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 |
|---|---|---|---|---|---|---|
102,385 | probability of collision | <p>my data's range is from 1 to 9 and I have two subsets of integers from this range.
the hash function takes each of this subsets and calculate product of these three integers and maps this set to the result of this multiplication.I want to know the probability of collision by this hash function with this two subs... | probability theory hash statistics | 1 | probability of collision -- (probability theory hash statistics)
<p>my data's range is from 1 to 9 and I have two subsets of integers from this range.
the hash function takes each of this subsets and calculate product of these three integers and maps this set to the result of this multiplication.I want to know the ... | habedi/stack-exchange-dataset |
102,391 | What, if any, is the term for a node whose children are all leaf nodes? | <p>More specifically, I'm interested to know if there is a term that describes a tree node that meets two conditions:
- It has >= one child
- Any children that it has are all leaf nodes.</p>
 | data structures terminology trees | 1 | What, if any, is the term for a node whose children are all leaf nodes? -- (data structures terminology trees)
<p>More specifically, I'm interested to know if there is a term that describes a tree node that meets two conditions:
- It has >= one child
- Any children that it has are all leaf nodes.</p>
 | habedi/stack-exchange-dataset |
102,393 | The complexity of the reachability-coreachability analysis of a finite state machine | <p>Let <span class="math-container">$A = \{\Sigma,Q,\delta,q_{0}, Q_{m}\}$</span> be a finite state machine (FSM). A state <span class="math-container">$q \in Q$</span> is reachable if there exists a string <span class="math-container">$s \in \Sigma^{*}$</span> such that <span class="math-container">$\delta(q_{0},s) = ... | complexity theory finite automata graph traversal | 1 | The complexity of the reachability-coreachability analysis of a finite state machine -- (complexity theory finite automata graph traversal)
<p>Let <span class="math-container">$A = \{\Sigma,Q,\delta,q_{0}, Q_{m}\}$</span> be a finite state machine (FSM). A state <span class="math-container">$q \in Q$</span> is reachabl... | habedi/stack-exchange-dataset |
102,395 | What should be the minimum value when the two threads are executed concurrently | <pre><code>int count=0;
void *thfunc()
{
 int ctr=0;
 for(ctr=0;ctr<100;ctr++)
 count++;
}
</code></pre>

<p>If *thfunc() is executed by two threads concurrently in a uniprocessor system, what will be the minimum value of count when both threads complete their execution? ... | operating systems parallel computing threads mutual exclusion | 1 | What should be the minimum value when the two threads are executed concurrently -- (operating systems parallel computing threads mutual exclusion)
<pre><code>int count=0;
void *thfunc()
{
 int ctr=0;
 for(ctr=0;ctr<100;ctr++)
 count++;
}
</code></pre>

<p>If *thfunc() is ... | habedi/stack-exchange-dataset |
102,399 | Is there an algorithm to achieve optimal compression in a "streamed" manner, assuming equal probability of each possibility? | <p><sup>(Sorry for the question title; edits are welcome.)</sup></p>

<p>Let's say that you have a set of data made of repeating units, consisting of a value with <span class="math-container">$2$</span> possibilities, a value with <span class="math-container">$3$</span> possibilities, <span class="math-containe... | algorithms data compression entropy | 1 | Is there an algorithm to achieve optimal compression in a "streamed" manner, assuming equal probability of each possibility? -- (algorithms data compression entropy)
<p><sup>(Sorry for the question title; edits are welcome.)</sup></p>

<p>Let's say that you have a set of data made of repeating units, consisting... | habedi/stack-exchange-dataset |
102,412 | Programming Language Hierarchy | <p>I know that Assembly is the lowest level of the stack besides machine code, but are the languages above it all considered "high level languages" or is there a hierarchy amongst these languages. For instance, are C++, Ruby, and Python all "high level languages"?</p>
 | programming languages | 1 | Programming Language Hierarchy -- (programming languages)
<p>I know that Assembly is the lowest level of the stack besides machine code, but are the languages above it all considered "high level languages" or is there a hierarchy amongst these languages. For instance, are C++, Ruby, and Python all "high level languages... | habedi/stack-exchange-dataset |
102,423 | Model Checking CTL* algorithm | <p>Currently I'm trying to understand the CTL* model checking algorithm from <a href="https://mitpress.mit.edu/books/principles-model-checking" rel="nofollow noreferrer">this book</a>. The basic idea is clear to that we can use the LTL algorithm to whenever we have a subformular <span class="math-container">$E\phi$</sp... | model checking | 1 | Model Checking CTL* algorithm -- (model checking)
<p>Currently I'm trying to understand the CTL* model checking algorithm from <a href="https://mitpress.mit.edu/books/principles-model-checking" rel="nofollow noreferrer">this book</a>. The basic idea is clear to that we can use the LTL algorithm to whenever we have a su... | habedi/stack-exchange-dataset |
102,427 | Construct PDA for ${ \{0^m1^n0^{2n} | n>0\}}$ | <p>I have to construct PDA for <span class="math-container">${ \{0^m1^n0^{2n} | n>0\}}$</span></p>

<p>So my idea is to (informally) not pushing anything into the stack while having 0s at first, then when automata start accepting 1s it should push X onto the stack twice on every 1 and then when start accepti... | pushdown automata | 1 | Construct PDA for ${ \{0^m1^n0^{2n} | n>0\}}$ -- (pushdown automata)
<p>I have to construct PDA for <span class="math-container">${ \{0^m1^n0^{2n} | n>0\}}$</span></p>

<p>So my idea is to (informally) not pushing anything into the stack while having 0s at first, then when automata start accepting 1s it shou... | habedi/stack-exchange-dataset |
102,429 | Why can't a left-recursive, non-deterministic, or ambiguous grammar be LL(1)? | <p>I've learned from several sources that an LL(1) grammar is:</p>

<ol>
<li>unambiguous,</li>
<li>not left-recursive,</li>
<li>and, deterministic (left-factorized).</li>
</ol>

<p>What I can't fully understand is why the above is true for any LL(1) grammar. I know the LL(1) parsing tabl... | formal languages formal grammars | 1 | Why can't a left-recursive, non-deterministic, or ambiguous grammar be LL(1)? -- (formal languages formal grammars)
<p>I've learned from several sources that an LL(1) grammar is:</p>

<ol>
<li>unambiguous,</li>
<li>not left-recursive,</li>
<li>and, deterministic (left-factorized).</li>
</ol>
... | habedi/stack-exchange-dataset |
102,435 | Can Non-Linear Grammars generate Regular Language? | <p>I stumbled upon the following non-linear grammar</p>

<p><span class="math-container">$$S \to AB$$</span>
<span class="math-container">$$A\to aaA\mid \epsilon$$</span>
<span class="math-container">$$B \to Bb\mid \epsilon$$</span></p>

<p>and the language generated by this non-linear grammar i... | regular languages context free | 1 | Can Non-Linear Grammars generate Regular Language? -- (regular languages context free)
<p>I stumbled upon the following non-linear grammar</p>

<p><span class="math-container">$$S \to AB$$</span>
<span class="math-container">$$A\to aaA\mid \epsilon$$</span>
<span class="math-container">$$B \to Bb\mid \e... | habedi/stack-exchange-dataset |
102,437 | Can the Dijkstra algorithm work with a negative arc? | <p>When there is no negative circle in the graph?
And can Dijkstra not work even if there is a negative arc that does not create a negative cycle?</p>
 | algorithms graphs | 1 | Can the Dijkstra algorithm work with a negative arc? -- (algorithms graphs)
<p>When there is no negative circle in the graph?
And can Dijkstra not work even if there is a negative arc that does not create a negative cycle?</p>
 | habedi/stack-exchange-dataset |
102,443 | Sublinear Homomorphism Property Testing Counter Example | <p>This is a homework question, so I'm not looking for answers, just general guidance.</p>

<p>I'm looking at a Sublinear Algorithms survey where (Group) Homomorphism property testing is discussed. The case of homomorphisms from <span class="math-container">$\left(\mathbb{Z}_{n}, +\right)$</span> to <span class... | algorithms randomized algorithms randomness linear algebra | 1 | Sublinear Homomorphism Property Testing Counter Example -- (algorithms randomized algorithms randomness linear algebra)
<p>This is a homework question, so I'm not looking for answers, just general guidance.</p>

<p>I'm looking at a Sublinear Algorithms survey where (Group) Homomorphism property testing is discu... | habedi/stack-exchange-dataset |
102,448 | Why do mainstream speech models no longer require a personalized training step? | <p>Back in the Windows XP era, when setting up Windows OS-built-in speech/dictation, I had to speak out a bunch of programmed-in text samples to the speech-to-text engine to personalize my voice profile.</p>

<p>Today, with networked speech-to-text engines like Siri or Cortana, I can just start dictating.</p>&#... | algorithms machine learning speech recognition | 1 | Why do mainstream speech models no longer require a personalized training step? -- (algorithms machine learning speech recognition)
<p>Back in the Windows XP era, when setting up Windows OS-built-in speech/dictation, I had to speak out a bunch of programmed-in text samples to the speech-to-text engine to personalize my... | habedi/stack-exchange-dataset |
102,463 | Looking for an algorithm to identify contiguous repeated series of lines in a long string | <p>I would like an algorithm that can identify repeated parts of big stack traces like this:</p>

