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 |
|---|---|---|---|---|---|---|
9,897 | Tool/app for learning category theory? | <p>Being a programmer I appreciate the errors given by a compiler for a programming language and come to rely on the compiler's error as a safety net.</p>

<p>In learning category theory I would like to have some tool that also acted as a safety net letting me experiment with diagrams and pointing out my mistak... | category theory | 1 | Tool/app for learning category theory? -- (category theory)
<p>Being a programmer I appreciate the errors given by a compiler for a programming language and come to rely on the compiler's error as a safety net.</p>

<p>In learning category theory I would like to have some tool that also acted as a safety net le... | habedi/stack-exchange-dataset |
9,899 | Why does a recurrence of $T(n - 1) + T(n - 2)$ yield something in $\Omega(2^{\frac{n}{2}})$? | <p>I am trying to analyze the running time of a bad implementation of generating the $n$th member of the fibonacci sequence (which requires generating the previous 2 values from the bottom up).</p>

<p>Why does this algorithm have a time complexity of $\Omega(2^{\frac{n}{2}})$? Where does the exponent come from... | algorithms algorithm analysis asymptotics runtime analysis recurrence relation | 1 | Why does a recurrence of $T(n - 1) + T(n - 2)$ yield something in $\Omega(2^{\frac{n}{2}})$? -- (algorithms algorithm analysis asymptotics runtime analysis recurrence relation)
<p>I am trying to analyze the running time of a bad implementation of generating the $n$th member of the fibonacci sequence (which requires gen... | habedi/stack-exchange-dataset |
9,902 | Formally describing a sensor network language | <p>I have a language for sensor networks (generates C code) and I want to define the formal semantics of it.</p>

<p>The language has this form:</p>

<pre><code>{STATE name_state:
EVERY time
SELECT {variable [, variable] ...}
[SENDIF send_condition]
[CHANGEIF change_condition GOTO new_st... | formal languages programming languages semantics | 1 | Formally describing a sensor network language -- (formal languages programming languages semantics)
<p>I have a language for sensor networks (generates C code) and I want to define the formal semantics of it.</p>

<p>The language has this form:</p>

<pre><code>{STATE name_state:
EVERY time
SELEC... | habedi/stack-exchange-dataset |
9,909 | The exact relation between complexity classes and algorithm complexities | <p>Are all algorithms which have polynomial time complexity belong to P class ? And P class do not have any algorithm which does have not polynomial complexity ? </p>

<p>Are all algorithms which have non polynomial complexity belong to NP or NP-Hard or both ?</p>

<p>I am just trying to understand the ... | complexity classes np polynomial time | 1 | The exact relation between complexity classes and algorithm complexities -- (complexity classes np polynomial time)
<p>Are all algorithms which have polynomial time complexity belong to P class ? And P class do not have any algorithm which does have not polynomial complexity ? </p>

<p>Are all algorithms which ... | habedi/stack-exchange-dataset |
9,911 | What are some problems which are easily solved by human brain but which would take more time computers? | <p>Are there any problems which can be solved by human brain in a very less time but a computer may take a lot of time or a computer could never solve it ?</p>
 | algorithms artificial intelligence computer vs human | 1 | What are some problems which are easily solved by human brain but which would take more time computers? -- (algorithms artificial intelligence computer vs human)
<p>Are there any problems which can be solved by human brain in a very less time but a computer may take a lot of time or a computer could never solve it ?</p... | habedi/stack-exchange-dataset |
9,914 | Finding the height of a d-ary heap | <p>I would like to find the height of a d-ary heap. Assuming you have an Array that starts indexing at $1$ we have the following:</p>

<p>The parent of a node $i$ is given by: $\left\lfloor\frac{i+1}{d}\right\rfloor$</p>

<p>The $d$ children of a parent at node $i$ are given by: $di-d+1, di-d+2,\ldots d... | data structures recurrence relation heaps | 1 | Finding the height of a d-ary heap -- (data structures recurrence relation heaps)
<p>I would like to find the height of a d-ary heap. Assuming you have an Array that starts indexing at $1$ we have the following:</p>

<p>The parent of a node $i$ is given by: $\left\lfloor\frac{i+1}{d}\right\rfloor$</p>

... | habedi/stack-exchange-dataset |
9,923 | A Good Resource for Christofides' Heuristic | <p>Is there an explanation Christofides's Heuristic for solving TSP which does not simply state the algorithm and go ahead to prove the bound?</p>

<p>To be specific:
(Disclaimer : I am an engineer who knows very little about graph theory but need this for a logistics course)</p>

<ul>
<li>I und... | algorithms heuristics graph traversal | 1 | A Good Resource for Christofides' Heuristic -- (algorithms heuristics graph traversal)
<p>Is there an explanation Christofides's Heuristic for solving TSP which does not simply state the algorithm and go ahead to prove the bound?</p>

<p>To be specific:
(Disclaimer : I am an engineer who knows very little a... | habedi/stack-exchange-dataset |
9,926 | Algorithm for graphically spacing items | <p><strong>I am developing a chart and graph library and am having trouble developing an algorithm.</strong> </p>

<p>**This is not a homework assignment for a student. See my open source project: <a href="https://github.com/eddieios/CoreChart" rel="nofollow">https://github.com/eddieios/CoreChart</a></p>
&#... | algorithms | 1 | Algorithm for graphically spacing items -- (algorithms)
<p><strong>I am developing a chart and graph library and am having trouble developing an algorithm.</strong> </p>

<p>**This is not a homework assignment for a student. See my open source project: <a href="https://github.com/eddieios/CoreChart" rel="nofoll... | habedi/stack-exchange-dataset |
9,938 | Lossless data compression must make some messages longer? | <p>I read on Wikipedia and in lecture notes that if a lossless data compression algorithm makes a message shorter, it must make another message longer.</p>

<p>E.g. In this set of notes, it says:</p>

<blockquote>
 <p>Consider, for example, the 8 possible 3 bit messages. If one is
 compressed ... | data structures data compression | 1 | Lossless data compression must make some messages longer? -- (data structures data compression)
<p>I read on Wikipedia and in lecture notes that if a lossless data compression algorithm makes a message shorter, it must make another message longer.</p>

<p>E.g. In this set of notes, it says:</p>

<blockq... | habedi/stack-exchange-dataset |
9,941 | How is the following ML Curry expression evaluated | <p>This question is not homework but it's related to material in a general course I take about programming languages, so I don't know whats the site policy about this</p>

<p>In ML the following expression:</p>

<pre><code>fun f x y z = x (y , z) = x (z, y) ;
</code></pre>

<p>Evaluates to t... | programming languages functional programming typing | 1 | How is the following ML Curry expression evaluated -- (programming languages functional programming typing)
<p>This question is not homework but it's related to material in a general course I take about programming languages, so I don't know whats the site policy about this</p>

<p>In ML the following expressio... | habedi/stack-exchange-dataset |
9,945 | How does interpreting a script work? | <p>Suppose I have a script (<code>.vbs</code>, for example) that is stored in a file. How does the code in the file get converted into machine instructions? What is between the vbs file and the processor?</p>
 | programming languages compilers interpreters | 1 | How does interpreting a script work? -- (programming languages compilers interpreters)
<p>Suppose I have a script (<code>.vbs</code>, for example) that is stored in a file. How does the code in the file get converted into machine instructions? What is between the vbs file and the processor?</p>
 | habedi/stack-exchange-dataset |
9,952 | Doron ZEILBERGER's P = NP computer proof | <p>In 2009 Doron has published a paper stating "Using 3000 hours of CPU time on a CRAY machine, we settle the notorious P vs. NP problem in the affirmative, by presenting a “polynomial” time algorithm for the NP-complete subset sum problem.". I've been looking for other people's opinions on this but I haven't found any... | complexity theory np complete | 1 | Doron ZEILBERGER's P = NP computer proof -- (complexity theory np complete)
<p>In 2009 Doron has published a paper stating "Using 3000 hours of CPU time on a CRAY machine, we settle the notorious P vs. NP problem in the affirmative, by presenting a “polynomial” time algorithm for the NP-complete subset sum problem.". I... | habedi/stack-exchange-dataset |
9,954 | Is there an efficient test for if an NFA accepts a subset of another NFA? | <p>So, I know that testing if a regular language $R$ is a subset of regular language $S$ is decidable, since we can convert them both to DFAs, compute $R \cap \bar{S}$, and then test if this language is empty.</p>

<p>However, since this requires converting to DFAs, it's possible that the DFAs, and thus the tes... | algorithms regular languages automata np complete decision problem | 1 | Is there an efficient test for if an NFA accepts a subset of another NFA? -- (algorithms regular languages automata np complete decision problem)
<p>So, I know that testing if a regular language $R$ is a subset of regular language $S$ is decidable, since we can convert them both to DFAs, compute $R \cap \bar{S}$, and t... | habedi/stack-exchange-dataset |
9,958 | Factorial usage within proof using the pumping lemma | <p>We are going over the pumping lemma in class and we recently went over the following example:</p>

