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 |
|---|---|---|---|---|---|---|
109,127 | Are there variations of the regular runtimes of the Big-O-Notation? | <p>There are multiple <span class="math-container">$O$</span>-Notations, like <span class="math-container">$O(n)$</span> or <span class="math-container">$O(n^2)$</span> and so on. I was wondering, if there are variations of those in reality such as <span class="math-container">$O(2n^2)$</span> or <span class="math-cont... | complexity theory time complexity optimization big o notation | 1 | Are there variations of the regular runtimes of the Big-O-Notation? -- (complexity theory time complexity optimization big o notation)
<p>There are multiple <span class="math-container">$O$</span>-Notations, like <span class="math-container">$O(n)$</span> or <span class="math-container">$O(n^2)$</span> and so on. I was... | habedi/stack-exchange-dataset |
109,136 | Why have quantum circuits won out over quantum Turing machines? | <p>As I understand it, quantum circuits as a model are equivalent to quantum Turing machines, or at least they can be simulated on each other.</p>

<p>So my question is, why have quantum circuits become the chosen implementation rather than quantum Turing machines, such as in the IBM Q?</p>

<p>Is it re... | quantum computing | 1 | Why have quantum circuits won out over quantum Turing machines? -- (quantum computing)
<p>As I understand it, quantum circuits as a model are equivalent to quantum Turing machines, or at least they can be simulated on each other.</p>

<p>So my question is, why have quantum circuits become the chosen implementat... | habedi/stack-exchange-dataset |
109,139 | Dana Angluin's L* algorithm - Hypothesis inconsistent | <p>is it possible for the Dana Angluin's L* algorithm that a hypothesis is inconsistent?</p>

<p>So assume we have a closded observation table for a regular language L. Now after creating the hypothesis we will get a counterexample w. </p>

<p>The Question is: Can the counterexample w be chosen in the h... | automata finite automata learning theory | 1 | Dana Angluin's L* algorithm - Hypothesis inconsistent -- (automata finite automata learning theory)
<p>is it possible for the Dana Angluin's L* algorithm that a hypothesis is inconsistent?</p>

<p>So assume we have a closded observation table for a regular language L. Now after creating the hypothesis we will g... | habedi/stack-exchange-dataset |
109,141 | Chordal graph question | <p>In the below image, the graph is being triangulated (added edges are in red). My question is simple :<br>
<strong>Is the red edge between nodes 7 and 10 necessary in order to obtain a chordal graph?</strong></p>

<p><a href="https://i.stack.imgur.com/AXKEV.png" rel="nofollow noreferrer"><img src="https:/... | graphs | 1 | Chordal graph question -- (graphs)
<p>In the below image, the graph is being triangulated (added edges are in red). My question is simple :<br>
<strong>Is the red edge between nodes 7 and 10 necessary in order to obtain a chordal graph?</strong></p>

<p><a href="https://i.stack.imgur.com/AXKEV.png" rel="nof... | habedi/stack-exchange-dataset |
109,147 | Ford-Fulkerson vs Edmonds-Karp | <p>I was reading about maximum flow algorithms comparing the efficiency of the different ones. On the <a href="https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm" rel="nofollow noreferrer">Wikipedia Ford-Fulkerson algorithm page</a>, they present the Edmonds-Karp algorithm as the BFS (instead of DFS) varian... | time complexity network flow | 1 | Ford-Fulkerson vs Edmonds-Karp -- (time complexity network flow)
<p>I was reading about maximum flow algorithms comparing the efficiency of the different ones. On the <a href="https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm" rel="nofollow noreferrer">Wikipedia Ford-Fulkerson algorithm page</a>, they pres... | habedi/stack-exchange-dataset |
109,150 | Which other programming languages apart from Python and predecessor are out there using indentation to define code blocks? | 

<p><a href="https://www.python.org/" rel="noreferrer">Python</a> quite famously uses indentation to <em>syntactically</em> define blocks of code. (See <a href="https://docs.python.org/3/reference/compound_stmts.html" rel="noreferrer">Compound statements</a> in the Python Language Reference). After years of us... | programming languages python syntax | 1 | Which other programming languages apart from Python and predecessor are out there using indentation to define code blocks? -- (programming languages python syntax)


<p><a href="https://www.python.org/" rel="noreferrer">Python</a> quite famously uses indentation to <em>syntactically</em> define blocks of code. ... | habedi/stack-exchange-dataset |
109,153 | Could all CPU instructions get fundamentally faster if a better multiplication method was developed | <p>I was reading the article <a href="https://hal.archives-ouvertes.fr/hal-02070778/document" rel="nofollow noreferrer">Integer multiplication in time O(n log n)</a> by David Harvey and Joris Van Der Hoeven, 2019.</p>

<p>Could this discovery increase the throughput of future CPU's? If so could we determine by ... | algorithms cpu multiplication | 1 | Could all CPU instructions get fundamentally faster if a better multiplication method was developed -- (algorithms cpu multiplication)
<p>I was reading the article <a href="https://hal.archives-ouvertes.fr/hal-02070778/document" rel="nofollow noreferrer">Integer multiplication in time O(n log n)</a> by David Harvey and... | habedi/stack-exchange-dataset |
109,164 | Proving NP hardness in Puzzle with SAT reduction | <h2>Introduction</h2>

<p>I have created an algorithm that generates <em>n^2 x n^2</em> Sudoku Grids. Out of those grids I remove elements to give only one solution. The algorithm follows an infinite language based on <em>circular matrix shift</em> of elements. It does so in such a way that allows valid grids t... | algorithms np complete reductions | 1 | Proving NP hardness in Puzzle with SAT reduction -- (algorithms np complete reductions)
<h2>Introduction</h2>

<p>I have created an algorithm that generates <em>n^2 x n^2</em> Sudoku Grids. Out of those grids I remove elements to give only one solution. The algorithm follows an infinite language based on <em>ci... | habedi/stack-exchange-dataset |
109,166 | If P = NP, does SAT, or any other NP-Complete poly-reduce to any language different from $\emptyset$ or $\Sigma^*$? | <p>I looked at Sipser ("Introduction to the Theory of Computation"), Problem 7.17:</p>

<blockquote>
 <p>Prove that if P = NP, then every language in P, except <span class="math-container">$\emptyset$</span> and
 <span class="math-container">$\Sigma^*$</span>, is NP-Complete.</p>
</blockquote>
... | complexity theory reductions | 1 | If P = NP, does SAT, or any other NP-Complete poly-reduce to any language different from $\emptyset$ or $\Sigma^*$? -- (complexity theory reductions)
<p>I looked at Sipser ("Introduction to the Theory of Computation"), Problem 7.17:</p>