<pre><code>java.lang.StackOverflowError
at transform.Erasure<span class="math-container">$Eraser.typed1(Erasure.scala:789)
at typechecker.Typers$</span>Typer.runTyper<span class="math-container">$1(Typers.s... | algorithms | 1 | Looking for an algorithm to identify contiguous repeated series of lines in a long string -- (algorithms)
<p>I would like an algorithm that can identify repeated parts of big stack traces like this:</p>

<pre><code>java.lang.StackOverflowError
at transform.Erasure<span class="math-container">$Eraser.typed1(... | habedi/stack-exchange-dataset |
102,466 | What important/crucial real-world applications use blockchain? | <p>As part of some blockchain-related research I am currently undertaking, the notion of using blockchains for a variety of real-world applications are thrown about loosely.</p>

<p>Therefore, I propose the following questions:</p>

<ol>
<li>What important/crucial real-world applications use blockch... | blockchain | 1 | What important/crucial real-world applications use blockchain? -- (blockchain)
<p>As part of some blockchain-related research I am currently undertaking, the notion of using blockchains for a variety of real-world applications are thrown about loosely.</p>

<p>Therefore, I propose the following questions:</p>&#... | habedi/stack-exchange-dataset |
102,471 | Increasing the weights of all edges in an undirected graph makes a minimum cut still minimum | <p>We have an undirected graph, with a weight function and a minimum cut. If you raise the weights of all the edges by one, the minimum cut remains minimal even with the new weights.</p>

<p>I know this is refutation, but I could not find a good example of refutation.
I would be happy if you would help me.<... | graphs minimum cuts | 1 | Increasing the weights of all edges in an undirected graph makes a minimum cut still minimum -- (graphs minimum cuts)
<p>We have an undirected graph, with a weight function and a minimum cut. If you raise the weights of all the edges by one, the minimum cut remains minimal even with the new weights.</p>

<p>I k... | habedi/stack-exchange-dataset |
102,475 | Is the following Grammar LL(1) | <p>I was given the following grammar </p>

<p><span class="math-container">$S \rightarrow S ( S ) S\mid \epsilon$</span> </p>

<p>First I was asked to eliminate left recursion, yielding me the following : </p>

<p><span class="math-container">$S \rightarrow S' $</span> </p>

<p><spa... | context free formal grammars parsers | 1 | Is the following Grammar LL(1) -- (context free formal grammars parsers)
<p>I was given the following grammar </p>

<p><span class="math-container">$S \rightarrow S ( S ) S\mid \epsilon$</span> </p>

<p>First I was asked to eliminate left recursion, yielding me the following : </p>

<p><span... | habedi/stack-exchange-dataset |
102,485 | Is OS mode required for accessing general purpose registers | <p>In which of the following cases a process executing in user model is required to enter into the OS mode?</p>

<p>(a) Decreasing the value of unsigned integer value in a register to less than 0</p>

<p>(b) Accessing general purpose register</p>

<p>(c) Executing printf()</p>

<p>(d) Ad... | computer architecture operating systems os kernel critical section | 1 | Is OS mode required for accessing general purpose registers -- (computer architecture operating systems os kernel critical section)
<p>In which of the following cases a process executing in user model is required to enter into the OS mode?</p>

<p>(a) Decreasing the value of unsigned integer value in a register... | habedi/stack-exchange-dataset |
102,490 | find all paths from source to destinations and then calculate the path with minimum cost | <p>I am trying to solve one problem. Please refer complete problem statement before proceeding.</p>
<blockquote>
<p>You are given a road network, with N cities and M bi-directional
roads. Each road has some positive amount of tax associated to
it,meaning if there is a road connecting cities A and B with... | algorithms graphs | 1 | find all paths from source to destinations and then calculate the path with minimum cost -- (algorithms graphs)
<p>I am trying to solve one problem. Please refer complete problem statement before proceeding.</p>
<blockquote>
<p>You are given a road network, with N cities and M bi-directional
roads. Each roa... | habedi/stack-exchange-dataset |
102,494 | No. of disk blocks writes required for writing the file | <p>Assume that a file is written using write(fd, buf, K) system calls, where fd is the file descriptor, and K, the number of files to be written to the current file offset which is a multiple of the disk block size D. The total number of disk block writes required to be executed before the system call returns is:</p>&#... | computer architecture database theory memory hardware filesystems | 1 | No. of disk blocks writes required for writing the file -- (computer architecture database theory memory hardware filesystems)
<p>Assume that a file is written using write(fd, buf, K) system calls, where fd is the file descriptor, and K, the number of files to be written to the current file offset which is a multiple o... | habedi/stack-exchange-dataset |
102,514 | Can I compute closest split pair of points where distance is strictly less than delta | <p>I've been studying the closest pair algorithm lately and I found this to be an extremely good and intuitive resource: <a href="http://serverbob.3x.ro/IA/DDU0221.html" rel="nofollow noreferrer">http://serverbob.3x.ro/IA/DDU0221.html</a>. It is also explained in section 33.4, "Finding the closest pair of points" of <e... | algorithms computational geometry | 1 | Can I compute closest split pair of points where distance is strictly less than delta -- (algorithms computational geometry)
<p>I've been studying the closest pair algorithm lately and I found this to be an extremely good and intuitive resource: <a href="http://serverbob.3x.ro/IA/DDU0221.html" rel="nofollow noreferrer"... | habedi/stack-exchange-dataset |
102,518 | Is Rice-Shapiro theorem bidirectional? | <p>Rice-Shapiro theorem states that</p>

<blockquote>
 <h2>version A</h2>
 
 <p>Let <span class="math-container">$\Gamma$</span> be a set of computably enumerable sets, and <span class="math-container">$I = \{e : W_e \in \Gamma\}$</span> its index set in some admissible enumeration of c.e sets. I... | computability semi decidability | 1 | Is Rice-Shapiro theorem bidirectional? -- (computability semi decidability)
<p>Rice-Shapiro theorem states that</p>

<blockquote>
 <h2>version A</h2>
 
 <p>Let <span class="math-container">$\Gamma$</span> be a set of computably enumerable sets, and <span class="math-container">$I = \{e : W_e \in ... | habedi/stack-exchange-dataset |
102,520 | When searching graphs breadth-first and depth-first color the graph. Who un-colors the graph when the search is completed? | <p>The depth-first and breadth-first algorithms for traversing graphs use a flag (or color) to mark nodes when they are visited. For example some forms of the algorithms use white/grey/black as colors. When the traversal is complete all the nodes in the graph are black.</p>

<p>None of the material I have been... | graphs graph traversal | 1 | When searching graphs breadth-first and depth-first color the graph. Who un-colors the graph when the search is completed? -- (graphs graph traversal)
<p>The depth-first and breadth-first algorithms for traversing graphs use a flag (or color) to mark nodes when they are visited. For example some forms of the algorithm... | habedi/stack-exchange-dataset |
102,529 | How do I construct a NTM that accepts the language consisting of the coding of turing machines that halt on one input? | <p>I currently have a problem with the following question:</p>

<p>Let <span class="math-container">$L = \{ \langle M \rangle \mid \exists w: \text{$M$ halts for $w$ in at most $|w|^3$ steps} \}$</span>.
Construct an NTM (non-deterministic Turing machine) that decides <span class="math-container">$L$</span>... | turing machines nondeterminism semi decidability | 1 | How do I construct a NTM that accepts the language consisting of the coding of turing machines that halt on one input? -- (turing machines nondeterminism semi decidability)
<p>I currently have a problem with the following question:</p>

<p>Let <span class="math-container">$L = \{ \langle M \rangle \mid \exists ... | habedi/stack-exchange-dataset |
102,533 | Distance Vector Routing Example | <p>Consider a network with five nodes, N1 to N5, as shown as below.</p>

<p><a href="https://i.stack.imgur.com/INH0h.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/INH0h.jpg" alt="enter image description here"></a></p>

<p>The network uses a Distance Vector Routing protocol. Once the... | routing gate cs | 1 | Distance Vector Routing Example -- (routing gate cs)
<p>Consider a network with five nodes, N1 to N5, as shown as below.</p>

<p><a href="https://i.stack.imgur.com/INH0h.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/INH0h.jpg" alt="enter image description here"></a></p>

<p>The netw... | habedi/stack-exchange-dataset |
102,535 | is reducing to normal form simply applying beta-reduction? | <p>See example below:</p>

<p>reduce to normal form:</p>

<p>(λ c . (λ a . (λ d . (λ h . (h (d (a (a (λ z y . y))) (d (a (a (λ f x . x))) (a (a (a (λ z x . x)))))) (h (a (a (λ z y . y))) (a (a (a (λ z x . x))))))) (λ n m . n (d m) (λ z y . y))) (λ n m . n a m)) (λ n z . c (n z) z)) (λ z g x . z (g x))</... | lambda calculus | 1 | is reducing to normal form simply applying beta-reduction? -- (lambda calculus)
<p>See example below:</p>