<ol>
<li>Let
$$ L = \{ w \mid w \text{ has a different number of 0s and 1s} \} $$</li>
<li>Consider
$$
s = 0^P1^\left(P+P!\right)
$$</li>
<li>$ s $ can be divided into $ s = xyz $</l... | pumping lemma | 1 | Factorial usage within proof using the pumping lemma -- (pumping lemma)
<p>We are going over the pumping lemma in class and we recently went over the following example:</p>

<ol>
<li>Let
$$ L = \{ w \mid w \text{ has a different number of 0s and 1s} \} $$</li>
<li>Consider
$$
s = 0^P1^\left(... | habedi/stack-exchange-dataset |
9,961 | How to define at least one occurrence of a string between two tokens in bottom up LALR(1) parser grammar | <p>I am trying to define a non terminal symbol in a LALR(1) grammar (with CUP parser). It is requested that </p>

<pre><code>the <code> token must appear exactly twice, 
while the <hour> token must appear at least once.
</code></pre>

<p>In the end I came up with this definition:</p>... | formal grammars parsing | 1 | How to define at least one occurrence of a string between two tokens in bottom up LALR(1) parser grammar -- (formal grammars parsing)
<p>I am trying to define a non terminal symbol in a LALR(1) grammar (with CUP parser). It is requested that </p>

<pre><code>the <code> token must appear exactly twice, &#x... | habedi/stack-exchange-dataset |
9,965 | When can one use a $O(n)$ time sorting algorithm? | <p>Some sorting algorithms like counting sort/insertion sort can work in $O(n)$ time while other algorithms such as quicksort require $O(n \log n)$ time.</p>

<p>As I understand it, it's not always possible to use the $O(n)$ sorting algorithms. What are those cases when they can not be used?</p>
 | algorithms sorting | 1 | When can one use a $O(n)$ time sorting algorithm? -- (algorithms sorting)
<p>Some sorting algorithms like counting sort/insertion sort can work in $O(n)$ time while other algorithms such as quicksort require $O(n \log n)$ time.</p>

<p>As I understand it, it's not always possible to use the $O(n)$ sorting algor... | habedi/stack-exchange-dataset |
9,969 | Finding a '1' cell with a '0' to its right in a binary array | <p>Given an array of size n that holds ones and zeros I need to find an index of a <code>1</code> cell that has <code>0</code> to his right (in then next cell) there could be more than one pair in a given array, any one of them is fine. The array is not sorted, but we do know that the first element is <code>1</code> a... | algorithms arrays search algorithms binary search | 1 | Finding a '1' cell with a '0' to its right in a binary array -- (algorithms arrays search algorithms binary search)
<p>Given an array of size n that holds ones and zeros I need to find an index of a <code>1</code> cell that has <code>0</code> to his right (in then next cell) there could be more than one pair in a give... | habedi/stack-exchange-dataset |
9,977 | Are all possible programming languages a formal system? | <p>Based on the Wikipedia page for <a href="http://en.wikipedia.org/wiki/Formal_system" rel="nofollow">a formal system</a>, will all programming languages be contained within the following rules?</p>

<ul>
<li><strong>A finite set of of symbols.</strong></li>
</ul>

<p>(This seems obvious since ... | formal languages | 1 | Are all possible programming languages a formal system? -- (formal languages)
<p>Based on the Wikipedia page for <a href="http://en.wikipedia.org/wiki/Formal_system" rel="nofollow">a formal system</a>, will all programming languages be contained within the following rules?</p>

<ul>
<li><strong>A finite set... | habedi/stack-exchange-dataset |
9,979 | Using tree search | <p>I have some questions regarding tree search and graph search (Uninformed search) as explained in chapter 3 of the book : <a href="http://aima.cs.berkeley.edu/" rel="nofollow">http://aima.cs.berkeley.edu/</a></p>

<p>As I see, the only difference between the two is that the graph search handles loops (avoids ... | artificial intelligence search algorithms | 1 | Using tree search -- (artificial intelligence search algorithms)
<p>I have some questions regarding tree search and graph search (Uninformed search) as explained in chapter 3 of the book : <a href="http://aima.cs.berkeley.edu/" rel="nofollow">http://aima.cs.berkeley.edu/</a></p>

<p>As I see, the only differenc... | habedi/stack-exchange-dataset |
9,985 | Anti-symmetry of polynomial time reductions | <p>I read somewhere that, if $A\leq_p B$ and $B\leq_p A$, then it is said that $A\equiv_p B$. What exactly does this mean? Is it saying that both $A$ and $B$ are the exact same level of complexity?</p>
 | complexity theory reductions | 1 | Anti-symmetry of polynomial time reductions -- (complexity theory reductions)
<p>I read somewhere that, if $A\leq_p B$ and $B\leq_p A$, then it is said that $A\equiv_p B$. What exactly does this mean? Is it saying that both $A$ and $B$ are the exact same level of complexity?</p>
 | habedi/stack-exchange-dataset |
9,987 | Tasks in which recursion is either the fastest or only way to produce a result | <p>I've just finished studying recursion at university. One thing that stood out for me however was that in both the lectures and in the practical we completed, all the tasks we were asked to do could be performed faster, and in less code, using iterative means.<br>
This was something the lecturer confirmed.</p>&#x... | recursion | 1 | Tasks in which recursion is either the fastest or only way to produce a result -- (recursion)
<p>I've just finished studying recursion at university. One thing that stood out for me however was that in both the lectures and in the practical we completed, all the tasks we were asked to do could be performed faster, and ... | habedi/stack-exchange-dataset |
9,998 | Equivalence of NFA and DFA - proof by construction | <p>I was looking at the construction proof showing the equivalence of NFA and DFA from Sipser's text. It started by taking number of states of DFA as $\mathcal{P}(Q)$, where $\mathcal{P}(Q)$ is the set of subsets of $Q$. </p>

<p>My doubt is when we construct DFA from NFA, all the subsets may not occur in that ... | automata nondeterminism automated theorem proving | 1 | Equivalence of NFA and DFA - proof by construction -- (automata nondeterminism automated theorem proving)
<p>I was looking at the construction proof showing the equivalence of NFA and DFA from Sipser's text. It started by taking number of states of DFA as $\mathcal{P}(Q)$, where $\mathcal{P}(Q)$ is the set of subsets o... | habedi/stack-exchange-dataset |
10,002 | Why do we use persistent data structures in functional programming? | <p>Functional programming employs persistent data structures and immutable objects. My question is why is it crucial to have such data structures here? I want to understand <strong>at a low level</strong> what would happen if the data structure is not persistent? Would the program crash more often? </p>
 | data structures functional programming programming paradigms persistent data structure | 1 | Why do we use persistent data structures in functional programming? -- (data structures functional programming programming paradigms persistent data structure)
<p>Functional programming employs persistent data structures and immutable objects. My question is why is it crucial to have such data structures here? I want t... | habedi/stack-exchange-dataset |
10,013 | If $L$ is a subset of $\{0\}^*$, then how can we show that $L^*$ is regular? | <p>Say, $L \subseteq \{0\}^*$. Then how can we prove that $L^*$ is regular?</p>

<p>If $L$ is regular, then of course $L^*$ is also regular. If $L$ is finite, then it is regular and again $L^*$ is regular.
Also I have noticed that, for $L = \{0^p \mid p \text{ is a prime}\}$, $L$ is not regular, $L \subsete... | formal languages regular languages | 1 | If $L$ is a subset of $\{0\}^*$, then how can we show that $L^*$ is regular? -- (formal languages regular languages)
<p>Say, $L \subseteq \{0\}^*$. Then how can we prove that $L^*$ is regular?</p>

<p>If $L$ is regular, then of course $L^*$ is also regular. If $L$ is finite, then it is regular and again $L^*$ i... | habedi/stack-exchange-dataset |
10,014 | How can I argue that $3\mathsf{SAT}\leq_p \mathsf{IndSet}$ is polynomial in time? | <p>Given the reduction $3\mathsf{SAT}\leq_p \mathsf{IndSet}$ as follows:</p>

<p><img src="https://i.stack.imgur.com/PCe9v.png" alt="enter image description here"></p>

<p>How can I argue that it's in polynomial time? I understand how the reduction works, but even though it appears rather trivial, I can... | complexity theory reductions | 1 | How can I argue that $3\mathsf{SAT}\leq_p \mathsf{IndSet}$ is polynomial in time? -- (complexity theory reductions)
<p>Given the reduction $3\mathsf{SAT}\leq_p \mathsf{IndSet}$ as follows:</p>

<p><img src="https://i.stack.imgur.com/PCe9v.png" alt="enter image description here"></p>

<p>How can I argue ... | habedi/stack-exchange-dataset |
10,016 | Prove that 2-Colourability is in L from Undir-Reachability is in L | <p>Let Undir-Reachability be the following problem:
given an undirected graph G and two specified vertices s and t in G, is there a path from s to t in G?</p>

<p>I need to prove that the 2-Colourability is in L, by knowing that Undir-Reachability belongs to the complexity class L.</p>

