to <a href="http://en.wikipedia.org/wiki/Algorithmic_information_theory#Overview">Wikipedia</a>:</p>

<blockquote>
 <p>Informally, from the poin... | habedi/stack-exchange-dataset |
971 | Quantum lambda calculus | <p>Classically, there are 3 popular ways to think about computation: Turing machine, circuits, and lambda-calculus (I use this as a catch all for most functional views). All 3 have been fruitful ways to think about different types of problems, and different fields use different formulation for this reason.</p>
<p>W... | lambda calculus quantum computing reference request computation models | 1 | Quantum lambda calculus -- (lambda calculus quantum computing reference request computation models)
<p>Classically, there are 3 popular ways to think about computation: Turing machine, circuits, and lambda-calculus (I use this as a catch all for most functional views). All 3 have been fruitful ways to think about diffe... | habedi/stack-exchange-dataset |
974 | How to prove that $n(\log_3(n))^5 = O(n^{1.2})$? | <p>This a homework question from Udi Manber's book. Any hint would be nice :)</p>

<p>I must show that:</p>

<blockquote>
 <p>$n(\log_3(n))^5 = O(n^{1.2})$</p>
</blockquote>

<p>I tried using Theorem 3.1 of book:</p>

<blockquote>
 <p>$f(n)^c = O(a^{f(n)})$ (for $c > 0$,... | asymptotics landau notation mathematical analysis | 1 | How to prove that $n(\log_3(n))^5 = O(n^{1.2})$? -- (asymptotics landau notation mathematical analysis)
<p>This a homework question from Udi Manber's book. Any hint would be nice :)</p>

<p>I must show that:</p>

<blockquote>
 <p>$n(\log_3(n))^5 = O(n^{1.2})$</p>
</blockquote>

<p>I tr... | habedi/stack-exchange-dataset |
982 | "NP-complete" optimization problems | <p>I am slightly confused by some terminology I have encountered regarding the complexity of optimization problems. In an algorithms class, I had the <a href="http://en.wikipedia.org/wiki/Maximum_parsimony_%28phylogenetics%29#Problems_with_maximum_parsimony_phylogeny_estimation">large parsimony</a> problem described a... | complexity theory np complete terminology | 1 | "NP-complete" optimization problems -- (complexity theory np complete terminology)
<p>I am slightly confused by some terminology I have encountered regarding the complexity of optimization problems. In an algorithms class, I had the <a href="http://en.wikipedia.org/wiki/Maximum_parsimony_%28phylogenetics%29#Problems_w... | habedi/stack-exchange-dataset |
991 | Are there minimum criteria for a programming language being Turing complete? | <p>Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete?</p>

<p>From what I can tell from <a href="http://en.wikipedia.org/wiki/Turing_completeness">wikipedia</a>, the language needs to support recursion, or, seemingly, must be abl... | computability programming languages turing machines turing completeness | 1 | Are there minimum criteria for a programming language being Turing complete? -- (computability programming languages turing machines turing completeness)
<p>Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete?</p>

<p>From what I c... | habedi/stack-exchange-dataset |
996 | About Codd's reduction algorithm | <p><a href="http://dictionary.reference.com/browse/Codd%27s+reduction+algorithm" rel="nofollow noreferrer">Codd's Algorithm</a> converts an expression in tuple relational calculus to Relational Algebra.</p>

<ol>
<li>Is there a standard implementation of the algorithm? </li>
<li>Is this algorithm used a... | algorithms database theory | 1 | About Codd's reduction algorithm -- (algorithms database theory)
<p><a href="http://dictionary.reference.com/browse/Codd%27s+reduction+algorithm" rel="nofollow noreferrer">Codd's Algorithm</a> converts an expression in tuple relational calculus to Relational Algebra.</p>

<ol>
<li>Is there a standard implem... | habedi/stack-exchange-dataset |
999 | Complexity of Towers of Hanoi | <p>I ran into the following doubts on the complexity of <a href="http://en.wikipedia.org/wiki/Tower_of_Hanoi">Towers of Hanoi</a>, on which I would like your comments.</p>

<ul>
<li><p><b>Is it in NP? </b> 
Attempted answer: Suppose Peggy (prover) solves the problem & submits it to Victor (verifier)... | complexity theory time complexity towers of hanoi | 1 | Complexity of Towers of Hanoi -- (complexity theory time complexity towers of hanoi)
<p>I ran into the following doubts on the complexity of <a href="http://en.wikipedia.org/wiki/Tower_of_Hanoi">Towers of Hanoi</a>, on which I would like your comments.</p>