<p>reduce to normal form:</p>

<p>(λ c . (λ a . (λ d . (λ h . (h (d (a (a (λ z y . y))) (d (a (a (λ f x . x))) (a (a (a (λ z x . x)))))) (h (a (a (λ z y . y))) (a (a (a (λ z x . x))))))) (λ n m . n... | habedi/stack-exchange-dataset |
102,537 | Expectation of $\langle s,x \rangle^2$ | <p>I'm studying dimensionality reduction (SVD in particular), and I saw the following question:</p>

<blockquote>
 <p>Assume we have a vector <span class="math-container">$x \in \mathbb R^d$</span>, and consider <span class="math-container">$F(x)=s^t x$</span> , where
 <span class="math-container">$s... | probability theory randomized algorithms | 1 | Expectation of $\langle s,x \rangle^2$ -- (probability theory randomized algorithms)
<p>I'm studying dimensionality reduction (SVD in particular), and I saw the following question:</p>

<blockquote>
 <p>Assume we have a vector <span class="math-container">$x \in \mathbb R^d$</span>, and consider <span clas... | habedi/stack-exchange-dataset |
102,542 | IEEE754 representation in hexadecimal? | <p>In class, I've heard hexadecimal representation for IEEE754 mentioned and described in 32bit length as a format that consists of one bit for sign, normalized 6-digit fraction (with an implied leading zero) and biased (+64) 7bit exponent, leading me to believe it's not just a made up spec. </p>

<p>However, g... | floating point number formats | 1 | IEEE754 representation in hexadecimal? -- (floating point number formats)
<p>In class, I've heard hexadecimal representation for IEEE754 mentioned and described in 32bit length as a format that consists of one bit for sign, normalized 6-digit fraction (with an implied leading zero) and biased (+64) 7bit exponent, leadi... | habedi/stack-exchange-dataset |
102,550 | The role of depth of a circuit in its hardware implementation | <p>The depth of a circuit is the maximal length of a path from an input gate to the output gate of the circuit <a href="https://en.wikipedia.org/wiki/Circuit_complexity" rel="nofollow noreferrer">[Reference]</a></p>

<p>Question: What is the relation between the depth of a circuit and hardware implementation of... | circuits | 1 | The role of depth of a circuit in its hardware implementation -- (circuits)
<p>The depth of a circuit is the maximal length of a path from an input gate to the output gate of the circuit <a href="https://en.wikipedia.org/wiki/Circuit_complexity" rel="nofollow noreferrer">[Reference]</a></p>

<p>Question: What i... | habedi/stack-exchange-dataset |
102,555 | Typing rule for binding groups | <p>In "<a href="https://web.cecs.pdx.edu/~mpj/thih/thih.pdf" rel="nofollow noreferrer">Typing Haskell in Haskell</a>", by Mark P. Jones, is provided a sort of haskell-like specification for typing Haskell. As stated in this paper, binding groups is a area "neglected in most theoretical treatments of type inference". Jo... | type theory type inference typing haskell | 1 | Typing rule for binding groups -- (type theory type inference typing haskell)
<p>In "<a href="https://web.cecs.pdx.edu/~mpj/thih/thih.pdf" rel="nofollow noreferrer">Typing Haskell in Haskell</a>", by Mark P. Jones, is provided a sort of haskell-like specification for typing Haskell. As stated in this paper, binding gro... | habedi/stack-exchange-dataset |
102,557 | Which of the following statements are true for the given special cases of the Traveling Salesman Problem? | <p>I'm taking the <a href="https://lagunita.stanford.edu/courses/course-v1:Engineering+Algorithms2+SelfPaced/about" rel="nofollow noreferrer">Algorithms: Design and Analysis II</a> class, one of the questions asks:</p>

<blockquote>
 <p>Which of the following statements is true?</p>
 
 <ul>
 ... | algorithms complexity theory np complete reductions traveling salesman | 1 | Which of the following statements are true for the given special cases of the Traveling Salesman Problem? -- (algorithms complexity theory np complete reductions traveling salesman)
<p>I'm taking the <a href="https://lagunita.stanford.edu/courses/course-v1:Engineering+Algorithms2+SelfPaced/about" rel="nofollow noreferr... | habedi/stack-exchange-dataset |
102,558 | Which of the following problems can be reduced to the Hamiltonian path problem? | <p>I'm taking the <a href="https://lagunita.stanford.edu/courses/course-v1:Engineering+Algorithms2+SelfPaced/about" rel="nofollow noreferrer">Algorithms: Design and Analysis II</a> class, one of the questions asks:</p>

<blockquote>
 <p>Assume that P ≠ NP. Consider undirected graphs with nonnegative edge&#... | algorithms complexity theory graphs np complete hamiltonian path | 1 | Which of the following problems can be reduced to the Hamiltonian path problem? -- (algorithms complexity theory graphs np complete hamiltonian path)
<p>I'm taking the <a href="https://lagunita.stanford.edu/courses/course-v1:Engineering+Algorithms2+SelfPaced/about" rel="nofollow noreferrer">Algorithms: Design and Analy... | habedi/stack-exchange-dataset |
102,564 | Set Difference of Two RE Languages - An Intuitive Idea of Why It's Not Closed | <p>I'm new to studying formal languages, so apologies if I get a lot of basic stuff wrong, but I'm trying to get an intuitive understanding of why the difference between two Recursively Enumerable languages (A and B, say) is not itself RE? I.e. why for A-B = Z, Z is not RE?</p>

<p>The basic set notation and ma... | formal languages turing machines formal grammars | 1 | Set Difference of Two RE Languages - An Intuitive Idea of Why It's Not Closed -- (formal languages turing machines formal grammars)
<p>I'm new to studying formal languages, so apologies if I get a lot of basic stuff wrong, but I'm trying to get an intuitive understanding of why the difference between two Recursively En... | habedi/stack-exchange-dataset |
102,574 | Max Weight Path in a Graph | <p>I know that this problem is a known NP-Complete problem, but I'm curious as to why a particular algorithm won't work. Given a graph <span class="math-container">$G = (V,E)$</span>, and edge weights <span class="math-container">$w(e)$</span>, why can we not create a new graph <span class="math-container">$G' = (V,E')... | algorithms graphs | 1 | Max Weight Path in a Graph -- (algorithms graphs)
<p>I know that this problem is a known NP-Complete problem, but I'm curious as to why a particular algorithm won't work. Given a graph <span class="math-container">$G = (V,E)$</span>, and edge weights <span class="math-container">$w(e)$</span>, why can we not create a n... | habedi/stack-exchange-dataset |
102,577 | Formal definition of an empty stack accepting PDA | <p>PDA's are usually defined using the 7-tuple convention.</p>

<p><span class="math-container">$M=(Q, \Sigma, \Gamma, \delta, q_{0}, Z, F)$</span></p>

<p>F is the set of accepting states. </p>

<p>I want to design a PDA accepting by empty stack, so using this notation makes no sense, as I don'... | pushdown automata | 1 | Formal definition of an empty stack accepting PDA -- (pushdown automata)
<p>PDA's are usually defined using the 7-tuple convention.</p>

<p><span class="math-container">$M=(Q, \Sigma, \Gamma, \delta, q_{0}, Z, F)$</span></p>

<p>F is the set of accepting states. </p>

<p>I want to design a PDA a... | habedi/stack-exchange-dataset |
102,580 | Proof of a lower bound of the recurrence relation (the CLRS's 4.6-2 exercise) | <p>I am trying to find a solution to the ex. 4.6-2 of the <em>Introduction to Algorithms by Cormen, Leiserson, Rivest, Stein (the third edition)</em>. It requires, for recurrence relations <span class="math-container">$T(n)=aT(n/b)+f(n)$</span> where <span class="math-container">$a\geq 1, b > 1$</span>, <span class=... | algorithm analysis recurrence relation | 1 | Proof of a lower bound of the recurrence relation (the CLRS's 4.6-2 exercise) -- (algorithm analysis recurrence relation)
<p>I am trying to find a solution to the ex. 4.6-2 of the <em>Introduction to Algorithms by Cormen, Leiserson, Rivest, Stein (the third edition)</em>. It requires, for recurrence relations <span cla... | habedi/stack-exchange-dataset |
102,585 | Is every subset of a RE language also RE, in general? | <p>I'm trying to understand the question in my title in an intuitive way: 
If I have an RE language A, then some TM, say TM(A) accepts on it. If I take a subset of A, say A2, then all elements of A2 will cause TM(A) to halt in the accept state.</p>

<p>However, is it in general possible to then create a TM ... | formal languages formal grammars chomsky hierarchy | 1 | Is every subset of a RE language also RE, in general? -- (formal languages formal grammars chomsky hierarchy)
<p>I'm trying to understand the question in my title in an intuitive way: 
If I have an RE language A, then some TM, say TM(A) accepts on it. If I take a subset of A, say A2, then all elements of A2 will ca... | habedi/stack-exchange-dataset |
102,597 | Buchi automata in formal software verification | <p>As I am studying the application of Buchi automata in formal software verification, I am interested in the computational complexity (or links to papers) for the algorithms used to solve the problem in practice.</p>