<p>I don't k... | complexity theory graphs space complexity colorings | 1 | Prove that 2-Colourability is in L from Undir-Reachability is in L -- (complexity theory graphs space complexity colorings)
<p>Let Undir-Reachability be the following problem:
given an undirected graph G and two specified vertices s and t in G, is there a path from s to t in G?</p>

<p>I need to prove that ... | habedi/stack-exchange-dataset |
10,017 | Prove that $0$-$1$ $\mathsf{ Ineq}$ is $\mathsf{NL}$-complete | <p>I need to prove that the following problem $0$-$1$ $\mathsf{ Ineq}$ is $\mathsf{NL}$-complete.</p>

<p>Given a finite set of variables $V$, a finite set of inequalities of the form $x \le y$ (where $x, y \in V$) and a finite set of equalities of the form $x=a$ (where $x \in V$ and $a \in \{0,1\}$), is there ... | complexity theory graphs reductions space complexity | 1 | Prove that $0$-$1$ $\mathsf{ Ineq}$ is $\mathsf{NL}$-complete -- (complexity theory graphs reductions space complexity)
<p>I need to prove that the following problem $0$-$1$ $\mathsf{ Ineq}$ is $\mathsf{NL}$-complete.</p>

<p>Given a finite set of variables $V$, a finite set of inequalities of the form $x \le y... | habedi/stack-exchange-dataset |
10,019 | How to apply the pumping lemma to $\{0^m 1^n \mid 2n \leq m \leq 3n, m,n \geq 0 \}$? | <p>I'm not really sure the how you would go about proving this language isn't regular with the pumping lemma:</p>

<p>$L= \{0^m 1^n | 2n \leq m \leq 3n, m,n \geq 0 \}$</p>

<p>Does this indicate that $S = 2$, so we start by by using a string $\geq 2$?</p>
 | regular languages proof techniques pumping lemma | 1 | How to apply the pumping lemma to $\{0^m 1^n \mid 2n \leq m \leq 3n, m,n \geq 0 \}$? -- (regular languages proof techniques pumping lemma)
<p>I'm not really sure the how you would go about proving this language isn't regular with the pumping lemma:</p>

<p>$L= \{0^m 1^n | 2n \leq m \leq 3n, m,n \geq 0 \}$</p>... | habedi/stack-exchange-dataset |
10,029 | DFA Minimization: Finding all equivalence classes of $\mathsf{R_L}$ for language $011(0+1)^*011$ | <p>How do we find all equivalence classes of $\mathsf{R_L}$ for a language? </p>

<p>Say I'm trying to look for all equivalent classes for the regular language $\mathsf{L}$ is $011(0+1)^*011$.</p>

<p>Here's an example they give us in the book
<a href="http://books.google.com/books?id=VEHYzv0GHt8C&a... | regular languages finite automata | 1 | DFA Minimization: Finding all equivalence classes of $\mathsf{R_L}$ for language $011(0+1)^*011$ -- (regular languages finite automata)
<p>How do we find all equivalence classes of $\mathsf{R_L}$ for a language? </p>

<p>Say I'm trying to look for all equivalent classes for the regular language $\mathsf{L}$ is ... | habedi/stack-exchange-dataset |
10,031 | Proof-sketch on the language accepted by a Turing machine | <p>Let $T$ be a Turing machine whose accepted language is $L(T)$. Let $X$ be another language. How do you approach a proof like $L(T)\subseteq X?$</p>
 | formal languages turing machines proof techniques | 1 | Proof-sketch on the language accepted by a Turing machine -- (formal languages turing machines proof techniques)
<p>Let $T$ be a Turing machine whose accepted language is $L(T)$. Let $X$ be another language. How do you approach a proof like $L(T)\subseteq X?$</p>
 | habedi/stack-exchange-dataset |
10,034 | Evaluation of reverse Polish notation | <p>We only consider the <a href="http://en.wikipedia.org/wiki/Reverse_Polish_notation" rel="nofollow noreferrer">reverse Polish notation</a> as an arithmetic expression.</p>

<p>Formally, RNP is a sequence consisted of numbers and arithmetic operators: $+,-,*,/$, and its syntax is:
$$\newcommand\RNF{\mathrm... | algorithms formal languages software verification | 1 | Evaluation of reverse Polish notation -- (algorithms formal languages software verification)
<p>We only consider the <a href="http://en.wikipedia.org/wiki/Reverse_Polish_notation" rel="nofollow noreferrer">reverse Polish notation</a> as an arithmetic expression.</p>

<p>Formally, RNP is a sequence consisted of ... | habedi/stack-exchange-dataset |
10,041 | Multithreaded access to a persistent linked list data structure | <p>I previously asked a question about persistent data structures <a href="https://cs.stackexchange.com/questions/10002/why-do-we-use-persistent-data-structures-in-functional-programming">here</a>. After that I came across an <a href="http://www.codeproject.com/Articles/9680/Persistent-Data-Structures" rel="nofollow no... | data structures concurrency persistent data structure | 1 | Multithreaded access to a persistent linked list data structure -- (data structures concurrency persistent data structure)
<p>I previously asked a question about persistent data structures <a href="https://cs.stackexchange.com/questions/10002/why-do-we-use-persistent-data-structures-in-functional-programming">here</a>.... | habedi/stack-exchange-dataset |
10,043 | CPU Cache is managed by which software component? | <p>CPU caches are used by exploiting temporal and spatial locality. My question is who is responsible for managing these caches? Is this Operating system that identifies a particular access pattern and then manages (i.e store the data in) cache, using low level OS function calls? </p>
 | computer architecture cpu cache | 1 | CPU Cache is managed by which software component? -- (computer architecture cpu cache)
<p>CPU caches are used by exploiting temporal and spatial locality. My question is who is responsible for managing these caches? Is this Operating system that identifies a particular access pattern and then manages (i.e store the dat... | habedi/stack-exchange-dataset |
10,044 | What graph data structure works fastest with Dijkstra's algorithm? | <p>What data structure should I store my graph in to get the best performance from the Dijkstra algorithm?</p>

<p>Object-pointer? Adjacency list? Something else?</p>

<p>I want the lowest O(). Any other tips are appreciated too!</p>
 | algorithms data structures | 1 | What graph data structure works fastest with Dijkstra's algorithm? -- (algorithms data structures)
<p>What data structure should I store my graph in to get the best performance from the Dijkstra algorithm?</p>

<p>Object-pointer? Adjacency list? Something else?</p>

<p>I want the lowest O(). Any other t... | habedi/stack-exchange-dataset |
10,047 | Is Dijkstra's algorithm just BFS with a priority queue? | <p>According to <a href="https://www.topcoder.com/community/data-science/data-science-tutorials/introduction-to-graphs-and-their-data-structures-section-3/" rel="noreferrer">this page</a>, Dijkstra's algorithm is just BFS with a priority queue. Is it really that simple? I think not.</p>
 | algorithms graphs shortest path | 1 | Is Dijkstra's algorithm just BFS with a priority queue? -- (algorithms graphs shortest path)
<p>According to <a href="https://www.topcoder.com/community/data-science/data-science-tutorials/introduction-to-graphs-and-their-data-structures-section-3/" rel="noreferrer">this page</a>, Dijkstra's algorithm is just BFS with ... | habedi/stack-exchange-dataset |
10,049 | Is search a binary heap operation? | <p>According to the <a href="http://en.wikipedia.org/wiki/Binary_heap" rel="noreferrer">Wikipedia page</a>, search is "not an operation" on binary heaps (see complexity box at top-right).</p>

<p>Why not? Binary heaps may not be sorted, but they are ordered, and a full graph traversal can find any object in $O(... | data structures search algorithms heaps | 1 | Is search a binary heap operation? -- (data structures search algorithms heaps)
<p>According to the <a href="http://en.wikipedia.org/wiki/Binary_heap" rel="noreferrer">Wikipedia page</a>, search is "not an operation" on binary heaps (see complexity box at top-right).</p>

<p>Why not? Binary heaps may not be sor... | habedi/stack-exchange-dataset |
10,056 | Leftist heap - determining time complexity | <p>The time complexity of merge (union) operation is said to be $O(\lg (n_1 + n_2))$, where $n_1$ and $n_2$ are the numbers of elements in the merged heaps, respectively. I do not understand this - the algorithm has to go through all the elements of both rightmost paths of the original heaps - lengths of these paths ar... | data structures runtime analysis heaps | 1 | Leftist heap - determining time complexity -- (data structures runtime analysis heaps)
<p>The time complexity of merge (union) operation is said to be $O(\lg (n_1 + n_2))$, where $n_1$ and $n_2$ are the numbers of elements in the merged heaps, respectively. I do not understand this - the algorithm has to go through all... | habedi/stack-exchange-dataset |
10,058 | Why does bubble sort do $\Theta(n^2)$ comparisons on an $n$ element list? | <p>I have a quick question on the bubble sort algorithm. Why does it perform $\Theta(n^2)$ comparisons on an $n$ element list?</p>

<p>I looked at the Wikipedia page and it does not seem to tell me. I know that because of its magnitude it takes a lot of work with large numbers.</p>
 | algorithms algorithm analysis sorting | 1 | Why does bubble sort do $\Theta(n^2)$ comparisons on an $n$ element list? -- (algorithms algorithm analysis sorting)
<p>I have a quick question on the bubble sort algorithm. Why does it perform $\Theta(n^2)$ comparisons on an $n$ element list?</p>

<p>I looked at the Wikipedia page and it does not seem to tell ... | habedi/stack-exchange-dataset |
10,059 | first order logic resolution unification | <p>Assuming I have shown part of the knowledge base in the clausal format:</p>

<pre><code>[1] p1(banana).