<blockquote>
 <p>Prove that if P = NP, then every language in P, exce... | habedi/stack-exchange-dataset |
109,188 | Connection between max independent set and graph coloring | <p>Is there any connection between the size of the largest independent set in a graph, and the minimum number of colors required to color the graph? I know that we can potentially color all the vertices in the largest independent set in the same color, but we know nothing about the rest of the vertices (besides being a... | graphs colorings | 1 | Connection between max independent set and graph coloring -- (graphs colorings)
<p>Is there any connection between the size of the largest independent set in a graph, and the minimum number of colors required to color the graph? I know that we can potentially color all the vertices in the largest independent set in the... | habedi/stack-exchange-dataset |
109,198 | Optimization of Church-encoded booleans in System F | <p>I can encode booleans in pure lambda calculus like this:</p>

<pre><code>type Bool = forall t. t -> t -> t 
true : Bool = \x y -> x
false : Bool = \x y -> y
</code></pre>

<p>Is there a procedure to optimize the following "dumb" function</p>

<pre><code>dumb = \(b : B... | lambda calculus | 1 | Optimization of Church-encoded booleans in System F -- (lambda calculus)
<p>I can encode booleans in pure lambda calculus like this:</p>

<pre><code>type Bool = forall t. t -> t -> t 
true : Bool = \x y -> x
false : Bool = \x y -> y
</code></pre>

<p>Is there a procedure to opti... | habedi/stack-exchange-dataset |
109,202 | Non consant size alphabet | <p>Sometimes I read that an algorithm works on constant size alphabet and it is clear for me but what means that an algorithm works with a non constant size alphabet? I would like to see an example.</p>
 | algorithms strings | 1 | Non consant size alphabet -- (algorithms strings)
<p>Sometimes I read that an algorithm works on constant size alphabet and it is clear for me but what means that an algorithm works with a non constant size alphabet? I would like to see an example.</p>
 | habedi/stack-exchange-dataset |
109,204 | Can the sorting of a list be verified without comparing neighbors? | <p>A <span class="math-container">$n$</span>-item list can be verified as sorted by comparing every item to its neighbor. In my application, I will not be able to compare <em>every</em> item with its neighbor: instead, the comparisons will sometimes be between distant elements. Given that the list contains more than th... | sorting | 1 | Can the sorting of a list be verified without comparing neighbors? -- (sorting)
<p>A <span class="math-container">$n$</span>-item list can be verified as sorted by comparing every item to its neighbor. In my application, I will not be able to compare <em>every</em> item with its neighbor: instead, the comparisons will ... | habedi/stack-exchange-dataset |
109,213 | NP hardness of unique Puzzle Generation | <h2>Introduction</h2>

<p>For those who did not read my prior question, I have created an algorithm that generates n^2 x n^2 Sudoku Grids. Out of those grids I remove elements to give only one solution. The algorithm follows an infinite language based on <em>circular matrix shift</em> of elements. It does so in... | np complete np decision problem | 1 | NP hardness of unique Puzzle Generation -- (np complete np decision problem)
<h2>Introduction</h2>

<p>For those who did not read my prior question, I have created an algorithm that generates n^2 x n^2 Sudoku Grids. Out of those grids I remove elements to give only one solution. The algorithm follows an infinit... | habedi/stack-exchange-dataset |
109,214 | How to prove a bound function for a sequence of numbers? | <p>Let <span class="math-container">$G_n$</span> be defined by</p>

<p><span class="math-container">$$G_n = \begin{cases} 1 & n=0 \\ 
2 & n = 1 \\ 
3 & n = 2 \\ 
4 & n = 3 \\
2G_{n-1}-2G_{n-3}+G_{n-4} & n\geq4
\end{cases}$$</span></p>

<p>How can I prove that <spa... | recurrence relation loop invariants | 1 | How to prove a bound function for a sequence of numbers? -- (recurrence relation loop invariants)
<p>Let <span class="math-container">$G_n$</span> be defined by</p>

<p><span class="math-container">$$G_n = \begin{cases} 1 & n=0 \\ 
2 & n = 1 \\ 
3 & n = 2 \\ 
4 & n = 3 \\
2G_{n-1... | habedi/stack-exchange-dataset |
109,216 | Calculating all products of $n-1$ factors when given $n$ factors | <p>Let's assume we have an operator
<span class="math-container">$$ \times: E^2\to E$$</span>
of which we merely know that it is associative. Let's say a multiplication <span class="math-container">$e\times f$</span> always takes up a time of <span class="math-container">$M$</span> for all <span class="math-con... | dynamic programming efficiency | 1 | Calculating all products of $n-1$ factors when given $n$ factors -- (dynamic programming efficiency)
<p>Let's assume we have an operator
<span class="math-container">$$ \times: E^2\to E$$</span>
of which we merely know that it is associative. Let's say a multiplication <span class="math-container">$e\times f$</... | habedi/stack-exchange-dataset |
109,218 | Reductions between LIS and LCS | <p>Given an oracle that returns both the length and the subsequence for the Longest Increasing Subsequence of a given input <span class="math-container">$A$</span> of <span class="math-container">$n$</span> elements <span class="math-container">$\text{LIS}(A,n)$</span>, can one use a polynomial number of calls to it to... | algorithms complexity theory reference request dynamic programming strings | 1 | Reductions between LIS and LCS -- (algorithms complexity theory reference request dynamic programming strings)
<p>Given an oracle that returns both the length and the subsequence for the Longest Increasing Subsequence of a given input <span class="math-container">$A$</span> of <span class="math-container">$n$</span> el... | habedi/stack-exchange-dataset |
109,221 | What is the time complexity of the following algorithm on graphs | <p>Consider undirected graph with <span class="math-container">$O(n)$</span> nodes and <span class="math-container">$O(m)$</span> edges. We store the edges in adjacent list, so for each node we keep list of the nodes such there exist edge between those nodes.</p>

<p>Our search goes as follows: For each node in... | time complexity | 1 | What is the time complexity of the following algorithm on graphs -- (time complexity)
<p>Consider undirected graph with <span class="math-container">$O(n)$</span> nodes and <span class="math-container">$O(m)$</span> edges. We store the edges in adjacent list, so for each node we keep list of the nodes such there exist ... | habedi/stack-exchange-dataset |
109,231 | Find plane within margin of error of >50% of points | <blockquote>
 <p>There are <span class="math-container">$N < 3\times10^4$</span> 3D points. At least 50% of them lie approximately in the same plane, i.e. the distance between the plane and each point is at most <span class="math-container">$p$</span>. Find such a plane.</p>
</blockquote>