<p>Let me recall the mathematical intuition behind model checking using these techniques.
... | formal languages formal grammars formal methods model checking buchi automata | 1 | Buchi automata in formal software verification -- (formal languages formal grammars formal methods model checking buchi automata)
<p>As I am studying the application of Buchi automata in formal software verification, I am interested in the computational complexity (or links to papers) for the algorithms used to solve t... | habedi/stack-exchange-dataset |
102,602 | Kiln optimization problem | <p>Say I have a kiln for making castings. There are 3 shapes. I need to produce the following castings:</p>

<p>102 of A</p>

<p>364 of B</p>

<p>70 of C</p>

<p>I can put 50 molds in the kiln at a time.
I can have 75 molds made in any combination.</p>

<p>First, what is the ... | algorithms optimization | 1 | Kiln optimization problem -- (algorithms optimization)
<p>Say I have a kiln for making castings. There are 3 shapes. I need to produce the following castings:</p>

<p>102 of A</p>

<p>364 of B</p>

<p>70 of C</p>

<p>I can put 50 molds in the kiln at a time.
I can have 75 molds made ... | habedi/stack-exchange-dataset |
102,604 | Drawbacks of adding type equality to 1ML | <p>In the <a href="https://people.mpi-sws.org/~rossberg/papers/Rossberg%20-%201ML%20--%20Core%20and%20modules%20united%20[JFP].pdf" rel="noreferrer">1ML – Core and Modules United (F-ing First-Class Modules)</a> paper, the author gives the following example for why module types do not form a lattice under subtyping:</p>... | type theory type checking type inference | 1 | Drawbacks of adding type equality to 1ML -- (type theory type checking type inference)
<p>In the <a href="https://people.mpi-sws.org/~rossberg/papers/Rossberg%20-%201ML%20--%20Core%20and%20modules%20united%20[JFP].pdf" rel="noreferrer">1ML – Core and Modules United (F-ing First-Class Modules)</a> paper, the author give... | habedi/stack-exchange-dataset |
102,612 | Why researchers don't study the parameterizations of the problems unlikely to be NP-Hard? | <p>I have seen the parameterization of the very well known problems like vertex cover, hitting set etc which are NP-hard (NP-complete precisely). Many researchers in the past have been studied the parameterization of these problems. My question is why researcher's don't study the parameterizations of the problems unli... | complexity theory | 1 | Why researchers don't study the parameterizations of the problems unlikely to be NP-Hard? -- (complexity theory)
<p>I have seen the parameterization of the very well known problems like vertex cover, hitting set etc which are NP-hard (NP-complete precisely). Many researchers in the past have been studied the parameteri... | habedi/stack-exchange-dataset |
102,613 | Optimal dividing of K people into N groups | <p>A teacher at a school has to do this on a regular basis. Let's say 12 students should be divided into either <code>4 groups of 3</code>, or <code>3 groups og 4</code>.
Each student can pick up to 3 other students that person would most rather be with. </p>

<p>I tried to set this up as an undirected we... | algorithms graphs | 1 | Optimal dividing of K people into N groups -- (algorithms graphs)
<p>A teacher at a school has to do this on a regular basis. Let's say 12 students should be divided into either <code>4 groups of 3</code>, or <code>3 groups og 4</code>.
Each student can pick up to 3 other students that person would most rather be w... | habedi/stack-exchange-dataset |
102,623 | Are the capabilities of programming languages the same? | <p>Is the capability of every programming language the same since it is eventually translated into machine code. Python, Java etc. are all together instructions the CPU is going to process. So, you could (theoretically) do the exact same thing with ever language, don't you? </p>
 | computability programming languages | 1 | Are the capabilities of programming languages the same? -- (computability programming languages)
<p>Is the capability of every programming language the same since it is eventually translated into machine code. Python, Java etc. are all together instructions the CPU is going to process. So, you could (theoretically) do ... | habedi/stack-exchange-dataset |
102,627 | Data hazard after in load word after addi | <p>5 stage pipline</p>

<pre><code>addi <span class="math-container">$t1,$</span>zero,0x30 
lw <span class="math-container">$t2,0($</span>t1) 
sw <span class="math-container">$t2,0xff18($</span>zero) 
addi <span class="math-container">$t2,$</span>zero,100
</code></pre>

<p>Question is ... | computer architecture mips | 1 | Data hazard after in load word after addi -- (computer architecture mips)
<p>5 stage pipline</p>

<pre><code>addi <span class="math-container">$t1,$</span>zero,0x30 
lw <span class="math-container">$t2,0($</span>t1) 
sw <span class="math-container">$t2,0xff18($</span>zero) 
addi <span class="math-... | habedi/stack-exchange-dataset |
102,634 | Cover the maximum of elements | <p>I have a collection of subsets <span class="math-container">$\{S_1,\ldots,S_m\}$</span> where each <span class="math-container">$S_i\subset \{1,\ldots,n\}$</span>. I would like to cover the maximum number of elements from <span class="math-container">$\{1,\ldots,n\}$</span> by choosing a single element from each <sp... | algorithms | 1 | Cover the maximum of elements -- (algorithms)
<p>I have a collection of subsets <span class="math-container">$\{S_1,\ldots,S_m\}$</span> where each <span class="math-container">$S_i\subset \{1,\ldots,n\}$</span>. I would like to cover the maximum number of elements from <span class="math-container">$\{1,\ldots,n\}$</sp... | habedi/stack-exchange-dataset |
102,641 | What are the things one can do with the internet without the World Wide Web? | <p>If the question above makes any sense!</p>
 | computer networks | 1 | What are the things one can do with the internet without the World Wide Web? -- (computer networks)
<p>If the question above makes any sense!</p>
 | habedi/stack-exchange-dataset |
102,647 | Do lossless compression algorithms reduce entropy? | <p>According to <a href="https://en.wikipedia.org/wiki/Entropy_(information_theory)" rel="noreferrer">Wikipedia</a>:</p>

<blockquote>
 <p>Shannon's entropy measures the information contained in a message as opposed to the portion of the message that is determined (or predictable). Examples of the latter i... | information theory data compression entropy | 1 | Do lossless compression algorithms reduce entropy? -- (information theory data compression entropy)
<p>According to <a href="https://en.wikipedia.org/wiki/Entropy_(information_theory)" rel="noreferrer">Wikipedia</a>:</p>

<blockquote>
 <p>Shannon's entropy measures the information contained in a message as... | habedi/stack-exchange-dataset |
102,650 | Solve recurrence T(n)=2T(n-1)+n for n greater than 1 and T(1)=1 | <p><strong>Problem statement</strong>: Solve <span class="math-container">$T(n)$</span> for <span class="math-container">$T(n)=2T(n-1)+n$</span>, <span class="math-container">$n > 1$</span>, and <span class="math-container">$T(1)=1$</span>.</p>

<p><strong>My attempt</strong>: I tried back substituting but ... | recurrence relation | 1 | Solve recurrence T(n)=2T(n-1)+n for n greater than 1 and T(1)=1 -- (recurrence relation)
<p><strong>Problem statement</strong>: Solve <span class="math-container">$T(n)$</span> for <span class="math-container">$T(n)=2T(n-1)+n$</span>, <span class="math-container">$n > 1$</span>, and <span class="math-container">$T(... | habedi/stack-exchange-dataset |
102,660 | Is the set of surjective recursive functions in RE/coRE? | <p>Let L be a set of recursive funtions with <span class="math-container">$L = \{i\in \mathbb{N}|f_i\space is\space surjective\}$</span> where <span class="math-container">$i$</span> is a gödel number of f.Is <span class="math-container">$L\in RE,\space coRE$</span>?</p>

<p>I can't think of a way to show eithe... | computability | 1 | Is the set of surjective recursive functions in RE/coRE? -- (computability)
<p>Let L be a set of recursive funtions with <span class="math-container">$L = \{i\in \mathbb{N}|f_i\space is\space surjective\}$</span> where <span class="math-container">$i$</span> is a gödel number of f.Is <span class="math-container">$L\in ... | habedi/stack-exchange-dataset |
102,667 | Solving recurrence relations with two variables | <p>I am trying to solve this recurrence relation with two variables:</p>

<p><span class="math-container">$$T(n, k) = T(n - 1, k - 1) + T(n - 1, k)$$</span></p>

<p>The base cases are:</p>

<ul>
<li><span class="math-container">$T(n, k) = 1$</span> if <span class="math-container">$k = 0$</sp... | recurrence relation | 1 | Solving recurrence relations with two variables -- (recurrence relation)
<p>I am trying to solve this recurrence relation with two variables:</p>

<p><span class="math-container">$$T(n, k) = T(n - 1, k - 1) + T(n - 1, k)$$</span></p>