[2] not p1(X) or p2(Y).
[3] p1(X) or not p3(F).
</code></pre>

<p>... and more rules.</p>

<p>Most of the books, would do something like this:</p>

<pre><code>[1,2]... | artificial intelligence first order logic knowledge representation | 1 | first order logic resolution unification -- (artificial intelligence first order logic knowledge representation)
<p>Assuming I have shown part of the knowledge base in the clausal format:</p>

<pre><code>[1] p1(banana).

[2] not p1(X) or p2(Y).
[3] p1(X) or not p3(F).
</code></pre>

<p>.... | habedi/stack-exchange-dataset |
10,064 | String of minimum length in $\{a, b\}^*$ not in a regular expression | <p>I'm doing an exercise in my <a href="http://rads.stackoverflow.com/amzn/click/0073191469" rel="nofollow">book</a>, the question is to find a string of minimum length in $\{a, b\}^*$ not in the language corresponding to the given regular expression.</p>

<p>a. $b^*(ab)^*a^*$</p>

<p>My answer: $aab$</... | formal languages regular languages regular expressions check my answer | 1 | String of minimum length in $\{a, b\}^*$ not in a regular expression -- (formal languages regular languages regular expressions check my answer)
<p>I'm doing an exercise in my <a href="http://rads.stackoverflow.com/amzn/click/0073191469" rel="nofollow">book</a>, the question is to find a string of minimum length in $\{... | habedi/stack-exchange-dataset |
10,074 | Constructing right-linear grammar | <p>Is the grammar</p>

<p>$\qquad S \to 1A0A \mid 0A \mid \varepsilon$</p>

<p>a right-linear grammar? $A$ is a nonterminal here, $0$ and $1$ are terminals.</p>

<p>I know $0A$ is right-linear but what about $1A0A$?</p>

<p>Trying to construct a right-linear grammar for language $10(0+1)... | regular languages formal grammars | 1 | Constructing right-linear grammar -- (regular languages formal grammars)
<p>Is the grammar</p>

<p>$\qquad S \to 1A0A \mid 0A \mid \varepsilon$</p>

<p>a right-linear grammar? $A$ is a nonterminal here, $0$ and $1$ are terminals.</p>

<p>I know $0A$ is right-linear but what about $1A0A$?</p>
... | habedi/stack-exchange-dataset |
10,077 | Finding simpler equivalent regular expressions | <p>I'm doing an exercise from my book that says:</p>
<blockquote>
<p>Let <span class="math-container">$r$</span> and <span class="math-container">$s$</span> be arbitrary regular expressions over the alphabet <span class="math-container">$\Sigma$</span>. Find a simpler equivalent regular expression:</p>
<p>a... | regular expressions | 1 | Finding simpler equivalent regular expressions -- (regular expressions)
<p>I'm doing an exercise from my book that says:</p>
<blockquote>
<p>Let <span class="math-container">$r$</span> and <span class="math-container">$s$</span> be arbitrary regular expressions over the alphabet <span class="math-container">$\S... | habedi/stack-exchange-dataset |
10,079 | Are there languages generated by linear grammar which aren't regular? | <p>Are there languages generated by linear grammer which aren't regular?</p>
 | formal languages formal grammars context free | 1 | Are there languages generated by linear grammar which aren't regular? -- (formal languages formal grammars context free)
<p>Are there languages generated by linear grammer which aren't regular?</p>
 | habedi/stack-exchange-dataset |
10,081 | What is the complexity of this matrix transposition? | <p>I'm working on some exercises regarding graph theory and complexity. 
Now I'm asked to give an algorithm that computes a transposed graph of $G$, $G^T$ given the adjacency matrix of $G$. So basically I just have to give an algorithm to transpose an $N \times N$ matrix.</p>

<p>My first thought was to loo... | graphs time complexity algorithm analysis linear algebra adjacency matrix | 1 | What is the complexity of this matrix transposition? -- (graphs time complexity algorithm analysis linear algebra adjacency matrix)
<p>I'm working on some exercises regarding graph theory and complexity. 
Now I'm asked to give an algorithm that computes a transposed graph of $G$, $G^T$ given the adjacency matrix of... | habedi/stack-exchange-dataset |
10,091 | What are the characteristics of a $\Theta(n \log n)$ time complexity algorithm? | <p>Sometimes it's easy to identify the time complexity of an algorithm my examining it carefully. Algorithms with two nested loops of $N$ are obviously $N^2$. Algorithms that explore all the possible combinations of $N$ groups of two values are obviously $2^N$.</p>

<p>However I don't know how to "spot" an algo... | algorithm analysis time complexity intuition | 1 | What are the characteristics of a $\Theta(n \log n)$ time complexity algorithm? -- (algorithm analysis time complexity intuition)
<p>Sometimes it's easy to identify the time complexity of an algorithm my examining it carefully. Algorithms with two nested loops of $N$ are obviously $N^2$. Algorithms that explore all the... | habedi/stack-exchange-dataset |
10,096 | Proving non-confluency and adding an equation to make it confluent and terminating | <p>I currently have a system that has <code>{f(a) = b, f(f(x)) = x}</code> (part of an <a href="http://folk.uio.no/peterol/INF3230V13/Oppgaver/midterm06.pdf" rel="nofollow">exam question</a> - look at page 5 - exercise 1).</p>

<p>To start off with proving non-confluency, I am thinking along these lines:</p>&#x... | logic proof techniques semantics term rewriting | 1 | Proving non-confluency and adding an equation to make it confluent and terminating -- (logic proof techniques semantics term rewriting)
<p>I currently have a system that has <code>{f(a) = b, f(f(x)) = x}</code> (part of an <a href="http://folk.uio.no/peterol/INF3230V13/Oppgaver/midterm06.pdf" rel="nofollow">exam questi... | habedi/stack-exchange-dataset |
10,098 | Why is MAX-2SAT not in P? | <blockquote>
 <p>Max-2-SAT is defined as follows. We are given a 2-CNF formula and a
 bound k, and asked to find an assignment to the variables that
 satisfies at least k of the clauses.</p>
</blockquote>

<p>I can understand the trick used to prove 2-SAT is in P. You use get a contradiction ... | complexity theory np complete satisfiability | 1 | Why is MAX-2SAT not in P? -- (complexity theory np complete satisfiability)
<blockquote>
 <p>Max-2-SAT is defined as follows. We are given a 2-CNF formula and a
 bound k, and asked to find an assignment to the variables that
 satisfies at least k of the clauses.</p>
</blockquote>

<p>I can un... | habedi/stack-exchange-dataset |
10,103 | applying CTL/LTL model-checking on some system | <p>I apologies if my title is vague, I'm trying to apply CTL/LTL model-checking on some system written in java, however, I still don't understand how to reach a result using either of the approaches mentioned. Do I model my LTS/write specification and use a tool like SPIN to validate that or? I'm mainly looking for a p... | concurrency model checking computation tree logic software verification | 1 | applying CTL/LTL model-checking on some system -- (concurrency model checking computation tree logic software verification)
<p>I apologies if my title is vague, I'm trying to apply CTL/LTL model-checking on some system written in java, however, I still don't understand how to reach a result using either of the approach... | habedi/stack-exchange-dataset |
10,121 | What is Harrison hashing, its applications in web search engines? | <p>What is Harrison hashing and what are its applications in web searching? 
Can some one give me some relevant information? </p>

<p><strong>Update:</strong></p>

<p>I found it <a href="http://www.cs.manchester.ac.uk/ugt/COMP26120/" rel="nofollow">here</a> , and is a part of M.Tech syllabus of a... | algorithms strings search algorithms hash | 1 | What is Harrison hashing, its applications in web search engines? -- (algorithms strings search algorithms hash)
<p>What is Harrison hashing and what are its applications in web searching? 
Can some one give me some relevant information? </p>

<p><strong>Update:</strong></p>

<p>I found it <a hre... | habedi/stack-exchange-dataset |
10,124 | Decidable languages and unrestricted grammars? | <p>Turing machines and unrestricted grammars are two different formalisms that define the RE languages. Some RE languages are decidable, but not all are.</p>

<p>We can define the decidable languages with Turing machines by saying that a language is decidable iff there is a TM for the language that halts and a... | computability turing machines formal grammars | 1 | Decidable languages and unrestricted grammars? -- (computability turing machines formal grammars)
<p>Turing machines and unrestricted grammars are two different formalisms that define the RE languages. Some RE languages are decidable, but not all are.</p>