<p><stron... | computational geometry data mining | 1 | Find plane within margin of error of >50% of points -- (computational geometry data mining)
<blockquote>
 <p>There are <span class="math-container">$N < 3\times10^4$</span> 3D points. At least 50% of them lie approximately in the same plane, i.e. the distance between the plane and each point is at most <span cl... | habedi/stack-exchange-dataset |
109,244 | Introduction To Algorithms 3rd Edition MIT Press: Red Black Tree insertion error in pseudo-code? | <p>I'm implementing the algorithm on page 316 of the book Introduction to Algorithms. When I look at the pseudo-code, I feel that there is something wrong between line 10 to 14. I feel it's missing a check. There is a YouTube video explaining this whole function (and it includes the pseudo-code plus line numbers): <a h... | data structures red black trees | 1 | Introduction To Algorithms 3rd Edition MIT Press: Red Black Tree insertion error in pseudo-code? -- (data structures red black trees)
<p>I'm implementing the algorithm on page 316 of the book Introduction to Algorithms. When I look at the pseudo-code, I feel that there is something wrong between line 10 to 14. I feel i... | habedi/stack-exchange-dataset |
109,247 | Asymptotics of a sinusoid | <p>Consider the function
<span class="math-container">$$
f(n) = 2n^2 |\sin(\pi \cdot n/2)|.
$$</span>
Which of the following classes does <span class="math-container">$f(n)$</span> belong to?
<span class="math-container">$$ O(n^2), \Omega(n^2), \Theta(n^2), \omega(n^2), o(n^2). $$</span></p>
&#x... | complexity theory asymptotics lower bounds upper bound | 1 | Asymptotics of a sinusoid -- (complexity theory asymptotics lower bounds upper bound)
<p>Consider the function
<span class="math-container">$$
f(n) = 2n^2 |\sin(\pi \cdot n/2)|.
$$</span>
Which of the following classes does <span class="math-container">$f(n)$</span> belong to?
<span class="math-cont... | habedi/stack-exchange-dataset |
109,256 | Can we find a computable function which cannot be calculated faster for any given time? | <p>Define <span class="math-container">$T\colon \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}$</span> by:</p>

<p><span class="math-container">$T(k,n) = 2^{T(k-1,n)}$</span></p>

<p><span class="math-container">$T(0,n) = 1$</span></p>

<p><span class="math-container">$T(1,n) = 2^n$</span><... | algorithms complexity theory time complexity | 1 | Can we find a computable function which cannot be calculated faster for any given time? -- (algorithms complexity theory time complexity)
<p>Define <span class="math-container">$T\colon \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}$</span> by:</p>

<p><span class="math-container">$T(k,n) = 2^{T(k-1,n)}$</... | habedi/stack-exchange-dataset |
109,262 | Shortest hamiltonian path for different dimension points | <p>The shortest Hamiltonian path (solution) for a set of points in <span class="math-container">$\mathbb{R}^k$</span> (in Euclidean space) changes subject to <span class="math-container">$k$</span>.</p>

<p>For example if for <span class="math-container">$k=1$</span>, the shortest Hamiltonian path will be the s... | np approximation hamiltonian path | 1 | Shortest hamiltonian path for different dimension points -- (np approximation hamiltonian path)
<p>The shortest Hamiltonian path (solution) for a set of points in <span class="math-container">$\mathbb{R}^k$</span> (in Euclidean space) changes subject to <span class="math-container">$k$</span>.</p>

<p>For examp... | habedi/stack-exchange-dataset |
109,263 | Non-deterministic Finite Automata | Sipser Example 1.16 | <p>I am working through the Sipser Book (2nd edition) and came across this example, which I do not understand. In the book it states that this NFA accepts the empty string, <span class="math-container">$\epsilon$</span>.</p>

<p>Could someone run me through why this is the case?</p>

<p>My understanding... | regular languages finite automata nondeterminism | 1 | Non-deterministic Finite Automata | Sipser Example 1.16 -- (regular languages finite automata nondeterminism)
<p>I am working through the Sipser Book (2nd edition) and came across this example, which I do not understand. In the book it states that this NFA accepts the empty string, <span class="math-container">$\epsilo... | habedi/stack-exchange-dataset |
109,285 | How is diagonalization a valid argument for the undecidability of the halting problem? | <p>All proofs for the undecidability of the halting problem seem to be based directly or indirectly on self-reference. </p>

<pre><code>def g():
 if halts(g):
 loop_forever()
</code></pre>

<p>My question is: how can the input of a TM contain the TM itself and its input? </p>
&... | turing machines | 1 | How is diagonalization a valid argument for the undecidability of the halting problem? -- (turing machines)
<p>All proofs for the undecidability of the halting problem seem to be based directly or indirectly on self-reference. </p>

<pre><code>def g():
 if halts(g):
 loop_forever()
</code>... | habedi/stack-exchange-dataset |
109,307 | NFA that accepts all numbers not divisible by 105 | <p>I have to create an NFA that accepts the following language L with no more than 15 states.</p>

<p><span class="math-container">$L = \{a^n \mid n \geq 1$</span> and <span class="math-container">$n \mod105 \neq 0 \}$</span>. </p>

<p>To me it seems that all multiples of 105 have the same properties:</... | finite automata | 1 | NFA that accepts all numbers not divisible by 105 -- (finite automata)
<p>I have to create an NFA that accepts the following language L with no more than 15 states.</p>

<p><span class="math-container">$L = \{a^n \mid n \geq 1$</span> and <span class="math-container">$n \mod105 \neq 0 \}$</span>. </p>

... | habedi/stack-exchange-dataset |
109,313 | Parametrized reduction from 3-SAT to Independent Set to lower bound running time under ETH assumption | <p>I want to prove that, assuming Exponential Time Hypothesis is true, there is no algorithm that solves Independent Set in <span class="math-container">$2^{o(|V|+|E|)}$</span> time. I want to apply the following strong parameterized many-one reduction <span class="math-container">$f$</span> from 3-Sat to Independent s... | complexity theory 3 sat parameterized complexity | 1 | Parametrized reduction from 3-SAT to Independent Set to lower bound running time under ETH assumption -- (complexity theory 3 sat parameterized complexity)
<p>I want to prove that, assuming Exponential Time Hypothesis is true, there is no algorithm that solves Independent Set in <span class="math-container">$2^{o(|V|+|... | habedi/stack-exchange-dataset |
109,315 | Understanding Correctness of Bidirectional Dijkstra | <p>I'm trying to understand the correctness of the bidirectional version of Dijkstras algorithm as mentioned here on slide 10: </p>