<ul>
<li><p><b>Is it in NP? </b> 
Attempted an... | habedi/stack-exchange-dataset |
1,001 | Optimal algorithm for finding the girth of a sparse graph? | <p>I wonder how to find the <a href="http://en.wikipedia.org/wiki/Girth_%28graph_theory%29">girth</a> of a sparse undirected graph. By sparse I mean $|E|=O(|V|)$. By optimum I mean the lowest time complexity.</p>

<p>I thought about some modification on <a href="http://en.wikipedia.org/wiki/Tarjan%27s_strongly_... | algorithms time complexity graphs | 1 | Optimal algorithm for finding the girth of a sparse graph? -- (algorithms time complexity graphs)
<p>I wonder how to find the <a href="http://en.wikipedia.org/wiki/Girth_%28graph_theory%29">girth</a> of a sparse undirected graph. By sparse I mean $|E|=O(|V|)$. By optimum I mean the lowest time complexity.</p>

... | habedi/stack-exchange-dataset |
1,002 | Showing that a problem in X is not X-Complete | <p>The <a href="http://en.wikipedia.org/wiki/Existential_theory_of_the_reals" rel="noreferrer">Existential Theory of the Reals</a> is in <strong>PSPACE</strong>, but I don't know whether it is <strong>PSPACE-Complete</strong>. If I believe that it is not the case, how could I prove it?</p>

<p>More generally,... | complexity theory proof techniques | 1 | Showing that a problem in X is not X-Complete -- (complexity theory proof techniques)
<p>The <a href="http://en.wikipedia.org/wiki/Existential_theory_of_the_reals" rel="noreferrer">Existential Theory of the Reals</a> is in <strong>PSPACE</strong>, but I don't know whether it is <strong>PSPACE-Complete</strong>. If I b... | habedi/stack-exchange-dataset |
1,012 | Lambda Calculus Evaluation | <p>I know this is a simple question but can someone show me how
$(\lambda y. \lambda x. \lambda y.y) (\lambda x. \lambda y. y)$ reduces to $\lambda x. \lambda y. y$.</p>
 | logic lambda calculus | 1 | Lambda Calculus Evaluation -- (logic lambda calculus)
<p>I know this is a simple question but can someone show me how
$(\lambda y. \lambda x. \lambda y.y) (\lambda x. \lambda y. y)$ reduces to $\lambda x. \lambda y. y$.</p>
 | habedi/stack-exchange-dataset |
1,017 | Regular Expression for the language that requires one symbol to occur at least once | <p>I am trying to figure out the simplest way to do this using a regular expression. </p>

<ul>
<li>Three symbols a, b, c.</li>
<li>The sequence length is unlimited, i.e. *.</li>
<li>The symbol a must be somewhere in the sequence at least once, but can appear more than once. </li>
<li>The sequen... | formal languages regular expressions | 1 | Regular Expression for the language that requires one symbol to occur at least once -- (formal languages regular expressions)
<p>I am trying to figure out the simplest way to do this using a regular expression. </p>

<ul>
<li>Three symbols a, b, c.</li>
<li>The sequence length is unlimited, i.e. *.</li>... | habedi/stack-exchange-dataset |
1,018 | Non-Parametric Methods Like K-Nearest-Neighbours in High Dimensional Feature Space | <p>The main idea of <a href="https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm">k-Nearest-Neighbour</a> takes into account the $k$ nearest points and decides the classification of the data by majority vote. If so, then it should not have problems in higher dimensional data because methods like <a href="https:/... | machine learning artificial intelligence | 1 | Non-Parametric Methods Like K-Nearest-Neighbours in High Dimensional Feature Space -- (machine learning artificial intelligence)
<p>The main idea of <a href="https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm">k-Nearest-Neighbour</a> takes into account the $k$ nearest points and decides the classification of th... | habedi/stack-exchange-dataset |
1,031 | How to prove that a language is not regular? | <p>We learned about the class of regular languages $\mathrm{REG}$. It is characterised by any one concept among regular expressions, finite automata and left-linear grammars, so it is easy to show that a given language is regular.</p>