<p>We can define the decidable languages with Turing m... | habedi/stack-exchange-dataset |
10,129 | How does 'deforestation' remove 'trees' from a program? | <p>I think understand how deforestation consumes and produces a list at the same time (from a fold and an unfold function -- <a href="https://codereview.stackexchange.com/questions/23180/how-to-make-this-python-function-and-its-inverse-more-beautiful-and-symmetric">see this good answer on CodeReview here</a>), but when... | terminology compilers functional programming | 1 | How does 'deforestation' remove 'trees' from a program? -- (terminology compilers functional programming)
<p>I think understand how deforestation consumes and produces a list at the same time (from a fold and an unfold function -- <a href="https://codereview.stackexchange.com/questions/23180/how-to-make-this-python-fun... | habedi/stack-exchange-dataset |
10,130 | Why can the state space of the 15 puzzle be divided into two separate parts? | <p>I am trying to understand the <a href="http://www.cut-the-knot.com/pythagoras/fifteen.shtml">proof here</a> of why the state space in 15 puzzle is divided into two separate parts, but the explanation is complicated for me.</p>

<p>Could someone please explain it in simpler terms? I have been struggling with ... | artificial intelligence search algorithms | 1 | Why can the state space of the 15 puzzle be divided into two separate parts? -- (artificial intelligence search algorithms)
<p>I am trying to understand the <a href="http://www.cut-the-knot.com/pythagoras/fifteen.shtml">proof here</a> of why the state space in 15 puzzle is divided into two separate parts, but the expla... | habedi/stack-exchange-dataset |
10,131 | ML - Type Interface | <p>From my recitation class - </p>

<p><img src="https://i.stack.imgur.com/Zn74M.jpg" alt="enter image description here"></p>

<p>Can you please explain </p>

<ul>
<li><p>why does operator $"+"$ signature is $ int \rightarrow (int \rightarrow int)$ ?</p></li>
<li><p>How does this gra... | programming languages functional programming type inference type checking | 1 | ML - Type Interface -- (programming languages functional programming type inference type checking)
<p>From my recitation class - </p>

<p><img src="https://i.stack.imgur.com/Zn74M.jpg" alt="enter image description here"></p>

<p>Can you please explain </p>

<ul>
<li><p>why does operator $"... | habedi/stack-exchange-dataset |
10,141 | 2-D peak finding complexity (MIT OCW 6.006) | <p>In a recitation video for <a href="http://www.youtube.com/watch?feature=player_embedded&v=P7frcB_-g4w" rel="noreferrer">MIT OCW 6.006</a> at 43:30,</p>
<p>Given an <span class="math-container">$m \times n$</span> matrix <span class="math-container">$A$</span> with <span class="math-container">$m$</span> colu... | algorithms algorithm analysis asymptotics matrices | 1 | 2-D peak finding complexity (MIT OCW 6.006) -- (algorithms algorithm analysis asymptotics matrices)
<p>In a recitation video for <a href="http://www.youtube.com/watch?feature=player_embedded&v=P7frcB_-g4w" rel="noreferrer">MIT OCW 6.006</a> at 43:30,</p>
<p>Given an <span class="math-container">$m \times n$</sp... | habedi/stack-exchange-dataset |
10,142 | Priority in formal grammar | <p>From my recitation class, I have the following exercise:</p>

<blockquote>
 <p>$\mathrm{EXP} = 0 \mid 1 \mid b \mathrm{EXP} \mid \mathrm{EXP} a \mid \mathrm{EXP} m \mathrm{EXP}$</p>
 
 <p>The above grammar is ambiguous.</p>
 
 <p>Make an unambiguous grammar which produce same languag... | formal languages formal grammars parsing ambiguity | 1 | Priority in formal grammar -- (formal languages formal grammars parsing ambiguity)
<p>From my recitation class, I have the following exercise:</p>

<blockquote>
 <p>$\mathrm{EXP} = 0 \mid 1 \mid b \mathrm{EXP} \mid \mathrm{EXP} a \mid \mathrm{EXP} m \mathrm{EXP}$</p>
 
 <p>The above grammar is am... | habedi/stack-exchange-dataset |
10,147 | Is The Following Language Regular? | <p>Let $L_{1}$ and $L_{2}$ be 2 languages over the same alphabet $\Sigma$. </p>

<p>$$A(L_1,L_2)=\{x\in \Sigma^*|\exists y,z\in L_2\text{ such that } yxz\in L_1\}$$</p>

<p>Assume that $L_{1}$ is regular and $L_{2}$ is context-free. The language $A(L_{1},L_{2})$:</p>

<ol>
<li>is always a r... | formal languages regular languages automata context free finite automata | 1 | Is The Following Language Regular? -- (formal languages regular languages automata context free finite automata)
<p>Let $L_{1}$ and $L_{2}$ be 2 languages over the same alphabet $\Sigma$. </p>

<p>$$A(L_1,L_2)=\{x\in \Sigma^*|\exists y,z\in L_2\text{ such that } yxz\in L_1\}$$</p>

<p>Assume that $L_{1... | habedi/stack-exchange-dataset |
10,152 | A* optimality of the expanded node | <p>Suppose I have a admissible and consistent heuristic.</p>

<p>Is it true, that when I expand a node, I have guaranteed that the path I found to this node is optimal?</p>

<p>Look at this pseudocode from wikipedia:</p>

<pre><code>function A*(start,goal)
 closedset := the empty set // T... | algorithms algorithm analysis search algorithms correctness proof | 1 | A* optimality of the expanded node -- (algorithms algorithm analysis search algorithms correctness proof)
<p>Suppose I have a admissible and consistent heuristic.</p>

<p>Is it true, that when I expand a node, I have guaranteed that the path I found to this node is optimal?</p>

<p>Look at this pseudoco... | habedi/stack-exchange-dataset |
10,158 | Origin of theta-joins | <p>I've taken an introductory database course where like many good database courses, they taught relational algebra, including $\theta$-joins. However, I've recently read E. F. Codd's 1970 paper, <a href="http://www.seas.upenn.edu/~zives/03f/cis550/codd.pdf" rel="nofollow"><em>A Relational Model of Data for Large Share... | reference request history relational algebra | 1 | Origin of theta-joins -- (reference request history relational algebra)
<p>I've taken an introductory database course where like many good database courses, they taught relational algebra, including $\theta$-joins. However, I've recently read E. F. Codd's 1970 paper, <a href="http://www.seas.upenn.edu/~zives/03f/cis550... | habedi/stack-exchange-dataset |
10,175 | Minimizing Turing machine-like automaton with no final states | <p>I have a deterministic finite automaton which behaves mostly like a Turing machine, with following difference (relevant to this question):</p>

<ul>
<li>The tape is initially finite.</li>
<li>The automaton can insert and delete cells from the tape.</li>
<li>Actions are associated with states rath... | turing machines automata finite automata | 1 | Minimizing Turing machine-like automaton with no final states -- (turing machines automata finite automata)
<p>I have a deterministic finite automaton which behaves mostly like a Turing machine, with following difference (relevant to this question):</p>

<ul>
<li>The tape is initially finite.</li>
<li>T... | habedi/stack-exchange-dataset |
10,178 | Algorithm for generating heat maps | <p>I am looking to generate a heat map from some data. I have a value and a location (longitude and latitude). I understand generating a colour from the value, however I'm not sure how I would go about generating the matrix to use for this. </p>

<p>I figure it's best to place the location points into buckets e... | algorithms matrices | 1 | Algorithm for generating heat maps -- (algorithms matrices)
<p>I am looking to generate a heat map from some data. I have a value and a location (longitude and latitude). I understand generating a colour from the value, however I'm not sure how I would go about generating the matrix to use for this. </p>

<p>I ... | habedi/stack-exchange-dataset |
10,180 | DFA to regular expression conversion | <p>I was looking at the question <a href="https://cs.stackexchange.com/questions/2016/how-to-convert-finite-automata-to-regular-expressions">How to convert finite automata to regular expressions?</a> to convert DFA to regex.</p>

<p>The question, I was trying to solve is:</p>

<p><img src="https://i.sta... | regular languages automata finite automata regular expressions | 1 | DFA to regular expression conversion -- (regular languages automata finite automata regular expressions)
<p>I was looking at the question <a href="https://cs.stackexchange.com/questions/2016/how-to-convert-finite-automata-to-regular-expressions">How to convert finite automata to regular expressions?</a> to convert DFA ... | habedi/stack-exchange-dataset |
10,181 | Longest path in undirected tree | <p>Given an undirected tree (with no specific root), how to find the longest path, i.e. 2 vertices that are the farthest apart from each other? There are no lengths associated with the edges (each edge has length 1 by default).<br>
Obviously one idea is to check the path lengths between all pairs of vertices (e.g. ... | algorithms graphs trees | 1 | Longest path in undirected tree -- (algorithms graphs trees)
<p>Given an undirected tree (with no specific root), how to find the longest path, i.e. 2 vertices that are the farthest apart from each other? There are no lengths associated with the edges (each edge has length 1 by default).<br>
Obviously one idea is t... | habedi/stack-exchange-dataset |
10,208 | Mutable Object Values in a Functional Interpreter | <p>I am writing a functional style interpreter for a non-functional programming language that supports both primitive and object values. Primitives are passed by value while objects are passed by reference. I understand how to deal with primitive values but cannot find any good resources on handling mutable object valu... | programming languages | 1 | Mutable Object Values in a Functional Interpreter -- (programming languages)
<p>I am writing a functional style interpreter for a non-functional programming language that supports both primitive and object values. Primitives are passed by value while objects are passed by reference. I understand how to deal with primit... | habedi/stack-exchange-dataset |
10,210 | Time units required for Interrupt Cycle | <p>I am reading William Stallings Computer Organization & Architecture to understand about control unit & micro-operations. </p>