<p><a href="https://www.cs.princeton.edu/courses/archive/spr06/cos423/Handouts/EPP%20shortest%20path%20algorithms.pdf" rel="nofollow noreferrer">https://www.cs.princeton.edu/cours... | algorithms search algorithms correctness proof | 1 | Understanding Correctness of Bidirectional Dijkstra -- (algorithms search algorithms correctness proof)
<p>I'm trying to understand the correctness of the bidirectional version of Dijkstras algorithm as mentioned here on slide 10: </p>

<p><a href="https://www.cs.princeton.edu/courses/archive/spr06/cos423/Hando... | habedi/stack-exchange-dataset |
109,316 | I have trouble translating Turing machine language, can you help me break down language notation to English? | <p>My problem is I don't have many issues with creating a Turing machine state table when given a string such as 01101, my issue arises when I am presented with a problem which requires the Turing machine to recognize the language {0<sup>n</sup>1<sup>n</sup> | n ≥ 0}.</p>

<p>I have found this guide on a <a hre... | formal languages turing machines automata | 1 | I have trouble translating Turing machine language, can you help me break down language notation to English? -- (formal languages turing machines automata)
<p>My problem is I don't have many issues with creating a Turing machine state table when given a string such as 01101, my issue arises when I am presented with a p... | habedi/stack-exchange-dataset |
109,318 | Finding longest subset arithmetic progression with given difference | <p>Given a list of distinct positive integers, I am trying to find the largest subset that forms an arithmetic sequence with a given difference D.</p>

<p>For example, given D = 5, with the set of numbers 1, 5, 10, 6, 7, 8, 15, 11 the longest sequence would be 5, 10, 15</p>

<p>I have tried using sets t... | binary trees sets | 1 | Finding longest subset arithmetic progression with given difference -- (binary trees sets)
<p>Given a list of distinct positive integers, I am trying to find the largest subset that forms an arithmetic sequence with a given difference D.</p>

<p>For example, given D = 5, with the set of numbers 1, 5, 10, 6, 7, ... | habedi/stack-exchange-dataset |
109,320 | Distributed MST Construction in O(log log n) Rounds in a Clique | <p>I'm reading the paper <a href="http://ce.sharif.ac.ir/~ghodsi/archive/d-papers/SPAA/2003/MST%20construction%20in%20O(log%20log%20n)%20communication%20rounds.pdf" rel="nofollow noreferrer">MST Construction in O(log log n) Communication Rounds in a Clique</a> and trying to understand the correctness analysis, in page ... | algorithms graphs distributed systems minimum spanning tree clique | 1 | Distributed MST Construction in O(log log n) Rounds in a Clique -- (algorithms graphs distributed systems minimum spanning tree clique)
<p>I'm reading the paper <a href="http://ce.sharif.ac.ir/~ghodsi/archive/d-papers/SPAA/2003/MST%20construction%20in%20O(log%20log%20n)%20communication%20rounds.pdf" rel="nofollow noref... | habedi/stack-exchange-dataset |
109,326 | Assembly writer vs compiler in VLIW architecture | <p>I read this sentence in a book: </p>

<blockquote>
 <p>In VLIW architecture, the compiler/and or assembly writer chooses instructions that can be executed in parallel.</p>
</blockquote>

<p>What is the difference between assembly writer and compiler? Would an assembly writer also mean the sa... | compilers assembly | 1 | Assembly writer vs compiler in VLIW architecture -- (compilers assembly)
<p>I read this sentence in a book: </p>

<blockquote>
 <p>In VLIW architecture, the compiler/and or assembly writer chooses instructions that can be executed in parallel.</p>
</blockquote>

<p>What is the difference betwee... | habedi/stack-exchange-dataset |
109,330 | How to draw an LTS based on the parallel process "|" in CCS Milner's logic? | <p>I'm trying to provide a Hennessy-Milner logic formula for CCS expressions that are not (strongly) bisimilar. An example with a sketch: </p>

<blockquote>
 <p>For each of the following CCS expressions, decide whether they are strongly bisimilar and if no, find a distinguishing formula in Hennessy-Milner ... | formal languages logic ccs | 1 | How to draw an LTS based on the parallel process "|" in CCS Milner's logic? -- (formal languages logic ccs)
<p>I'm trying to provide a Hennessy-Milner logic formula for CCS expressions that are not (strongly) bisimilar. An example with a sketch: </p>

<blockquote>
 <p>For each of the following CCS expressi... | habedi/stack-exchange-dataset |
109,343 | What is the connection between the logic and the logic programming? | <p>As I understand, then logic (i.e. particular theory of logic with some theory's axioms and some possible assignments of the variables) describes some specific world (in the non-modal case) or some set of related worlds (in the modal case) and deduction just explores this one world (this set of related worlds) and di... | logic prolog | 1 | What is the connection between the logic and the logic programming? -- (logic prolog)
<p>As I understand, then logic (i.e. particular theory of logic with some theory's axioms and some possible assignments of the variables) describes some specific world (in the non-modal case) or some set of related worlds (in the moda... | habedi/stack-exchange-dataset |
109,347 | Clarification on interplay between cache line size and read/write sizes | <p>Say that you have cache lines with the size of 64 bytes and a set-associative or directly mapped cache. Let's also say that the word size is 8 bytes. </p>

<p>According to my understanding, we use a number of the most significant bits of a memory address in order to determine where in the cache to place the ... | memory management cpu cache memory access | 1 | Clarification on interplay between cache line size and read/write sizes -- (memory management cpu cache memory access)
<p>Say that you have cache lines with the size of 64 bytes and a set-associative or directly mapped cache. Let's also say that the word size is 8 bytes. </p>

<p>According to my understanding, ... | habedi/stack-exchange-dataset |
109,354 | What does "Kan" mean in "Kan operations"? | <p>I'm studying Cubical Type Theory and I see the word "Kan operations" (<a href="http://www.cs.cmu.edu/~rwh/talks/POPL18-Tutorial.pdf" rel="nofollow noreferrer">ref1</a>, <a href="https://github.com/RedPRL/redtt/issues/247" rel="nofollow noreferrer">ref2</a>, <a href="https://homotopytypetheory.org/2018/12/06/cubical-... | cubical type theory | 1 | What does "Kan" mean in "Kan operations"? -- (cubical type theory)
<p>I'm studying Cubical Type Theory and I see the word "Kan operations" (<a href="http://www.cs.cmu.edu/~rwh/talks/POPL18-Tutorial.pdf" rel="nofollow noreferrer">ref1</a>, <a href="https://github.com/RedPRL/redtt/issues/247" rel="nofollow noreferrer">re... | habedi/stack-exchange-dataset |
109,356 | How to find the number of intervals containing a point when given a static set of intervals? | <p>I've seen similar questions around here but I'm trying to address this problem with a slight change and maybe it makes it easier to solve. </p>