<p>How do I show the opposite, though? My TA has been adamant that in order ... | formal languages regular languages proof techniques reference question | 1 | How to prove that a language is not regular? -- (formal languages regular languages proof techniques reference question)
<p>We learned about the class of regular languages $\mathrm{REG}$. It is characterised by any one concept among regular expressions, finite automata and left-linear grammars, so it is easy to show th... | habedi/stack-exchange-dataset |
1,039 | Number of words in the regular language $(00)^*$ | <p><a href="http://en.wikipedia.org/wiki/Regular_language#The_number_of_words_in_a_regular_language">According to Wikipedia</a>, for any regular language $L$ there exist constants $\lambda_1,\ldots,\lambda_k$ and polynomials $p_1(x),\ldots,p_k(x)$ such that for every $n$ the number $s_L(n)$ of words of length $n$ in $L... | formal languages regular languages combinatorics word combinatorics | 1 | Number of words in the regular language $(00)^*$ -- (formal languages regular languages combinatorics word combinatorics)
<p><a href="http://en.wikipedia.org/wiki/Regular_language#The_number_of_words_in_a_regular_language">According to Wikipedia</a>, for any regular language $L$ there exist constants $\lambda_1,\ldots,... | habedi/stack-exchange-dataset |
1,045 | Number of words of a given length in a regular language | <p>Is there an algebraic characterization of the number of words of a given length in a regular language?</p>

<p><a href="http://en.wikipedia.org/wiki/Regular_language#The_number_of_words_in_a_regular_language" rel="nofollow noreferrer">Wikipedia</a> states a result somewhat imprecisely:</p>

<blockquo... | formal languages regular languages word combinatorics | 1 | Number of words of a given length in a regular language -- (formal languages regular languages word combinatorics)
<p>Is there an algebraic characterization of the number of words of a given length in a regular language?</p>

<p><a href="http://en.wikipedia.org/wiki/Regular_language#The_number_of_words_in_a_reg... | habedi/stack-exchange-dataset |
1,058 | Supporting data structures for SAT local search | <p><a href="http://en.wikipedia.org/wiki/WalkSAT" rel="nofollow noreferrer">WalkSAT and GSAT</a> are well-known and simple local search algorithms for solving the Boolean satisfiability problem. The pseudocode for the GSAT algorithm is copied from the question <a href="https://cs.stackexchange.com/questions/219/impleme... | algorithms data structures satisfiability | 1 | Supporting data structures for SAT local search -- (algorithms data structures satisfiability)
<p><a href="http://en.wikipedia.org/wiki/WalkSAT" rel="nofollow noreferrer">WalkSAT and GSAT</a> are well-known and simple local search algorithms for solving the Boolean satisfiability problem. The pseudocode for the GSAT al... | habedi/stack-exchange-dataset |
1,060 | Confluence proof for a simple rewriting system | <p>Assume we have a simple language that consists of the terms:</p>

<ul>
<li>$\mathtt{true}$</li>
<li>$\mathtt{false}$</li>
<li>if $t_1,t_2,t_3$ are terms then so is $\mathtt{if}\: t_1 \:\mathtt{then}\: t_2 \:\mathtt{else}\: t_3$</li>
</ul>

<p>Now assume the following logical evaluatio... | logic semantics proof techniques term rewriting | 1 | Confluence proof for a simple rewriting system -- (logic semantics proof techniques term rewriting)
<p>Assume we have a simple language that consists of the terms:</p>

<ul>
<li>$\mathtt{true}$</li>
<li>$\mathtt{false}$</li>
<li>if $t_1,t_2,t_3$ are terms then so is $\mathtt{if}\: t_1 \:\mathtt{then... | habedi/stack-exchange-dataset |
1,062 | How many shortest distances change when adding an edge to a graph? | <p>Let $G=(V,E)$ be some complete, weighted, undirected graph. We construct a second graph $G'=(V, E')$ by adding edges one by one from $E$ to $E'$. We add $\Theta(|V|)$ edges to $G'$ in total.</p>

<p>Every time we add one edge $(u,v)$ to $E'$, we consider the shortest distances between all... | algorithms graphs shortest path | 1 | How many shortest distances change when adding an edge to a graph? -- (algorithms graphs shortest path)
<p>Let $G=(V,E)$ be some complete, weighted, undirected graph. We construct a second graph $G'=(V, E')$ by adding edges one by one from $E$ to $E'$. We add $\Theta(|V|)$ edges to $G'$ in total.</p>&#x... | habedi/stack-exchange-dataset |
1,065 | What is the difference between user-level threads and kernel-level threads? | <p>After reading several sources I'm still confused about user- and kernel-level threads. </p>

<p>In particular:</p>

<blockquote>
 <p>Threads can exist at both the user level and the kernel level</p>
</blockquote>

<p>What is the difference between the user level and kernel level? </p... | operating systems terminology concurrency os kernel | 1 | What is the difference between user-level threads and kernel-level threads? -- (operating systems terminology concurrency os kernel)
<p>After reading several sources I'm still confused about user- and kernel-level threads. </p>