<p>Stallings explain that interrupt cycle requires 3 time units to complete : </p>

<pre><code>t1 : MBR <- (PC)
t2 : MAR <- Save_Address
 PC <- R... | computer architecture | 1 | Time units required for Interrupt Cycle -- (computer architecture)
<p>I am reading William Stallings Computer Organization & Architecture to understand about control unit & micro-operations. </p>

<p>Stallings explain that interrupt cycle requires 3 time units to complete : </p>

<pre><code>t1 :... | habedi/stack-exchange-dataset |
10,216 | Speeding up a program solving Icosoku | <p>I bought a great puzzle called <a href="http://en.wikipedia.org/wiki/Icosoku" rel="nofollow">Icosoku</a>. Wikipedia describes it as: "The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles with black dots and 12 yellow pins for the corners. The pins are print... | efficiency computer games | 1 | Speeding up a program solving Icosoku -- (efficiency computer games)
<p>I bought a great puzzle called <a href="http://en.wikipedia.org/wiki/Icosoku" rel="nofollow">Icosoku</a>. Wikipedia describes it as: "The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles w... | habedi/stack-exchange-dataset |
10,224 | Input size of 3-SAT when analyzing complexity | <p>We know that $\text{3-SAT}$ problem is NP-complete, but I am not sure what is meant by size of input. Does this mean number of literals, or number of variables?</p>
 | complexity theory | 1 | Input size of 3-SAT when analyzing complexity -- (complexity theory)
<p>We know that $\text{3-SAT}$ problem is NP-complete, but I am not sure what is meant by size of input. Does this mean number of literals, or number of variables?</p>
 | habedi/stack-exchange-dataset |
10,229 | Are probabilistic search data structures useful? | <p>A SkipList provides the same $O(\log n)$ bounds for search as a balanced tree with the advantage that rebalancing isn't necessary. Since the SkipList is constructed using random coin flips, these bounds only hold as long as the structure of the SkipList is sufficiently "balanced". In particular, with probability $1/... | data structures search trees probabilistic algorithms | 1 | Are probabilistic search data structures useful? -- (data structures search trees probabilistic algorithms)
<p>A SkipList provides the same $O(\log n)$ bounds for search as a balanced tree with the advantage that rebalancing isn't necessary. Since the SkipList is constructed using random coin flips, these bounds only h... | habedi/stack-exchange-dataset |
10,233 | The "CPS" approach has done great harm to performance in SML/NJ; reasoning desired | <p>In a comment to <a href="https://stackoverflow.com/q/12662896/1243762">Learning F#: What books using other programming languages can be translated to F# to learn functional concepts?</a> <a href="https://stackoverflow.com/users/2121246/makarius">Makarius</a> stated:</p>

<blockquote>
 <p>Note that the "... | compilers functional programming proof assistants continuations | 1 | The "CPS" approach has done great harm to performance in SML/NJ; reasoning desired -- (compilers functional programming proof assistants continuations)
<p>In a comment to <a href="https://stackoverflow.com/q/12662896/1243762">Learning F#: What books using other programming languages can be translated to F# to learn fun... | habedi/stack-exchange-dataset |
10,238 | Fastest mode of data transfer | <p>Which of the following modes of data transfer is the fastest?</p>

<p>a. DMA</p>

<p>b. Interrupt-based</p>

<p>c. Polling</p>

<p>d. All are equally fast</p>

<p>I do not have the answer, so I cannot check, that's why I am posting here. </p>

<p>I think the answer is ... | computer architecture | 1 | Fastest mode of data transfer -- (computer architecture)
<p>Which of the following modes of data transfer is the fastest?</p>

<p>a. DMA</p>

<p>b. Interrupt-based</p>

<p>c. Polling</p>

<p>d. All are equally fast</p>

<p>I do not have the answer, so I cannot check, that's why I... | habedi/stack-exchange-dataset |
10,242 | Solve a recurrence by drawing the recursion tree? | <p>I'm studying for an entrance exam and I have sample questions. One of the questions is this</p>

<blockquote>
 <p>Prove that recurrence $T(n) = T(n/5) + T(4n/5)+n/2$
 has a solution $T(n) = \omega(n \log n)$. </p>
 
 <p>Solve by drawing the recursion tree.</p>
</blockquote>

... | asymptotics recurrence relation | 1 | Solve a recurrence by drawing the recursion tree? -- (asymptotics recurrence relation)
<p>I'm studying for an entrance exam and I have sample questions. One of the questions is this</p>

<blockquote>
 <p>Prove that recurrence $T(n) = T(n/5) + T(4n/5)+n/2$
 has a solution $T(n) = \omega(n \log n)$. <... | habedi/stack-exchange-dataset |
10,245 | Lookahead set: Determining minimum $k$ such that $G$ is a strong $LL(k)$ grammar | <p>How do we determine minimum $k$ such that $G$ is a strong $LL(k)$ Grammar</p>

<p>Like for grammar $G$ with the following rules
$S\rightarrow aAcaa \mid bAbcc,A\rightarrow a \mid ab \mid \epsilon$</p>
 | context free formal grammars parsers ll k | 1 | Lookahead set: Determining minimum $k$ such that $G$ is a strong $LL(k)$ grammar -- (context free formal grammars parsers ll k)
<p>How do we determine minimum $k$ such that $G$ is a strong $LL(k)$ Grammar</p>

<p>Like for grammar $G$ with the following rules
$S\rightarrow aAcaa \mid bAbcc,A\rightarrow a \mi... | habedi/stack-exchange-dataset |
10,250 | Test if there are two subsets which cover a set | <p>Given a set $S$ of $n$ elements, and a set $\mathcal{X}$ of $m$ subsets of $S$, decide if there exist $U,V \in \mathcal{X}$, s.t. $U \cup V = S$.</p>

<p>Brute force would take time $O(nm^2)$ but is there any way of solving this more efficiently?</p>
 | algorithms data structures sets | 1 | Test if there are two subsets which cover a set -- (algorithms data structures sets)
<p>Given a set $S$ of $n$ elements, and a set $\mathcal{X}$ of $m$ subsets of $S$, decide if there exist $U,V \in \mathcal{X}$, s.t. $U \cup V = S$.</p>

<p>Brute force would take time $O(nm^2)$ but is there any way of solving ... | habedi/stack-exchange-dataset |
10,255 | min-cut with extra condition | <p>I have a undirected graph with no edge costs. A subset of the nodes are labeled $c_1, c_2, ..., c_k$ and one node is labeled $K$. I want to find the minimum cut of the graph with the extra condition that all nodes $c_i$ are in the same half of the cut and the node K is in the other cut.</p>

<p>My idea was t... | algorithms complexity theory np complete | 1 | min-cut with extra condition -- (algorithms complexity theory np complete)
<p>I have a undirected graph with no edge costs. A subset of the nodes are labeled $c_1, c_2, ..., c_k$ and one node is labeled $K$. I want to find the minimum cut of the graph with the extra condition that all nodes $c_i$ are in the same half o... | habedi/stack-exchange-dataset |
10,257 | How to show that the complement of a language in $\mathsf P$ is also in $\mathsf P$? | <p>If $L$ is a binary language (that is, $L \subseteq \Sigma = \{0,1\}^∗$) and $\overline{L}$ is the complement of $L$:</p>

<p>How can I show that if $L \in \mathsf P$, then $\overline{L} \in \mathsf P$ as well?</p>
 | complexity theory formal languages time complexity complexity classes | 1 | How to show that the complement of a language in $\mathsf P$ is also in $\mathsf P$? -- (complexity theory formal languages time complexity complexity classes)
<p>If $L$ is a binary language (that is, $L \subseteq \Sigma = \{0,1\}^∗$) and $\overline{L}$ is the complement of $L$:</p>

<p>How can I show that if $... | habedi/stack-exchange-dataset |
10,265 | Show complement of language in same complexity class? | <p>If $L$ is a binary language ($\Sigma = (0, 1)^*$) and $\overline{L}$ is the complement of $L$, the set of binary strings not in $L$.</p>

<p>How can I show that, if $L$ is in the complexity class $P$, then so is $\overline{L}$?</p>
 | complexity classes formal languages | 1 | Show complement of language in same complexity class? -- (complexity classes formal languages)
<p>If $L$ is a binary language ($\Sigma = (0, 1)^*$) and $\overline{L}$ is the complement of $L$, the set of binary strings not in $L$.</p>