<p>I'm given a set of intervals <span class="math-container">$\{s_1,s_2,...,s_n\}$</span> where each interval has a starting point <span class="math-container">$b_i... | balanced search trees intervals | 1 | How to find the number of intervals containing a point when given a static set of intervals? -- (balanced search trees intervals)
<p>I've seen similar questions around here but I'm trying to address this problem with a slight change and maybe it makes it easier to solve. </p>

<p>I'm given a set of intervals <s... | habedi/stack-exchange-dataset |
109,357 | Is a "local" version of 3-SAT NP-hard? | <p>Below is my simplification of part of a larger research project on spatial Bayesian networks:</p>

<p>Say a variable is "<span class="math-container">$k$</span>-local" in a string <span class="math-container">$C \in 3\text{-CNF}$</span> if there are fewer than <span class="math-container">$k$</span> clauses ... | np hard satisfiability polynomial time 3 sat 2 sat | 1 | Is a "local" version of 3-SAT NP-hard? -- (np hard satisfiability polynomial time 3 sat 2 sat)
<p>Below is my simplification of part of a larger research project on spatial Bayesian networks:</p>

<p>Say a variable is "<span class="math-container">$k$</span>-local" in a string <span class="math-container">$C \i... | habedi/stack-exchange-dataset |
109,368 | Prior probability in HMM | <p><a href="https://i.stack.imgur.com/E3u45.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/E3u45.jpg" alt="HMM model"></a></p>

<p>This is the HMM model considered in the question
<a href="https://i.stack.imgur.com/XDGFn.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/... | machine learning probability theory hidden markov models | 1 | Prior probability in HMM -- (machine learning probability theory hidden markov models)
<p><a href="https://i.stack.imgur.com/E3u45.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/E3u45.jpg" alt="HMM model"></a></p>

<p>This is the HMM model considered in the question
<a href="https://i.st... | habedi/stack-exchange-dataset |
109,370 | Are "of the order of n" and "Big O" the same thing? | <p>I am learning from the MIT <a href="https://youtu.be/XNhOk80CeWo?t=1420" rel="nofollow noreferrer">course</a> Introduction to Algorithms.</p>

<p>The professor says:</p>

<blockquote>
 <p>Now, remember <span class="math-container">$\Theta(n)$</span> is essentially something
 that says "... | terminology asymptotics big o notation | 1 | Are "of the order of n" and "Big O" the same thing? -- (terminology asymptotics big o notation)
<p>I am learning from the MIT <a href="https://youtu.be/XNhOk80CeWo?t=1420" rel="nofollow noreferrer">course</a> Introduction to Algorithms.</p>

<p>The professor says:</p>

<blockquote>
 <p>Now, remembe... | habedi/stack-exchange-dataset |
109,371 | Number of ways of tiling a 3*N board with 2*1 dominoes problem | <p>I came across this problem,
 <a href="https://www.geeksforgeeks.org/tiling-with-dominoes/" rel="nofollow noreferrer">Tiling with Dominoes</a>
and initially I faced difficulty in understanding the logic behind recurrence relation, but after reading it from <a href="https://www.algorithmist.com/index.php/UVa_1... | algorithms data structures dynamic programming tiling | 1 | Number of ways of tiling a 3*N board with 2*1 dominoes problem -- (algorithms data structures dynamic programming tiling)
<p>I came across this problem,
 <a href="https://www.geeksforgeeks.org/tiling-with-dominoes/" rel="nofollow noreferrer">Tiling with Dominoes</a>
and initially I faced difficulty in understan... | habedi/stack-exchange-dataset |
109,380 | Reaching Shannon capacity of a channel | <p>Suppose I have the following from alphabet <span class="math-container">$\mathcal{X} = \{0 ,1\}$</span> to <span class="math-container">$\mathcal{Y} = \{0 ,1\}$</span>. The channel simply does</p>

<p><span class="math-container">\begin{align}
 0 \rightarrow 0&\quad \text{with probability 1} \\
... | information theory communication protocols | 1 | Reaching Shannon capacity of a channel -- (information theory communication protocols)
<p>Suppose I have the following from alphabet <span class="math-container">$\mathcal{X} = \{0 ,1\}$</span> to <span class="math-container">$\mathcal{Y} = \{0 ,1\}$</span>. The channel simply does</p>

<p><span class="math-con... | habedi/stack-exchange-dataset |
109,392 | How does casting really work for primitive data types? | <p>I have written the following C code which purpose it is to flip an <strong>unsigned</strong> number in binary representation and give back an <strong>unsigned</strong> number:</p>

<pre><code>long flippingBits(long n) {
 return (unsigned)(~n);
}

int main(){
 long a = flippingBits(s... | c | 1 | How does casting really work for primitive data types? -- (c)
<p>I have written the following C code which purpose it is to flip an <strong>unsigned</strong> number in binary representation and give back an <strong>unsigned</strong> number:</p>

<pre><code>long flippingBits(long n) {
 return (unsigned)(~... | habedi/stack-exchange-dataset |
109,398 | MSO (Monadic second-order logic) Logic On Words | <p>Let L be a language over <span class="math-container">$\Sigma = \{a,b,c\}$</span> that contains all words, where the length <span class="math-container">$|w|_b$</span> (number of all b's) has remainder 1 if divided by 3.</p>

<p>MSO logic over words are definded as follow:
<a href="https://i.stack.imgur.... | automata logic first order logic | 1 | MSO (Monadic second-order logic) Logic On Words -- (automata logic first order logic)
<p>Let L be a language over <span class="math-container">$\Sigma = \{a,b,c\}$</span> that contains all words, where the length <span class="math-container">$|w|_b$</span> (number of all b's) has remainder 1 if divided by 3.</p>
&#... | habedi/stack-exchange-dataset |
109,400 | Doubt in vertex connectivity less than edge connectivity | <p>Sir i recently started graph theory. I understood the reason why edge connectivity is less than min degree(remove all vertices incident to min degree vertex). I have doubt in 2nd part of proof when given graph is not complete graph. how to prove here vertex connectivity less than edge connectivity?
confused here... | graphs | 1 | Doubt in vertex connectivity less than edge connectivity -- (graphs)
<p>Sir i recently started graph theory. I understood the reason why edge connectivity is less than min degree(remove all vertices incident to min degree vertex). I have doubt in 2nd part of proof when given graph is not complete graph. how to prove he... | habedi/stack-exchange-dataset |
109,403 | 2-SAT reduction to Easy Puzzle Solving | <h2>Introduction</h2>