<p>The base cases are:</p>

<ul>
<li><span class="math-co... | habedi/stack-exchange-dataset |
102,668 | How does quicksort with 3-way partitioning ~ $(2 ln 2) NH$ become linear time complexity with many duplicated keys? | <p>From <em>Algorithms 4th</em>:</p>

<blockquote>
 <p>Quicksort with 3-way partitioning uses ~<span class="math-container">$(2\ln 2)NH$</span> compares to sort <span class="math-container">$N$</span> items, where <span class="math-container">$H$</span> is the Shannon entropy, defined from the frequencies ... | complexity theory time complexity | 1 | How does quicksort with 3-way partitioning ~ $(2 ln 2) NH$ become linear time complexity with many duplicated keys? -- (complexity theory time complexity)
<p>From <em>Algorithms 4th</em>:</p>

<blockquote>
 <p>Quicksort with 3-way partitioning uses ~<span class="math-container">$(2\ln 2)NH$</span> compares... | habedi/stack-exchange-dataset |
102,673 | "Mathematical Physics"'s equivalent for Computer Science | <p>Mathematical Physics is a <strong>well defined</strong> scientific fields that deals with the application of mathematics , mathematical tools , and mathematical methods in the theories and the problems of physics.</p>

<p>Is there a <strong>well defined</strong> scientific field that deals with the applicati... | mathematical foundations | 1 | "Mathematical Physics"'s equivalent for Computer Science -- (mathematical foundations)
<p>Mathematical Physics is a <strong>well defined</strong> scientific fields that deals with the application of mathematics , mathematical tools , and mathematical methods in the theories and the problems of physics.</p>

<p>... | habedi/stack-exchange-dataset |
102,681 | Which address bits are used for set selection/tag check in a cache? | <p>If </p>

<blockquote>
 <p>Capacity = 24 KiB Associativity = 6 Line Size = 32 B</p>
</blockquote>

<p>As far as I know:</p>

<p><span class="math-container">$$Capacity = Associtivity * Line Size * Sets$$</span></p>

<p>so
<span class="math-container">$24576 = 32 * 6 * Sets... | computer architecture | 1 | Which address bits are used for set selection/tag check in a cache? -- (computer architecture)
<p>If </p>

<blockquote>
 <p>Capacity = 24 KiB Associativity = 6 Line Size = 32 B</p>
</blockquote>

<p>As far as I know:</p>

<p><span class="math-container">$$Capacity = Associtivity * Line ... | habedi/stack-exchange-dataset |
102,682 | Is there a name for this type of Turing machine? | <p>I'm considering turing machines with tape alphabet equal to <span class="math-container">$\{0,1\}$</span> and the blank symbol equal to <span class="math-container">$0$</span>. Is there a name for this type of Turing machines? Isn't this type the one computers are based on?</p>
 | turing machines | 1 | Is there a name for this type of Turing machine? -- (turing machines)
<p>I'm considering turing machines with tape alphabet equal to <span class="math-container">$\{0,1\}$</span> and the blank symbol equal to <span class="math-container">$0$</span>. Is there a name for this type of Turing machines? Isn't this type the ... | habedi/stack-exchange-dataset |
102,687 | N subsets with a given sum? | <p>How to efficiently ¹⁾ choose from a set of numbers <span class="math-container">$S$</span>, a given number <span class="math-container">$n$</span> of disjoint subsets, each with a given sum <span class="math-container">$K$</span> of chosen elements?</p>

<p>¹⁾ Not as in <span class="math-container">$P$</span... | sets subset sum | 1 | N subsets with a given sum? -- (sets subset sum)
<p>How to efficiently ¹⁾ choose from a set of numbers <span class="math-container">$S$</span>, a given number <span class="math-container">$n$</span> of disjoint subsets, each with a given sum <span class="math-container">$K$</span> of chosen elements?</p>

<p>¹⁾... | habedi/stack-exchange-dataset |
102,700 | If you have a smallest grammar approximation, do you immediately have a CFG inference algorithm? | <p>The smallest grammar problem is to find a single-string CFG. So given a finite list of language samples, known to all lie in some CFG, can we, using the smallest grammars (approximated) of each respective sample, compute an approximate smallest CFG for the language?</p>

<p>I want to make a parser generator... | algorithms formal languages optimization context free formal grammars | 1 | If you have a smallest grammar approximation, do you immediately have a CFG inference algorithm? -- (algorithms formal languages optimization context free formal grammars)
<p>The smallest grammar problem is to find a single-string CFG. So given a finite list of language samples, known to all lie in some CFG, can we, u... | habedi/stack-exchange-dataset |
102,709 | Word-hyphenation algorithm for monospaced fonts | <p>I have seen a few standard hyphenation algorithms for non-monospaced fonts, where you are free to squeeze and separate words and letters, but I haven't seen any related to monospaced fonts specifically. Wondering if there are any good resources on the topic. Such as how to best properties to use when hyphenating a m... | algorithms | 1 | Word-hyphenation algorithm for monospaced fonts -- (algorithms)
<p>I have seen a few standard hyphenation algorithms for non-monospaced fonts, where you are free to squeeze and separate words and letters, but I haven't seen any related to monospaced fonts specifically. Wondering if there are any good resources on the t... | habedi/stack-exchange-dataset |
102,712 | What's the right way to think about a CFG symbol with an infinite null derivation? | <p>I'm curious about the right way to characterize symbol <span class="math-container">$A$</span> in a CFG like this one:</p>

<p><span class="math-container">$$
\begin{align*}
A &\to A B\\
A &\to x\\
B &\to y\\
B &\to \varepsilon
\end{align*}
$$</span></p>

<... | context free formal grammars | 1 | What's the right way to think about a CFG symbol with an infinite null derivation? -- (context free formal grammars)
<p>I'm curious about the right way to characterize symbol <span class="math-container">$A$</span> in a CFG like this one:</p>

<p><span class="math-container">$$
\begin{align*}
A &\to... | habedi/stack-exchange-dataset |
102,720 | How to transform a Infinite decimal of $\frac{23}{6}$ into binary? | <p>How to transform a decimal of <span class="math-container">$\frac{23}{6}$</span> into binary?</p>

<p><span class="math-container">$\frac{23}{6}$</span> is equal to <span class="math-container">$3.83333\bar{33}$</span>, where the digit <span class="math-container">$3$</span>s are repeated forever.</p>
&... | binary | 1 | How to transform a Infinite decimal of $\frac{23}{6}$ into binary? -- (binary)
<p>How to transform a decimal of <span class="math-container">$\frac{23}{6}$</span> into binary?</p>

<p><span class="math-container">$\frac{23}{6}$</span> is equal to <span class="math-container">$3.83333\bar{33}$</span>, where the... | habedi/stack-exchange-dataset |
102,724 | How can I efficiently find the largest positive interval in an unsorted array? | <p>Given a set of values like [4, 8, 1, 5, 2, 6, 9, 2, 3, 5, 11, 9], how can I find the largest positive interval between any two of them? For example in the one I just listed, index 0 to index 1 has an interval of 4 because <code>8 - 4 = 4</code>. But the largest positive interval is between index 2 and index 10, beca... | algorithms subsequences | 1 | How can I efficiently find the largest positive interval in an unsorted array? -- (algorithms subsequences)
<p>Given a set of values like [4, 8, 1, 5, 2, 6, 9, 2, 3, 5, 11, 9], how can I find the largest positive interval between any two of them? For example in the one I just listed, index 0 to index 1 has an interval ... | habedi/stack-exchange-dataset |
102,730 | Recognizer for decidable language and words it doesn't halt on | <p>Suppose we have a decidable language <code>B</code> (there exists some TM that decides it). Suppose we have another TM <code>M</code> which <strong>only</strong> recognizes B but does not decide it - there are words not in B that <code>M</code> <strong>doesn't halt on</strong> (for words not in B M might either reje... | turing machines computability undecidability halting problem | 1 | Recognizer for decidable language and words it doesn't halt on -- (turing machines computability undecidability halting problem)
<p>Suppose we have a decidable language <code>B</code> (there exists some TM that decides it). Suppose we have another TM <code>M</code> which <strong>only</strong> recognizes B but does not ... | habedi/stack-exchange-dataset |
102,740 | Why do I get different results from two calculation methods? | <p>I am wondering what the reason for the following is </p>

<p>We know that ,</p>

<p>exponential has a taylor representation :
<span class="math-container">$$exp(x)=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+...$$</span></p>

<p>Using the first n terms , in R , I compute</p>

<p><span ... | floating point numerical analysis | 1 | Why do I get different results from two calculation methods? -- (floating point numerical analysis)
<p>I am wondering what the reason for the following is </p>

<p>We know that ,</p>

<p>exponential has a taylor representation :
<span class="math-container">$$exp(x)=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}... | habedi/stack-exchange-dataset |
102,742 | Which is better ? Iterations or Recursions? | <p>I've heard that any algorithm using iterations can be changed into one that uses recursions and vice-versa. </p>

<p>But which type of repetition is preferable for minimum amount of computational effort and resource consumption ? Iteration or Recursion ?</p>
 | algorithms optimization recursion iteration | 1 | Which is better ? Iterations or Recursions? -- (algorithms optimization recursion iteration)
<p>I've heard that any algorithm using iterations can be changed into one that uses recursions and vice-versa. </p>