<p>How can I show that, if $L$ is in the complexity class $P$, then so is $\... | habedi/stack-exchange-dataset |
10,274 | How to find the maximum independent set of a directed graph? | <p>I'm trying to solve <a href="http://www.spoj.com/problems/DIVREL/" rel="nofollow">this problem</a>. </p>

<blockquote>
 <p><strong>Problem</strong>: Given $n$ positive integers, your task is to select a maximum number of integers so that there are no two numbers $a, b$ in which $a$ is divisible by $b$.... | algorithms graphs bipartite matching | 1 | How to find the maximum independent set of a directed graph? -- (algorithms graphs bipartite matching)
<p>I'm trying to solve <a href="http://www.spoj.com/problems/DIVREL/" rel="nofollow">this problem</a>. </p>

<blockquote>
 <p><strong>Problem</strong>: Given $n$ positive integers, your task is to select... | habedi/stack-exchange-dataset |
10,279 | Maximum variance and useful information of dataset | <p>I am reading through PCA and it says that the maximum variance principal component has most of the information. Can we apply that to any data set? If a data set has n attributes and most of the attributes show high variance then can we infer that the dataset has captured lot of useful information? </p>

<p>I... | terminology data mining data sets statistics | 1 | Maximum variance and useful information of dataset -- (terminology data mining data sets statistics)
<p>I am reading through PCA and it says that the maximum variance principal component has most of the information. Can we apply that to any data set? If a data set has n attributes and most of the attributes show high v... | habedi/stack-exchange-dataset |
10,280 | Practical application of Finite State Machines | <p>I am looking for practical applications of Finite State Machines like DFA, NFA, Moore, Mealy machines...</p>

<p>It would be helpful if someone point to examples from Linux Kernel. I know that DFA is used in string matching like KMP algorithm.</p>

<p>What is the significance of NFA, Moore and Mealy ... | reference request automata finite automata | 1 | Practical application of Finite State Machines -- (reference request automata finite automata)
<p>I am looking for practical applications of Finite State Machines like DFA, NFA, Moore, Mealy machines...</p>

<p>It would be helpful if someone point to examples from Linux Kernel. I know that DFA is used in string... | habedi/stack-exchange-dataset |
10,281 | Why is $n \log \log n$ not tightly bounded by $n$? | <p>I don't understand why $n \log \log n $ is not $\Theta (n)$.</p>

<p>Suppose we give $n$ a value of $10,000$. Then $n \log \log n$ is $6020.6$. So isn't $n \log \log n$ upper- and lower-bounded by $n$, as $n \log \log n \geq Cn$?</p>
 | terminology asymptotics | 1 | Why is $n \log \log n$ not tightly bounded by $n$? -- (terminology asymptotics)
<p>I don't understand why $n \log \log n $ is not $\Theta (n)$.</p>

<p>Suppose we give $n$ a value of $10,000$. Then $n \log \log n$ is $6020.6$. So isn't $n \log \log n$ upper- and lower-bounded by $n$, as $n \log \log n \geq Cn$?... | habedi/stack-exchange-dataset |
10,289 | Why does PCP theorem imply that NP problems are hard to approximate? | <p>What I only got currently from PCP theorem is that it needs at most $O(\log n)$ randomness and $O(1)$ query of proof to approximate. So how does this result relate to the fact that solution to NP problems are hard to approximate?</p>
 | complexity theory randomized algorithms | 1 | Why does PCP theorem imply that NP problems are hard to approximate? -- (complexity theory randomized algorithms)
<p>What I only got currently from PCP theorem is that it needs at most $O(\log n)$ randomness and $O(1)$ query of proof to approximate. So how does this result relate to the fact that solution to NP problem... | habedi/stack-exchange-dataset |
10,292 | What is the Meaning of the Notation | <p>What is meant by saying an algorithm runs in time $Poly(|S|,n,\frac{1}{\epsilon})$.</p>

<p>Can somebody explain with an example.</p>
 | complexity theory machine learning | 1 | What is the Meaning of the Notation -- (complexity theory machine learning)
<p>What is meant by saying an algorithm runs in time $Poly(|S|,n,\frac{1}{\epsilon})$.</p>

<p>Can somebody explain with an example.</p>
 | habedi/stack-exchange-dataset |
10,300 | $1+\epsilon$ approximation for inapproximable problems | <p>I am currently confused by the following situation: </p>

<p>1) The metric $k$-center problem is inapproximable in polynomial time within $2-\epsilon$ unless $P=NP$. <br>
2) The metric $k$-center problem can approximated within $1+\epsilon$ in time $O(k^{O(k/ \epsilon)})$</p>

<p>Did I just win a... | complexity theory np complete approximation p vs np parameterized complexity | 1 | $1+\epsilon$ approximation for inapproximable problems -- (complexity theory np complete approximation p vs np parameterized complexity)
<p>I am currently confused by the following situation: </p>

<p>1) The metric $k$-center problem is inapproximable in polynomial time within $2-\epsilon$ unless $P=NP$. <br>&#... | habedi/stack-exchange-dataset |
10,305 | Number of Hamiltonian cycles on a Sierpiński graph | <p>I am new to this forum and just a physicist who does this to keep his brain in shape, so please show grace if I do not use the most elegant language. Also please leave a comment, if you think other tags would be more appropriate.</p>

<p>I am trying to solve <a href="http://projecteuler.net/problem=312">this... | graphs combinatorics check my proof | 1 | Number of Hamiltonian cycles on a Sierpiński graph -- (graphs combinatorics check my proof)
<p>I am new to this forum and just a physicist who does this to keep his brain in shape, so please show grace if I do not use the most elegant language. Also please leave a comment, if you think other tags would be more appropri... | habedi/stack-exchange-dataset |
10,317 | Witness length independent $\exists$-Operator | <p>Short version:</p>

<p>Is there an operator $\exists$ (on complexity classes) s.t. $\exists P = NP$ and $\exists REC=RE$, i.e. you can use the same operator on multiple interesting classes without explicitly stating a class of functions that limits the length of the witnesses?
The construction should not... | complexity theory | 1 | Witness length independent $\exists$-Operator -- (complexity theory)
<p>Short version:</p>

<p>Is there an operator $\exists$ (on complexity classes) s.t. $\exists P = NP$ and $\exists REC=RE$, i.e. you can use the same operator on multiple interesting classes without explicitly stating a class of functions tha... | habedi/stack-exchange-dataset |
10,318 | The math behind converting from any base to any base without going through base 10? | <p>I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum.org but I'm still not sure if I have it right. I have the converting from a larger base to a smaller base down okay because it is simpl... | algorithms arithmetic number formats | 1 | The math behind converting from any base to any base without going through base 10? -- (algorithms arithmetic number formats)
<p>I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum.org but I... | habedi/stack-exchange-dataset |
10,319 | Constructing PDA to accept language { $a^i b^j c^k \mid i,j,k \geq0, i+2k = j$ } | <p>I'm trying to understand the approach to constructing a PDA which accepts the language { $a^i b^j c^k \mid i,j,k \geq0, i+2k = j$ }</p>
 | pushdown automata | 1 | Constructing PDA to accept language { $a^i b^j c^k \mid i,j,k \geq0, i+2k = j$ } -- (pushdown automata)
<p>I'm trying to understand the approach to constructing a PDA which accepts the language { $a^i b^j c^k \mid i,j,k \geq0, i+2k = j$ }</p>
 | habedi/stack-exchange-dataset |
10,329 | Formal Language Syntax | <p>Here is the question:</p>

<p>Show that $L = \{0^m1^n : m > 1, n > 1, n < m \}$ is not regular.</p>

<p>I am not sure what superscripts mean in this situation? Does it mean something like this:</p>

<p>$0^5 = 00000$ or $1^7 = 1111111$.</p>
 | formal languages regular languages automata | 1 | Formal Language Syntax -- (formal languages regular languages automata)
<p>Here is the question:</p>

<p>Show that $L = \{0^m1^n : m > 1, n > 1, n < m \}$ is not regular.</p>

<p>I am not sure what superscripts mean in this situation? Does it mean something like this:</p>

<p>$0^5 = 000... | habedi/stack-exchange-dataset |
10,333 | Dijkstra algorithm: equal number of shortest paths | <p>If I had a Dijkstra graph with the number shortest paths from Node A to O being 1,
would it be correct to say: <strong>the equal number of shortest paths from A to O is 1 and not 0</strong>, because that node is included as an 'equal shortest path'? I am really confused.</p>