<p>I've been developing interest in complexity classes and thought I was unable to prove my problem is <em>NP hard</em>, so I wanted to see if it was <em>P-hard</em>. I wanted to see if my puzzle solving is special. <em>I have linked a previous question of mine to help clarify what is me... | complexity theory sudoku | 1 | 2-SAT reduction to Easy Puzzle Solving -- (complexity theory sudoku)
<h2>Introduction</h2>

<p>I've been developing interest in complexity classes and thought I was unable to prove my problem is <em>NP hard</em>, so I wanted to see if it was <em>P-hard</em>. I wanted to see if my puzzle solving is special. <em... | habedi/stack-exchange-dataset |
109,414 | Two questions on MSO | <p><strong>First question :</strong> </p>

<p>Is the following formula a valid MSO formula? </p>

<p><span class="math-container">$\theta(S, r) = \exists (e_1, t_1), ... ,(e_h, t_h) \bigwedge\limits_{(e_i, e_j) \in \rho(S,r)} \mathcal{R}((e_i, t_i), (e_j, t_j))$</span></p>

<p>So my main con... | logic | 1 | Two questions on MSO -- (logic)
<p><strong>First question :</strong> </p>

<p>Is the following formula a valid MSO formula? </p>

<p><span class="math-container">$\theta(S, r) = \exists (e_1, t_1), ... ,(e_h, t_h) \bigwedge\limits_{(e_i, e_j) \in \rho(S,r)} \mathcal{R}((e_i, t_i), (e_j, t_j))$</span... | habedi/stack-exchange-dataset |
109,419 | Suggest a Data Structure To Manage 2 Sets | <p>I was given the following problem which really baffled me, and I would like some guidance in solving it.</p>

<p>I want to make a data-structure which represents two sets <span class="math-container">$A,B\subseteq \mathbb{R}$</span>, so that I can Insert an element to a set of my choosing in <span class="mat... | data structures trees sets | 1 | Suggest a Data Structure To Manage 2 Sets -- (data structures trees sets)
<p>I was given the following problem which really baffled me, and I would like some guidance in solving it.</p>

<p>I want to make a data-structure which represents two sets <span class="math-container">$A,B\subseteq \mathbb{R}$</span>, s... | habedi/stack-exchange-dataset |
109,420 | How to approach analysis of randomized algorithm | <p>Let us suppose we have a sequence of values <span class="math-container">$C(i)$</span> that represent some counter for a given <span class="math-container">$i$</span> for <span class="math-container">$i \in \lbrace 1, \cdots, n \rbrace$</span>. Let us assume some uniform distribution <span class="math-container">$U$... | algorithms algorithm analysis probability theory randomized algorithms | 1 | How to approach analysis of randomized algorithm -- (algorithms algorithm analysis probability theory randomized algorithms)
<p>Let us suppose we have a sequence of values <span class="math-container">$C(i)$</span> that represent some counter for a given <span class="math-container">$i$</span> for <span class="math-con... | habedi/stack-exchange-dataset |
109,421 | Is the IO monad technically incorrect? | <p>On the haskell wiki there is the following example of conditional usage of the IO monad <a href="https://wiki.haskell.org/IO_inside#Welcome_to_the_RealWorld.2C_baby" rel="noreferrer">(see here)</a>.</p>

<pre><code>when :: Bool -> IO () -> IO ()
when condition action world =
 if condition&#x... | programming languages functional programming haskell | 1 | Is the IO monad technically incorrect? -- (programming languages functional programming haskell)
<p>On the haskell wiki there is the following example of conditional usage of the IO monad <a href="https://wiki.haskell.org/IO_inside#Welcome_to_the_RealWorld.2C_baby" rel="noreferrer">(see here)</a>.</p>

<pre><co... | habedi/stack-exchange-dataset |
109,426 | Orthogonal range reporting with fixed upper rectangular corner | <p>Consider the following special case of <a href="https://en.wikipedia.org/wiki/Range_searching#Orthogonal_range_searching" rel="nofollow noreferrer">orthogonal range searching</a>:</p>

<p>Given a set <span class="math-container">$S$</span> of <span class="math-container">$n$</span> points in <span class="mat... | algorithms data structures computational geometry | 1 | Orthogonal range reporting with fixed upper rectangular corner -- (algorithms data structures computational geometry)
<p>Consider the following special case of <a href="https://en.wikipedia.org/wiki/Range_searching#Orthogonal_range_searching" rel="nofollow noreferrer">orthogonal range searching</a>:</p>

<p>Giv... | habedi/stack-exchange-dataset |
109,430 | In instructions pipelining, why does register read/write take up only half clock cycle? | <p><br>
While studying instruction pipelining in MIPS processor, we make an assumption that registers read/write stages take only a half clock cycle, as this picture shows (half clock cycles are dotted in register operations):
<a href="https://i.stack.imgur.com/IsPaj.gif" rel="nofollow noreferrer"><img src="htt... | cpu pipelines mips | 1 | In instructions pipelining, why does register read/write take up only half clock cycle? -- (cpu pipelines mips)
<p><br>
While studying instruction pipelining in MIPS processor, we make an assumption that registers read/write stages take only a half clock cycle, as this picture shows (half clock cycles are dotted in... | habedi/stack-exchange-dataset |
109,432 | Uniqueness of minimum spanning tree | <p>If G has a unique minimum spanning tree, does that mean the edge weights in G are also unique? if yes why and if no why?</p>
 | graphs weighted graphs minimum spanning tree | 1 | Uniqueness of minimum spanning tree -- (graphs weighted graphs minimum spanning tree)
<p>If G has a unique minimum spanning tree, does that mean the edge weights in G are also unique? if yes why and if no why?</p>
 | habedi/stack-exchange-dataset |
109,438 | Why anyone learn compiler? | <p>I am learning compiler in my Uni. I have been through all major compiler techniques like top-down parsing, bottom-up parsing, Lexical analyzer, Symbol table, etc. I have a good understanding of them, but I am still confused about the course. </p>

<p>What is the point of learning all these things? What are t... | compilers | 1 | Why anyone learn compiler? -- (compilers)
<p>I am learning compiler in my Uni. I have been through all major compiler techniques like top-down parsing, bottom-up parsing, Lexical analyzer, Symbol table, etc. I have a good understanding of them, but I am still confused about the course. </p>