<p>But which type of repetition is preferable for minimum amount of computational effort and resource ... | habedi/stack-exchange-dataset |
102,752 | Multi-variate complexity semplification | <p>I developed an algorithm with the following multi-variate complexity:
<span class="math-container">$$O((k^n+kn)l^{kn}),$$</span>
where <span class="math-container">$n,k,l$</span> are variables.</p>

<p>I have very little knowledge of complexity theory, and I'm not sure whether this expression can be ... | complexity theory time complexity | 1 | Multi-variate complexity semplification -- (complexity theory time complexity)
<p>I developed an algorithm with the following multi-variate complexity:
<span class="math-container">$$O((k^n+kn)l^{kn}),$$</span>
where <span class="math-container">$n,k,l$</span> are variables.</p>

<p>I have very little k... | habedi/stack-exchange-dataset |
102,753 | Why 2 different edge min-cuts in an undirected multigraph must be completely disjoint? | <p>For the proof of a maximum of (n 2) min-cuts in any n-vertex undirected multigraph using the random contraction algorithm, we need to know that no min-cut shares an edge with another different one.</p>

<p>My attempt to prove this was using a contradiction argument, supposing there was a common edge across 2... | graphs combinatorics probabilistic algorithms minimum cuts | 1 | Why 2 different edge min-cuts in an undirected multigraph must be completely disjoint? -- (graphs combinatorics probabilistic algorithms minimum cuts)
<p>For the proof of a maximum of (n 2) min-cuts in any n-vertex undirected multigraph using the random contraction algorithm, we need to know that no min-cut shares an e... | habedi/stack-exchange-dataset |
102,761 | Why it is not a Huffman code | <p>I have been given several examples I the aim is to explain why it is not a Huffman code. So, for instance, the first one was:</p>

<p><span class="math-container">$\{00,01,10,110\}$</span></p>

<p>This code is not Huffman becuase it has just one codeword of maximum length whereas there should be two ... | information theory entropy huffman coding | 1 | Why it is not a Huffman code -- (information theory entropy huffman coding)
<p>I have been given several examples I the aim is to explain why it is not a Huffman code. So, for instance, the first one was:</p>

<p><span class="math-container">$\{00,01,10,110\}$</span></p>

<p>This code is not Huffman bec... | habedi/stack-exchange-dataset |
102,771 | Bachmair and Ganzinger, ordering of equations | <p>Bachmair and Ganzinger (1991), 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', page 4, defines an order on equations. (This is an arcane piece of machinery but a critical one in the overall attempt to get to the point where equations can be applied in one direction, thereby dramatically... | logic first order logic automated theorem proving | 1 | Bachmair and Ganzinger, ordering of equations -- (logic first order logic automated theorem proving)
<p>Bachmair and Ganzinger (1991), 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', page 4, defines an order on equations. (This is an arcane piece of machinery but a critical one in the over... | habedi/stack-exchange-dataset |
102,773 | Proof of the master thorem case with floors and b = 2 | <p>This question is related to <a href="https://cs.stackexchange.com/questions/102119/missing-part-of-the-proof-of-master-theorems-case-2-with-ceilings-and-floors">my previous one</a>.</p>

<p>Let the following recurrence relation be given: <span class="math-container">$T(n)=aT(\lfloor n/b \rfloor)+f(n)$</span>... | algorithm analysis master theorem | 1 | Proof of the master thorem case with floors and b = 2 -- (algorithm analysis master theorem)
<p>This question is related to <a href="https://cs.stackexchange.com/questions/102119/missing-part-of-the-proof-of-master-theorems-case-2-with-ceilings-and-floors">my previous one</a>.</p>

<p>Let the following recurren... | habedi/stack-exchange-dataset |
102,777 | Doubt regarding foreign key and referential integrity | <p>I am studying database from <a href="http://db-book.com/" rel="nofollow noreferrer">Database System Concepts</a>.</p>

<p>The author was explaining foreign keys and referential integrity with the help of following schemas:</p>

<p><span class="math-container">$$ instructor(\underline{ID},\space name,... | database theory databases relational algebra | 1 | Doubt regarding foreign key and referential integrity -- (database theory databases relational algebra)
<p>I am studying database from <a href="http://db-book.com/" rel="nofollow noreferrer">Database System Concepts</a>.</p>

<p>The author was explaining foreign keys and referential integrity with the help of f... | habedi/stack-exchange-dataset |
102,780 | How does the equation for min heap array indexing work? | <p>I've been reading about min heaps, currently looking at <a href="https://codeburst.io/implementing-a-complete-binary-heap-in-javascript-the-priority-queue-7d85bd256ecf" rel="nofollow noreferrer">this article</a>, and I am very confused by something.</p>

<p>The article makes the following statement:</p>
... | heaps | 1 | How does the equation for min heap array indexing work? -- (heaps)
<p>I've been reading about min heaps, currently looking at <a href="https://codeburst.io/implementing-a-complete-binary-heap-in-javascript-the-priority-queue-7d85bd256ecf" rel="nofollow noreferrer">this article</a>, and I am very confused by something.<... | habedi/stack-exchange-dataset |
102,789 | Ketama hash explanation | <p>(I originally posted this on stackoverflow but thought it would be a better fit here)</p>

<p>I'm trying to understand the Ketama hash code used in consistent hashing.</p>

<p><a href="https://github.com/RJ/ketama/blob/master/java_ketama/SockIOPool.java#L517-L532" rel="nofollow noreferrer">link</a> a... | hashing | 1 | Ketama hash explanation -- (hashing)
<p>(I originally posted this on stackoverflow but thought it would be a better fit here)</p>

<p>I'm trying to understand the Ketama hash code used in consistent hashing.</p>

<p><a href="https://github.com/RJ/ketama/blob/master/java_ketama/SockIOPool.java#L517-L532"... | habedi/stack-exchange-dataset |
102,801 | Why is $\{a^nb^n \mid n \geq 1\}$ not type 3 (regular)? | <p>My book states that the language
<span class="math-container">$$L_1 = \{a^nb^n\mid n\geq 1\}$$</span>
is of type 2 (context-free) but not of type 3 (regular) since there is no regular grammar to produce it. However, I can't really imagine how this grammar should not be applicable or why it shouldn't be a val... | formal languages regular languages | 1 | Why is $\{a^nb^n \mid n \geq 1\}$ not type 3 (regular)? -- (formal languages regular languages)
<p>My book states that the language
<span class="math-container">$$L_1 = \{a^nb^n\mid n\geq 1\}$$</span>
is of type 2 (context-free) but not of type 3 (regular) since there is no regular grammar to produce it. Howeve... | habedi/stack-exchange-dataset |
102,806 | Proccess scheduling arrival time | <p>If I have a set of processes, let's say 9 and I know the burst time and the waiting time for SJF algorithm and also know that processes arrive in groups of 3 processes at M1 moment, M2 moment, M3 moment (M1, M2 and M3 are given), how can I decide at what moment each process will arrive?</p>

<p><a href="htt... | scheduling process scheduling | 1 | Proccess scheduling arrival time -- (scheduling process scheduling)
<p>If I have a set of processes, let's say 9 and I know the burst time and the waiting time for SJF algorithm and also know that processes arrive in groups of 3 processes at M1 moment, M2 moment, M3 moment (M1, M2 and M3 are given), how can I decide a... | habedi/stack-exchange-dataset |
102,819 | Convert NURBS curve into Cubic Bezier Curve | <p>From <a href="https://www.gamedev.net/forums/topic/587450-nurbs-to-bezier-curves/" rel="nofollow noreferrer">this</a>:</p>

<blockquote>
 <p>Maybe you already know this, but it's impossible to convert nurbs to bezier splines exactly because nurbs are rational functions, and bezier splines are polynomial... | algorithms computational geometry graphics topology digital curve | 1 | Convert NURBS curve into Cubic Bezier Curve -- (algorithms computational geometry graphics topology digital curve)
<p>From <a href="https://www.gamedev.net/forums/topic/587450-nurbs-to-bezier-curves/" rel="nofollow noreferrer">this</a>:</p>

<blockquote>
 <p>Maybe you already know this, but it's impossible... | habedi/stack-exchange-dataset |
102,821 | Intersection of two incomplete DFAs | <p>Let assume that I have the following two automata A1 and A2 :</p>

<p><a href="https://i.stack.imgur.com/RVSpx.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RVSpx.png" alt="A1"></a>
<a href="https://i.stack.imgur.com/hqILt.png" rel="nofollow noreferrer"><img src="https://i.stack.imgu... | automata finite automata | 1 | Intersection of two incomplete DFAs -- (automata finite automata)
<p>Let assume that I have the following two automata A1 and A2 :</p>