<p>Here is an image to illu... | algorithms shortest path | 1 | Dijkstra algorithm: equal number of shortest paths -- (algorithms shortest path)
<p>If I had a Dijkstra graph with the number shortest paths from Node A to O being 1,
would it be correct to say: <strong>the equal number of shortest paths from A to O is 1 and not 0</strong>, because that node is included as an 'equ... | habedi/stack-exchange-dataset |
10,338 | What is the exact relation between programming languages and Turing machines? | <p>I don't know much about yacc, bison, flex or lex and please correct me if I'm wrong but a programming language is also a Turing machine and a Turing machine is defined as the tuple $(Q, \Gamma, b, \Sigma, \delta, q_0, F)$ where $Q$, $\Gamma$, $b \in \Gamma$, $\Sigma \subseteq \Gamma \smallsetminus \{ b \}$ as input,... | turing machines formal grammars programming languages computation models | 1 | What is the exact relation between programming languages and Turing machines? -- (turing machines formal grammars programming languages computation models)
<p>I don't know much about yacc, bison, flex or lex and please correct me if I'm wrong but a programming language is also a Turing machine and a Turing machine is d... | habedi/stack-exchange-dataset |
10,339 | $st$-path with fewest leaving edges | <p>Given an undirected unweighted multigraph $G=(V,E)$ and $s,t \in V$ find a simple $st$-path $P$ s.t. the number of edges leaving $P$ (i.e. the edges with exaclty one endpoint in $P$ ) is minimized.</p>

<p>Does anybody have any idea how to solve this?
I first thought about replacing edges by two arcs an... | algorithms graphs | 1 | $st$-path with fewest leaving edges -- (algorithms graphs)
<p>Given an undirected unweighted multigraph $G=(V,E)$ and $s,t \in V$ find a simple $st$-path $P$ s.t. the number of edges leaving $P$ (i.e. the edges with exaclty one endpoint in $P$ ) is minimized.</p>

<p>Does anybody have any idea how to solve thi... | habedi/stack-exchange-dataset |
10,341 | Is $\{\Theta(f)|f:\mathbb{N}\rightarrow\mathbb{N}\}$ Dedekind-complete? | <p>Let $\Theta$ and $o$ be defined as usual (Landau-notation).
For two equivalence classes defined by $\Theta$ we define
$$\Theta(f) <_o \Theta(g) :\Leftrightarrow f \in o(g)\qquad.$$
Let $$\mathbb{F}:= \{\Theta(f)\mid f:\mathbb{N}\rightarrow\mathbb{N}\}$$</p>

<p><strong>My question</strong>:&#x... | landau notation | 1 | Is $\{\Theta(f)|f:\mathbb{N}\rightarrow\mathbb{N}\}$ Dedekind-complete? -- (landau notation)
<p>Let $\Theta$ and $o$ be defined as usual (Landau-notation).
For two equivalence classes defined by $\Theta$ we define
$$\Theta(f) <_o \Theta(g) :\Leftrightarrow f \in o(g)\qquad.$$
Let $$\mathbb{F}:= \{\Theta(... | habedi/stack-exchange-dataset |
10,347 | How does one deduce small step operational semantics? | <p>This question arises from my reading of <a href="http://www.cis.upenn.edu/~bcpierce/tapl/" rel="nofollow">"Types and Programming Languages"</a> (<a href="http://www.worldcat.org/oclc/47705787" rel="nofollow">WoldCat</a>) by Benjamin C. Pierce.</p>

<p>For the small step operational semantic evaluation rules ... | semantics operational semantics small step semantics | 1 | How does one deduce small step operational semantics? -- (semantics operational semantics small step semantics)
<p>This question arises from my reading of <a href="http://www.cis.upenn.edu/~bcpierce/tapl/" rel="nofollow">"Types and Programming Languages"</a> (<a href="http://www.worldcat.org/oclc/47705787" rel="nofollo... | habedi/stack-exchange-dataset |
10,352 | Are functions in O(n) that are nor in o(n) all in Θ(n)? | <p>One of my lectures makes the following statement:</p>

<p>$$( f(n)=O(n) \land f(n)\neq o(n) )\implies f(n)=\Theta(n)$$</p>

<p>Maybe I'm missing something in the definitions, but for example bubble sort is $O(n^2)$ and not $o(n^2)$ but it's also not $\theta(n^2)$ since it's best case run time $\Omega... | asymptotics landau notation | 1 | Are functions in O(n) that are nor in o(n) all in Θ(n)? -- (asymptotics landau notation)
<p>One of my lectures makes the following statement:</p>

<p>$$( f(n)=O(n) \land f(n)\neq o(n) )\implies f(n)=\Theta(n)$$</p>

<p>Maybe I'm missing something in the definitions, but for example bubble sort is $O(n^2... | habedi/stack-exchange-dataset |
10,354 | Common Algorithms without Asymptotically Tight Bounds | <p>I can think of functions such as $n^2 \sin^2 n$ that don't have asymptotically tight bounds, but are there actually common algorithms in computer science that don't have asymptotically tight bounds on their worst case running times?</p>
 | time complexity algorithm analysis asymptotics runtime analysis | 1 | Common Algorithms without Asymptotically Tight Bounds -- (time complexity algorithm analysis asymptotics runtime analysis)
<p>I can think of functions such as $n^2 \sin^2 n$ that don't have asymptotically tight bounds, but are there actually common algorithms in computer science that don't have asymptotically tight bo... | habedi/stack-exchange-dataset |
10,360 | Floyd's Cycle detection algorithm | Determining the starting point of cycle | <p>I am seeking help understanding Floyd's cycle detection algorithm. I have gone through the explanation on wikipedia (<a href="http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_hare">http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_hare</a>)</p>

<p>I can see how the algorithm detects cycle i... | algorithms linked lists | 1 | Floyd's Cycle detection algorithm | Determining the starting point of cycle -- (algorithms linked lists)
<p>I am seeking help understanding Floyd's cycle detection algorithm. I have gone through the explanation on wikipedia (<a href="http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_hare">http://en.wikipedia.or... | habedi/stack-exchange-dataset |
10,369 | Upper Bound on Runtime of Memoized DP Algorithms | <p>I find it fairly easy to generate an upper bound for nearly any iterative solution (e.g. look at the limits on each loop, etc.), and can oftentimes create an upper bound for normal recursive functions.</p>

<p>However, I am now trying to determine a "Big-O" for a DP problem I've memoized. I don't really car... | algorithm analysis runtime analysis dynamic programming memoization | 1 | Upper Bound on Runtime of Memoized DP Algorithms -- (algorithm analysis runtime analysis dynamic programming memoization)
<p>I find it fairly easy to generate an upper bound for nearly any iterative solution (e.g. look at the limits on each loop, etc.), and can oftentimes create an upper bound for normal recursive func... | habedi/stack-exchange-dataset |
10,386 | TAPL: Explanation and example(s) for satisfied | <p>This question arises from my reading of <a href="http://www.cis.upenn.edu/~bcpierce/tapl/" rel="nofollow">"Types and Programming Languages"</a> (<a href="http://www.worldcat.org/oclc/47705787" rel="nofollow">WorldCat</a>) by Benjamin C. Pierce.</p>

<p>On page 36 is the definition for <em>satisfied</em></p>&... | satisfiability operational semantics small step semantics term rewriting | 1 | TAPL: Explanation and example(s) for satisfied -- (satisfiability operational semantics small step semantics term rewriting)
<p>This question arises from my reading of <a href="http://www.cis.upenn.edu/~bcpierce/tapl/" rel="nofollow">"Types and Programming Languages"</a> (<a href="http://www.worldcat.org/oclc/47705787"... | habedi/stack-exchange-dataset |
10,396 | Pointwise mutual information vs. Mutual information? | <p>I am learning about information theory and mutual information. However, I am quite confused with MI(Mutual information) vs. PMI(Pointwise mutual information) especially signs of MI and PMI values. Here are my questions. </p>

<ul>
<li><p>Is MI values a non-negative value or it can be either positive o... | probability theory information theory entropy | 1 | Pointwise mutual information vs. Mutual information? -- (probability theory information theory entropy)
<p>I am learning about information theory and mutual information. However, I am quite confused with MI(Mutual information) vs. PMI(Pointwise mutual information) especially signs of MI and PMI values. Here are my ques... | habedi/stack-exchange-dataset |
10,398 | What are some of the practical applications of CSP process algebra? | <p>CSP is used for the description and representation of concurrent systems, how it is used in practice (theoretically and programmatically)? </p>

<p>What are the application areas (other than concurrent and parallel systems) where it is used?</p>
 | process algebras | 1 | What are some of the practical applications of CSP process algebra? -- (process algebras)
<p>CSP is used for the description and representation of concurrent systems, how it is used in practice (theoretically and programmatically)? </p>

<p>What are the application areas (other than concurrent and parallel syst... | habedi/stack-exchange-dataset |
10,411 | How do we know to what community a vertex belongs to in the Girvan-Newman algorithm? | <p>So I've been doing some reading on community detection in graphs as I'm planning on working on my thesis for it. I've been reviewing papers regarding the same and came across the <a href="http://www.pnas.org/content/99/12/7821.abstract" rel="nofollow">Girvan-Newman algorithm</a>. I've read the paper and have a doubt... | algorithms graphs network analysis | 1 | How do we know to what community a vertex belongs to in the Girvan-Newman algorithm? -- (algorithms graphs network analysis)
<p>So I've been doing some reading on community detection in graphs as I'm planning on working on my thesis for it. I've been reviewing papers regarding the same and came across the <a href="http... | habedi/stack-exchange-dataset |
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