<p>What is the poin... | habedi/stack-exchange-dataset |
109,442 | Is there purely recursive functions? | <p>Is there any problem that can be only solved with recursion, and not with iteration? (haven't been able to find anything online).</p>

<p>If there isn't any, is there a reason why?</p>

<p>Thanks in advance!</p>
 | recursion | 1 | Is there purely recursive functions? -- (recursion)
<p>Is there any problem that can be only solved with recursion, and not with iteration? (haven't been able to find anything online).</p>

<p>If there isn't any, is there a reason why?</p>

<p>Thanks in advance!</p>
 | habedi/stack-exchange-dataset |
109,451 | Solving using the master theorem: T(n)=T(n/2)+n⋅log n and T(n)=T(n/8)+2.n | <p>Could someone help me with these 2 questions?</p>

<p>I do not understand the case 3</p>

<ol>
<li><p><span class="math-container">$T(n) = T(n/2) + n \log n$</span></p></li>
<li><p><span class="math-container">$T(n)=T(n/8)+2 n$</span></p></li>
</ol>
 | algorithms master theorem | 1 | Solving using the master theorem: T(n)=T(n/2)+n⋅log n and T(n)=T(n/8)+2.n -- (algorithms master theorem)
<p>Could someone help me with these 2 questions?</p>

<p>I do not understand the case 3</p>

<ol>
<li><p><span class="math-container">$T(n) = T(n/2) + n \log n$</span></p></li>
<li><p><span c... | habedi/stack-exchange-dataset |
109,458 | Quick sort worst case complexity improvement | <p>Can the worst case time complexity of quick sort be changed from <span class="math-container">$O(n^2)$</span> to <span class="math-container">$O(n\log n)$</span> by modifying it?</p>
 | time complexity sorting quicksort | 1 | Quick sort worst case complexity improvement -- (time complexity sorting quicksort)
<p>Can the worst case time complexity of quick sort be changed from <span class="math-container">$O(n^2)$</span> to <span class="math-container">$O(n\log n)$</span> by modifying it?</p>
 | habedi/stack-exchange-dataset |
109,461 | What does "bounded above" mean in Family of Bachmann–Landau notations? | <p>Per <a href="https://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachmann%E2%80%93Landau_notations" rel="nofollow noreferrer">wiki</a> </p>

<blockquote>
 <p>|f| is bounded above by g (up to constant factor) asymptotically</p>
</blockquote>

<p>with this concrete example,</p>

<p>... | algorithms terminology asymptotics big o notation | 1 | What does "bounded above" mean in Family of Bachmann–Landau notations? -- (algorithms terminology asymptotics big o notation)
<p>Per <a href="https://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachmann%E2%80%93Landau_notations" rel="nofollow noreferrer">wiki</a> </p>

<blockquote>
 <p>|f| is bounded ab... | habedi/stack-exchange-dataset |
109,469 | If a problem Q is NP complete, is another problem reducible to Q also NP complete? | <p>Let's say <span class="math-container">$\mathcal{P}$</span> is a yes/no prolem with an existing reduction to the problem <span class="math-container">$\mathcal{Q}$</span> (with time complexity <span class="math-container">$\mathcal{O}(n^2)$</span>). <span class="math-container">$\mathcal{Q}$</span> is NP complete. D... | complexity theory np complete reductions | 1 | If a problem Q is NP complete, is another problem reducible to Q also NP complete? -- (complexity theory np complete reductions)
<p>Let's say <span class="math-container">$\mathcal{P}$</span> is a yes/no prolem with an existing reduction to the problem <span class="math-container">$\mathcal{Q}$</span> (with time comple... | habedi/stack-exchange-dataset |
109,470 | Creating a CFG from a specific CFL | <p>I am pretty desperate finding the correct context free grammar for the following language:
<span class="math-container">$$L=\{a^lb^mc^n \mid l,m,n \in \mathbb{N}_0, \, l\geq 2n+m\}$$</span></p>

<p>I would really appreciate if anyone could tell me how to generate the CFG from this language as I am stuck ... | context free | 1 | Creating a CFG from a specific CFL -- (context free)
<p>I am pretty desperate finding the correct context free grammar for the following language:
<span class="math-container">$$L=\{a^lb^mc^n \mid l,m,n \in \mathbb{N}_0, \, l\geq 2n+m\}$$</span></p>

<p>I would really appreciate if anyone could tell me how ... | habedi/stack-exchange-dataset |
109,481 | Single-source shortest paths with even weight | <p>I need help to find an algorithm that calculates the single-source shortest paths in a graph, with an extra condition that the weight of the path has to be even.
In another words, we have to find the shortest way with the minimum even weight.</p>

<p>I'd like to have some ideas how we solve this.</p>
... | algorithms graphs shortest path weighted graphs | 1 | Single-source shortest paths with even weight -- (algorithms graphs shortest path weighted graphs)
<p>I need help to find an algorithm that calculates the single-source shortest paths in a graph, with an extra condition that the weight of the path has to be even.
In another words, we have to find the shortest way w... | habedi/stack-exchange-dataset |
109,493 | First time visited nodes form a spanning tree that has a same number of edges in both BFS and DFS | <p>I am trying to state, whether the statement is true: During a DFS/BFS, first time visited nodes form a spanning tree, that has the same number of edges whether you use DFS or BFS. Is it true? </p>

<p>What I tried was to do both DFS and BFS on a couple of graph and the spanning tree I got was the same each t... | graphs spanning trees | 1 | First time visited nodes form a spanning tree that has a same number of edges in both BFS and DFS -- (graphs spanning trees)
<p>I am trying to state, whether the statement is true: During a DFS/BFS, first time visited nodes form a spanning tree, that has the same number of edges whether you use DFS or BFS. Is it true? ... | habedi/stack-exchange-dataset |
109,503 | Running time for Breadth-First-Search vs Depth-First-Search | <p>Can someone explain why BFS is <span class="math-container">$O(V + E)$</span> whereas DFS is <span class="math-container">$\Theta(V + E)$</span>.
I understand the definitions of both notations, but I just don't see why the bound for DFS should be tighter than that of BFS.</p>

<p>Is it because DFS is gua... | algorithms time complexity runtime analysis | 1 | Running time for Breadth-First-Search vs Depth-First-Search -- (algorithms time complexity runtime analysis)
<p>Can someone explain why BFS is <span class="math-container">$O(V + E)$</span> whereas DFS is <span class="math-container">$\Theta(V + E)$</span>.
I understand the definitions of both notations, but I just... | habedi/stack-exchange-dataset |
109,505 | Bellman-Ford - is number of interations greater than diameter? | <blockquote>
 <p>Diameter of a connected, undirected graph is the smallest natural
 number <em>d</em>, so that between any two vertices of the graph exist path
 of length at most <em>d</em>.</p>
 