<p><a href="https://i.stack.imgur.com/RVSpx.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RVSpx.png" alt="A1"></a>
<a href="https://i.stack.imgur.com/h... | habedi/stack-exchange-dataset |
102,825 | Is there an existing algorithm for this type of sorting? | <p><a href="https://www.youtube.com/watch?v=WaNLJf8xzC4" rel="nofollow noreferrer">This TED-ED video</a> talks about some of the most basic sorting methods (bubble sort, insertion sort and quick sort,) in response to a scenario where a librarian ends up with a stack of 1,280 unsorted books, and must quickly sort them i... | algorithms sorting | 1 | Is there an existing algorithm for this type of sorting? -- (algorithms sorting)
<p><a href="https://www.youtube.com/watch?v=WaNLJf8xzC4" rel="nofollow noreferrer">This TED-ED video</a> talks about some of the most basic sorting methods (bubble sort, insertion sort and quick sort,) in response to a scenario where a lib... | habedi/stack-exchange-dataset |
102,828 | Why is a heap better than a linked list for implementation of a priority queue? | <p>Using a heap, you have O(log(n)) insertion and O(log(n)) removal. Using a linked list, you have O(n) insertion and O(1) removal.</p>

<p>Why is it better to have log-n for both than n for one and constant time for the other?</p>
 | complexity theory time complexity runtime analysis heaps priority queues | 1 | Why is a heap better than a linked list for implementation of a priority queue? -- (complexity theory time complexity runtime analysis heaps priority queues)
<p>Using a heap, you have O(log(n)) insertion and O(log(n)) removal. Using a linked list, you have O(n) insertion and O(1) removal.</p>

<p>Why is it bett... | habedi/stack-exchange-dataset |
102,829 | When is this even possible (even for a dense graphs) $|E| = \Theta (|V|^2)$ | <p>Wikipedia says that "a dense graph is a graph in which the number of edges is close to the maximal number of edges." and "The maximum number of edges for an undirected graph is <span class="math-container">$|V|(|V|-1)/2$</span>". Then why do even use <span class="math-container">$ |E| = \Theta (|V|^2)$</span>?, un... | graphs asymptotics | 1 | When is this even possible (even for a dense graphs) $|E| = \Theta (|V|^2)$ -- (graphs asymptotics)
<p>Wikipedia says that "a dense graph is a graph in which the number of edges is close to the maximal number of edges." and "The maximum number of edges for an undirected graph is <span class="math-container">$|V|(|V|-1... | habedi/stack-exchange-dataset |
102,834 | What is happening during "table walk"? | <p>I am trying to understand what is a table walk. I have found when it occurs - 
whenever there is a TLB miss. If no descriptor is found – TLB miss occurs and further behavior depends on the implementation of a paging unit. (TLB - Translation look aside buffer)</p>

<p>But i still do not understand what ex... | computer architecture | 1 | What is happening during "table walk"? -- (computer architecture)
<p>I am trying to understand what is a table walk. I have found when it occurs - 
whenever there is a TLB miss. If no descriptor is found – TLB miss occurs and further behavior depends on the implementation of a paging unit. (TLB - Translation look a... | habedi/stack-exchange-dataset |
102,835 | How to find the angle of an arc to draw graphic | <p>I would like to draw an arc from a specific point to a goal point, during the process of drawing a larger path. I would like to do it using bezier curves, which aren't adequate for modeling circular arcs, but these equations found <a href="https://stackoverflow.com/questions/30277646/svg-convert-arcs-to-cubic-bezier... | algorithms computational geometry graphics | 1 | How to find the angle of an arc to draw graphic -- (algorithms computational geometry graphics)
<p>I would like to draw an arc from a specific point to a goal point, during the process of drawing a larger path. I would like to do it using bezier curves, which aren't adequate for modeling circular arcs, but these equati... | habedi/stack-exchange-dataset |
102,848 | What's the difference between cache miss penalty and latency to memory? | <p>Can I say that cache miss penalty includes latency to memory? My current understanding is that cache miss penalty is the time moving data from the layer closer to main memory to it. But I'm not sure about what's the meaning of latency to memory? If they're not the same what's the overlapping part?</p>
 | cpu cache | 1 | What's the difference between cache miss penalty and latency to memory? -- (cpu cache)
<p>Can I say that cache miss penalty includes latency to memory? My current understanding is that cache miss penalty is the time moving data from the layer closer to main memory to it. But I'm not sure about what's the meaning of lat... | habedi/stack-exchange-dataset |
102,849 | Alternatives to directly connected networks for representing frequently-updated graphs | <p>What are the relative merits of the various graph representations, such as adjacency matrix, edge list, adjacency list, directly connected network etc. Given that this graph will be frequently updated, split, joined to other graphs?</p>

<p>Business Context: I am writing a molecule editor in C# and have curr... | graphs | 1 | Alternatives to directly connected networks for representing frequently-updated graphs -- (graphs)
<p>What are the relative merits of the various graph representations, such as adjacency matrix, edge list, adjacency list, directly connected network etc. Given that this graph will be frequently updated, split, joined to... | habedi/stack-exchange-dataset |
102,851 | d-ary heap implementation vs Fibonacci heap implementation Dijkstra performance comparions | <p>Let's say that Dijkstra’s algorithm with the priority queue using a d-ary heap. if adjusting d, we can try to achieve the best runtimes for the algorithm with d being <span class="math-container">$\sim |E|/|V|$</span>.</p>

<p>Then for a fixed <span class="math-container">$|V|$</span>, what is the largest ... | asymptotics heaps performance comparison | 1 | d-ary heap implementation vs Fibonacci heap implementation Dijkstra performance comparions -- (asymptotics heaps performance comparison)
<p>Let's say that Dijkstra’s algorithm with the priority queue using a d-ary heap. if adjusting d, we can try to achieve the best runtimes for the algorithm with d being <span class... | habedi/stack-exchange-dataset |
102,853 | Transforming a byte with a subset of a small, fixed set of values and xor into any other value | <p>If I have some collection of bits, -- a byte, say -- of arbitrary value then I can transform it into some other value by means of exclusive-oring it with a subset of (in this case) eight fixed values, each affecting a single bit 0x80, 0x40, ... 0x01: every possible value is represented by some combination of operati... | linear algebra group theory | 1 | Transforming a byte with a subset of a small, fixed set of values and xor into any other value -- (linear algebra group theory)
<p>If I have some collection of bits, -- a byte, say -- of arbitrary value then I can transform it into some other value by means of exclusive-oring it with a subset of (in this case) eight fi... | habedi/stack-exchange-dataset |
102,855 | Confusion about proof of undecidability of REGULAR TM in Sipser's book | <p>in the book "Introduction to the Theory of Computation" by Michael Sipser there is an example of undecidable languages in which there is a language REGULR_TM which is described as follows :</p>

<p><code>REGULAR_TM = { <M> | M is a Turing machine and L(M) is regular language }.</code>
 Well, Sipser... | turing machines reductions undecidability | 1 | Confusion about proof of undecidability of REGULAR TM in Sipser's book -- (turing machines reductions undecidability)
<p>in the book "Introduction to the Theory of Computation" by Michael Sipser there is an example of undecidable languages in which there is a language REGULR_TM which is described as follows :</p>
&... | habedi/stack-exchange-dataset |
102,862 | fixing a slightly broken BST tree | <p>I'm stuck on this question, a BST is slightly broken only if there is a node with value x in which :</p>

<p>there is at least one value less than x on its right branch or atleast one value greater than x on its left branch.</p>

<p>for example : </p>

<pre><code> 3
 ... | binary search trees | 1 | fixing a slightly broken BST tree -- (binary search trees)
<p>I'm stuck on this question, a BST is slightly broken only if there is a node with value x in which :</p>

<p>there is at least one value less than x on its right branch or atleast one value greater than x on its left branch.</p>

<p>for examp... | habedi/stack-exchange-dataset |
102,863 | How to perform local search to find maximal induced subgraphs? | <p>I'm looking for efficient ways to perform local search to find maximal induced subgraphs that satisfy certain properties : a tree, a forest or a bipartite subgraph for example.</p>

<p>What I mean by local search is moving from solution to solution by applying local changes, until a solution deemed optimal i... | graphs graph traversal heuristics | 1 | How to perform local search to find maximal induced subgraphs? -- (graphs graph traversal heuristics)
<p>I'm looking for efficient ways to perform local search to find maximal induced subgraphs that satisfy certain properties : a tree, a forest or a bipartite subgraph for example.</p>

<p>What I mean by local s... | habedi/stack-exchange-dataset |
102,866 | Applying minimax tree to this array | <p>Please tell me how I should apply minimax algorithm to the array
<span class="math-container">$$ 15, 12, 14, 16, 11, 13$$</span>
and make a tree?(I understand how minimax algorithm works but I can't apply it to an array)</p>
 | algorithms arrays | 1 | Applying minimax tree to this array -- (algorithms arrays)
<p>Please tell me how I should apply minimax algorithm to the array
<span class="math-container">$$ 15, 12, 14, 16, 11, 13$$</span>
and make a tree?(I understand how minimax algorithm works but I can't apply it to an array)</p>
 | habedi/stack-exchange-dataset |
102,868 | When estimating camera motion from the fundamental matrix, why can translation only be recovered up to scale using epipolar geometry? | <p>I was wondering once you have recovered the fundamental matrix F such that xFx' = 0. If you try to recover translation and rotation from F, I am told that this is possible only up to scale? Why so?</p>
 | computer vision | 1 | When estimating camera motion from the fundamental matrix, why can translation only be recovered up to scale using epipolar geometry? -- (computer vision)
<p>I was wondering once you have recovered the fundamental matrix F such that xFx' = 0. If you try to recover translation and rotation from F, I am told that this is... | habedi/stack-exchange-dataset |
102,874 | What is the Big-Ω of the following function? | <p>For the following function:</p>