<p>In particular:</p>

<blockquote>
 <p>Threads can exist at both the ... | habedi/stack-exchange-dataset |
1,071 | Is there an algorithm which finds sorted subsequences of size three in $O(n)$ time? | <p>I want to prove or disprove the existence of an algorithm which, given an array $A$ of integers, finds three indices $i, j$ and $k$ such that $i < j < k$ and $A[i] < A[j] < A[k]$ (or finds that there is no such triple) in linear time.</p>

<p>This is not a homework question; I saw it on a program... | algorithms arrays subsequences | 1 | Is there an algorithm which finds sorted subsequences of size three in $O(n)$ time? -- (algorithms arrays subsequences)
<p>I want to prove or disprove the existence of an algorithm which, given an array $A$ of integers, finds three indices $i, j$ and $k$ such that $i < j < k$ and $A[i] < A[j] < A[k]$ (or fi... | habedi/stack-exchange-dataset |
1,074 | What is the purpose of M:N (Hybrid) threading? | <p>In other words, what advantages does <a href="http://en.wikipedia.org/wiki/Thread_%28computer_science%29#M%3aN_.28Hybrid_threading.29" rel="noreferrer">Hybrid threading</a> have over 1:1 (kernel only) and N:1 (user only) threading?</p>

<p><sub>This is a follow-up to <a href="https://cs.stackexchange.com/que... | operating systems concurrency os kernel | 1 | What is the purpose of M:N (Hybrid) threading? -- (operating systems concurrency os kernel)
<p>In other words, what advantages does <a href="http://en.wikipedia.org/wiki/Thread_%28computer_science%29#M%3aN_.28Hybrid_threading.29" rel="noreferrer">Hybrid threading</a> have over 1:1 (kernel only) and N:1 (user only) thre... | habedi/stack-exchange-dataset |
1,084 | How to implement the details of shotgun hill climbing to make it effective? | <p>I am currently working on a solution to a problem for which (after a bit of research) the use of a hill climbing, and more specificly a <em>shotgun</em> (or <em>random-restart</em>) <a href="http://en.wikipedia.org/wiki/Hill_climbing" rel="nofollow">hill climbing</a> algorithmic idea seems to be the best fit, as I h... | algorithms optimization heuristics | 1 | How to implement the details of shotgun hill climbing to make it effective? -- (algorithms optimization heuristics)
<p>I am currently working on a solution to a problem for which (after a bit of research) the use of a hill climbing, and more specificly a <em>shotgun</em> (or <em>random-restart</em>) <a href="http://en.... | habedi/stack-exchange-dataset |
1,088 | What happens to the cache contents on a context switch? | <p>In a multicore processor, what happens to the contents of a core's cache (say L1) when a context switch occurs on that cache?</p>

<p>Is the behaviour dependent on the architecture or is it a general behaviour followed by all chip manufacturers?</p>
 | computer architecture operating systems cpu cache | 1 | What happens to the cache contents on a context switch? -- (computer architecture operating systems cpu cache)
<p>In a multicore processor, what happens to the contents of a core's cache (say L1) when a context switch occurs on that cache?</p>

<p>Is the behaviour dependent on the architecture or is it a genera... | habedi/stack-exchange-dataset |
1,100 | How are statistics being applied in computer science to evaluate accuracy in research claims? | <p>I have noticed in my short academic life that many published papers in our area sometimes do not have much rigor regarding statistics. This is not just an assumption; I have heard professors say the same. </p>

<p>For example, in CS disciplines I see papers being published claiming that methodology X has bee... | software engineering empirical research statistics | 1 | How are statistics being applied in computer science to evaluate accuracy in research claims? -- (software engineering empirical research statistics)
<p>I have noticed in my short academic life that many published papers in our area sometimes do not have much rigor regarding statistics. This is not just an assumption; ... | habedi/stack-exchange-dataset |
1,106 | Which queue does the long-term scheduler maintain? | <p>There are different queues of processes (in an operating system):</p>

<p><em>Job Queue:</em> Each new process goes into the job queue. Processes in the job queue reside on mass storage and await the allocation of main memory.</p>

<p><em>Ready Queue:</em> The set of all processes that are in main me... | operating systems terminology process scheduling | 1 | Which queue does the long-term scheduler maintain? -- (operating systems terminology process scheduling)
<p>There are different queues of processes (in an operating system):</p>