<p><span class="math-container">$$
\sum_{n=1}^{2n}x+x^2
$$</span></p>

<p>It is easy to see the (tightest) Big-Oh is <span class="math-container">$O(n^3)$</span>, but I am not so sure about the Big-Omega. Here is my attempt:</p>

<p><span class="math-c... | asymptotics | 1 | What is the Big-Ω of the following function? -- (asymptotics)
<p>For the following function:</p>

<p><span class="math-container">$$
\sum_{n=1}^{2n}x+x^2
$$</span></p>

<p>It is easy to see the (tightest) Big-Oh is <span class="math-container">$O(n^3)$</span>, but I am not so sure about the Big-... | habedi/stack-exchange-dataset |
102,875 | Normal form after decomposition of a relation | <p>I came across a text recently which claims that if we perform a lossless decomposition of a relation R into smaller relations R1 and R2, and if R is in 3NF, both R1 and R2 are 3NF.</p>

<p>I felt a bit suspicious regarding this claim, but couldn't find anything to prove this statement wrong. </p>

<p... | database theory normal forms relational calculus functional dependencies | 1 | Normal form after decomposition of a relation -- (database theory normal forms relational calculus functional dependencies)
<p>I came across a text recently which claims that if we perform a lossless decomposition of a relation R into smaller relations R1 and R2, and if R is in 3NF, both R1 and R2 are 3NF.</p>

... | habedi/stack-exchange-dataset |
102,886 | Difference between stable marriage problem and assignment problem | <p>What is the difference between the <a href="https://en.wikipedia.org/wiki/Stable_marriage_problem" rel="nofollow noreferrer">stable marriage problem</a> and an <a href="https://en.wikipedia.org/wiki/Assignment_problem" rel="nofollow noreferrer">assignment problem</a>? Both refer to a <a href="https://en.wikipedia.or... | assignment problem | 1 | Difference between stable marriage problem and assignment problem -- (assignment problem)
<p>What is the difference between the <a href="https://en.wikipedia.org/wiki/Stable_marriage_problem" rel="nofollow noreferrer">stable marriage problem</a> and an <a href="https://en.wikipedia.org/wiki/Assignment_problem" rel="nof... | habedi/stack-exchange-dataset |
102,889 | What's the worst case complexity of Robert W. Floyd's cycle detection algorithm? | <p><strong>Givens</strong>. I understand Floyd's algorithm can determine the length <span class="math-container">$\lambda$</span> of the loop and the length <span class="math-container">$m$</span> of the tail. The hare will not necessarily catch the tortoise on the first cycle, but it is guaranteed to catch it after a... | time complexity | 1 | What's the worst case complexity of Robert W. Floyd's cycle detection algorithm? -- (time complexity)
<p><strong>Givens</strong>. I understand Floyd's algorithm can determine the length <span class="math-container">$\lambda$</span> of the loop and the length <span class="math-container">$m$</span> of the tail. The har... | habedi/stack-exchange-dataset |
102,899 | is $0^x1^y$ context-free? | <p>given that L is regular, does the following make a context-free language?:</p>

<p>i) <span class="math-container">$\{0^x1^y \mid 0^{x+y} \in L\}$</span></p>

<p>ii) <span class="math-container">$\{0^x1^y \mid 0^{x-y} \in L\}$</span></p>

<p>since L is regular, i presumed that i) can be put i... | automata regular languages context free | 1 | is $0^x1^y$ context-free? -- (automata regular languages context free)
<p>given that L is regular, does the following make a context-free language?:</p>

<p>i) <span class="math-container">$\{0^x1^y \mid 0^{x+y} \in L\}$</span></p>

<p>ii) <span class="math-container">$\{0^x1^y \mid 0^{x-y} \in L\}$</sp... | habedi/stack-exchange-dataset |
102,906 | Either find a perfect matching, or return a witness that none exist | <p>I am looking for a polynomial-time algorithm that takes as input a bipartite graph <span class="math-container">$(X\cup Y, E)$</span>, and returns one of two options:</p>

<ol>
<li><p>If a perfect matching exists, it returns the matching;</p></li>
<li><p>Otherwise, it returns a witness based on Hall'... | graphs matching bipartite matching | 1 | Either find a perfect matching, or return a witness that none exist -- (graphs matching bipartite matching)
<p>I am looking for a polynomial-time algorithm that takes as input a bipartite graph <span class="math-container">$(X\cup Y, E)$</span>, and returns one of two options:</p>

<ol>
<li><p>If a perfect ... | habedi/stack-exchange-dataset |
102,908 | Space and time complexity of $L = \{a^nb^{n^2} \mid n≥1\}$ | <p>Consider the following language:
<span class="math-container">$$L = \{a^nb^{n^2} \mid n≥1\}\,$$</span></p>

<p>When it comes to determining time and space complexity of a multi-tape TM, we can use two memory tapes, the first one to count <span class="math-container">$n$</span>, and the second one to repe... | complexity theory turing machines | 1 | Space and time complexity of $L = \{a^nb^{n^2} \mid n≥1\}$ -- (complexity theory turing machines)
<p>Consider the following language:
<span class="math-container">$$L = \{a^nb^{n^2} \mid n≥1\}\,$$</span></p>

<p>When it comes to determining time and space complexity of a multi-tape TM, we can use two memory... | habedi/stack-exchange-dataset |
102,919 | Reducing a graph without changing its chromatic number | <p>Does reducing a graph (removing or replacing vertices or edges) without changing its chromatic number has a specific name?</p>

<p>Take this cactus graph as an example (although my question is about an arbitrary graph):</p>

<p><a href="https://i.stack.imgur.com/MmzUf.png" rel="nofollow noreferrer"><... | graphs colorings | 1 | Reducing a graph without changing its chromatic number -- (graphs colorings)
<p>Does reducing a graph (removing or replacing vertices or edges) without changing its chromatic number has a specific name?</p>

<p>Take this cactus graph as an example (although my question is about an arbitrary graph):</p>

... | habedi/stack-exchange-dataset |
102,922 | System restarted before transaction is committed | <p>Consider the following log sequence of two transactions on a bank account, with initial balance 12000, that transfer 2000 to a mortgage payment and then apply a 5% interest. </p>

<pre><code>T1 start 
T1 B old=1200 new=10000
T1 M old=0 new=2000
T1 commit
T2 start
T2 B old=10000 new=10500&... | concurrency database theory | 1 | System restarted before transaction is committed -- (concurrency database theory)
<p>Consider the following log sequence of two transactions on a bank account, with initial balance 12000, that transfer 2000 to a mortgage payment and then apply a 5% interest. </p>

<pre><code>T1 start 
T1 B old=1200 new=1000... | habedi/stack-exchange-dataset |
102,929 | Bucket computation, cutting array with lines | <p>Given an NxN array, drawing a line from the edge's midpoint to the opposite field how can the N buckets be found covering the majority of the line's path? </p>

<p>A visual aid:
<a href="https://i.stack.imgur.com/ke9V8.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ke9V8.png" alt="ent... | algorithms computational geometry | 1 | Bucket computation, cutting array with lines -- (algorithms computational geometry)
<p>Given an NxN array, drawing a line from the edge's midpoint to the opposite field how can the N buckets be found covering the majority of the line's path? </p>

<p>A visual aid:
<a href="https://i.stack.imgur.com/ke9V8.pn... | habedi/stack-exchange-dataset |
102,931 | Decidability of $SEQ_{CFG} = \{⟨G,H⟩ \mid \text{$G,H$ are CFGs and $L(G) ⊆ L(H)$}\}$ | <p>How can I prove that <span class="math-container">$SEQ_{CFG} = \{⟨G,H⟩ \mid \text{$G,H$ are CFGs and $L(G) ⊆ L(H)$}\}$</span> is decidable ?</p>

<p>I know that <span class="math-container">$EQ_{CFG} = \{⟨G, H⟩ \mid \text{$G,H$ are CFGs and $L(G) = L(H)$}\}$</span> is not.</p>
 | context free proof techniques | 1 | Decidability of $SEQ_{CFG} = \{⟨G,H⟩ \mid \text{$G,H$ are CFGs and $L(G) ⊆ L(H)$}\}$ -- (context free proof techniques)
<p>How can I prove that <span class="math-container">$SEQ_{CFG} = \{⟨G,H⟩ \mid \text{$G,H$ are CFGs and $L(G) ⊆ L(H)$}\}$</span> is decidable ?</p>

<p>I know that <span class="math-container"... | habedi/stack-exchange-dataset |
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