<p><em>Job Queue:</em> Each new process goes into the job queue. Processes in the job queue reside on mass storage and await the allo... | habedi/stack-exchange-dataset |
1,113 | How to construct the found path in bidirectional search | <p>I am trying to implement bidirectional search in a graph. I am using two breadth first searches from the start node and the goal node. The states that have been checked are stored in two hash tables (closed lists).
How can I get the solution (path from the start to the goal), when I find that a state that is che... | algorithms graphs shortest path | 1 | How to construct the found path in bidirectional search -- (algorithms graphs shortest path)
<p>I am trying to implement bidirectional search in a graph. I am using two breadth first searches from the start node and the goal node. The states that have been checked are stored in two hash tables (closed lists).
How c... | habedi/stack-exchange-dataset |
1,121 | Choosing taps for Linear Feedback Shift Register | <p>I am confused about how taps are chosen for Linear Feedback Shift Registers.</p>
<p>I have a diagram which shows a LFSR with connection polynomial <span class="math-container">$C(X) = X^5 + X^2 + 1$</span>. The five stages are labelled: <span class="math-container">$R4, R3, R2, R1$</span> and <span class="math-c... | cryptography pseudo random generators shift register | 1 | Choosing taps for Linear Feedback Shift Register -- (cryptography pseudo random generators shift register)
<p>I am confused about how taps are chosen for Linear Feedback Shift Registers.</p>
<p>I have a diagram which shows a LFSR with connection polynomial <span class="math-container">$C(X) = X^5 + X^2 + 1$</span>.... | habedi/stack-exchange-dataset |
1,122 | Is it viable to use an HMM to evaluate how well a catalogue is used? | <p>I was interested on evaluating a catalogue that students would be using to observe how is it being used probabilistically. </p>

<p>The catalogue works by choosing cells in a temporal sequence, so for example:</p>

<ul>
<li>Student A has: ($t_1$,$Cell_3$),($t_2$,$Cell_4$)</li>
<li>Student B h... | probability theory empirical research modelling hidden markov models | 1 | Is it viable to use an HMM to evaluate how well a catalogue is used? -- (probability theory empirical research modelling hidden markov models)
<p>I was interested on evaluating a catalogue that students would be using to observe how is it being used probabilistically. </p>

<p>The catalogue works by choosing ce... | habedi/stack-exchange-dataset |
1,137 | What is the difference between "Decision" and "Verification" in complexity theory? | <p>In Michael Sipser's <em>Theory of Computation</em> on page 270 he writes:</p>

<blockquote>
 <p>P = the class of languages for which membership can be decided quickly.<br>
 NP = the class of languages for which membership can be verified quickly.</p>
</blockquote>

<p>What is the differ... | complexity theory terminology decision problem | 1 | What is the difference between "Decision" and "Verification" in complexity theory? -- (complexity theory terminology decision problem)
<p>In Michael Sipser's <em>Theory of Computation</em> on page 270 he writes:</p>

<blockquote>
 <p>P = the class of languages for which membership can be decided quickly.<b... | habedi/stack-exchange-dataset |
1,138 | For every computable function $f$ does there exist a problem that can be solved at best in $\Theta(f(n))$ time? | <p>For every computable function $f$ does there exist a problem that can be solved at best in $\Theta(f(n))$ time or is there a computable function $f$ such that every problem that can be solved in $O(f(n))$ can also be solved in $o(f(n))$ time?</p>

<p>This question popped into my head yesterday. I've been thi... | complexity theory | 1 | For every computable function $f$ does there exist a problem that can be solved at best in $\Theta(f(n))$ time? -- (complexity theory)
<p>For every computable function $f$ does there exist a problem that can be solved at best in $\Theta(f(n))$ time or is there a computable function $f$ such that every problem that can ... | habedi/stack-exchange-dataset |
1,142 | A continuous optimization problem that reduces to TSP | <p>Suppose I am given a finite set of points $p_1,p_2,..p_n$ in the plane, and asked to draw a twice-differentiable curve $C(P)$ through the $p_i$'s, such that its perimeter is as small as possible. Assuming $p_i=(x_i,y_i)$ and $x_i<x_{i+1}$, I can formalize this problem as:</p>

<p><i> Problem 1 (edited in... | complexity theory np hard optimization computable analysis | 1 | A continuous optimization problem that reduces to TSP -- (complexity theory np hard optimization computable analysis)
<p>Suppose I am given a finite set of points $p_1,p_2,..p_n$ in the plane, and asked to draw a twice-differentiable curve $C(P)$ through the $p_i$'s, such that its perimeter is as small as possible. As... | habedi/stack-exchange-dataset |
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