 <p>Prove or disprove: in Bellman-Ford is the number of iterations always
 equal or lower tha... | graphs shortest path | 1 | Bellman-Ford - is number of interations greater than diameter? -- (graphs shortest path)
<blockquote>
 <p>Diameter of a connected, undirected graph is the smallest natural
 number <em>d</em>, so that between any two vertices of the graph exist path
 of length at most <em>d</em>.</p>
 
 <p>Prove... | habedi/stack-exchange-dataset |
109,510 | How to prove the emptiness of intersection of two context free languages is undecidable? | <p>Where can I find a proof that the emptiness problem for the intersection of two context free languages is undecidable? I searched on the internet but could not find anything helpful.</p>

<p>Do you maybe have a book or paper I should investigate?</p>
 | formal languages context free reference request undecidability | 1 | How to prove the emptiness of intersection of two context free languages is undecidable? -- (formal languages context free reference request undecidability)
<p>Where can I find a proof that the emptiness problem for the intersection of two context free languages is undecidable? I searched on the internet but could not ... | habedi/stack-exchange-dataset |
109,524 | DFA for a language that accepts the addition of multiple of 2 and multiple of 5 | <p>I am trying to draw a DFA that accepts the following language:</p>

<p><span class="math-container">$L=\{a^{2i+5j} : i , j \geq 0\}$</span></p>

<p>I started out by drawing an NFA, which I can then convert to a DFA but I am not sure if my NFA is correct.</p>

<p><a href="https://i.stack.imgur... | finite automata | 1 | DFA for a language that accepts the addition of multiple of 2 and multiple of 5 -- (finite automata)
<p>I am trying to draw a DFA that accepts the following language:</p>

<p><span class="math-container">$L=\{a^{2i+5j} : i , j \geq 0\}$</span></p>

<p>I started out by drawing an NFA, which I can then co... | habedi/stack-exchange-dataset |
109,527 | Linear programming IFF with equality constrain | <p>Is it possible to write the following logical constrain in linear programming? </p>

<p>Let <span class="math-container">$v$</span> be an integer variable and <span class="math-container">$k$</span> an integer constant. Let <span class="math-container">$y$</span> be a binary variable. The logical constraint ... | optimization linear programming integer programming mathematical programming | 1 | Linear programming IFF with equality constrain -- (optimization linear programming integer programming mathematical programming)
<p>Is it possible to write the following logical constrain in linear programming? </p>

<p>Let <span class="math-container">$v$</span> be an integer variable and <span class="math-con... | habedi/stack-exchange-dataset |
109,537 | Shortest Path in Layerwise Complete Graph | <p>Consider a directed <span class="math-container">$k$</span> partite graph <span class="math-container">$G$</span> with a source node <span class="math-container">$s$</span> and a sink node <span class="math-container">$t$</span>. Each vertex in the graph is labeled with a positive integer value. Both the source and ... | algorithms data structures search algorithms shortest path | 1 | Shortest Path in Layerwise Complete Graph -- (algorithms data structures search algorithms shortest path)
<p>Consider a directed <span class="math-container">$k$</span> partite graph <span class="math-container">$G$</span> with a source node <span class="math-container">$s$</span> and a sink node <span class="math-cont... | habedi/stack-exchange-dataset |
109,540 | Translation of diagnosis problem to SAT | <p>I have the following diagnosis problem:<br>
h(A): z1 = not(in1)<br>
h(D): z2 = not(in2)<br>
h(B): z3 = z1 or z2<br>
h(C): out1 = not(z3)<br>
h(E): out2 = not(z3)</p>

<p>This is an image of the system:<br>
<a href="https://i.stack.imgur.com/ngiVc.png" rel="nofollow noreferrer"><img sr... | logic satisfiability sat solvers | 1 | Translation of diagnosis problem to SAT -- (logic satisfiability sat solvers)
<p>I have the following diagnosis problem:<br>
h(A): z1 = not(in1)<br>
h(D): z2 = not(in2)<br>
h(B): z3 = z1 or z2<br>
h(C): out1 = not(z3)<br>
h(E): out2 = not(z3)</p>

<p>This is an image of the system:<br>
<... | habedi/stack-exchange-dataset |
109,546 | Determining the number of walks between two vertices in a graph | <blockquote>
 <blockquote>
 <p>Given a graph G and a set of vertices <span class="math-container">$(v_1, v_2)$</span>.</p>
 </blockquote>
</blockquote>

<p>How can you determine whether there is <span class="math-container">$\textit{one}$</span> unique walk between <span class="math-contain... | graphs | 1 | Determining the number of walks between two vertices in a graph -- (graphs)
<blockquote>
 <blockquote>
 <p>Given a graph G and a set of vertices <span class="math-container">$(v_1, v_2)$</span>.</p>
 </blockquote>
</blockquote>

<p>How can you determine whether there is <span class="math-co... | habedi/stack-exchange-dataset |
109,550 | Copying items in arrays while checking their indexes | <blockquote>
 <p>Array <span class="math-container">$P$</span> of length <span class="math-container">$n$</span> is a permutations of <span class="math-container">$\{0, ..., n-1\}$</span> </p>
 
 <p>Write a code, which would in <span class="math-container">$O(n)$</span> create an array <span class="math-... | time complexity arrays | 1 | Copying items in arrays while checking their indexes -- (time complexity arrays)
<blockquote>
 <p>Array <span class="math-container">$P$</span> of length <span class="math-container">$n$</span> is a permutations of <span class="math-container">$\{0, ..., n-1\}$</span> </p>
 
 <p>Write a code, which would... | habedi/stack-exchange-dataset |
109,551 | Is $L = \{ \langle \langle \ M\ \rangle \rangle \ | \ M \ \text{does not accept}\ 010 \} $ Turing recognizeable? | <p>I'm working on the following problem:</p>

<blockquote>
 <p>Is the following language Turing recognizable (recursively enumerable)
 ? </p>
 
 <p><span class="math-container">$$L = \{ \langle \langle \ M\ \rangle \rangle \ | \ M \ \text{does not
> accept}\ 010 \} $$</span></p>
<... | turing machines undecidability | 1 | Is $L = \{ \langle \langle \ M\ \rangle \rangle \ | \ M \ \text{does not accept}\ 010 \} $ Turing recognizeable? -- (turing machines undecidability)
<p>I'm working on the following problem:</p>

<blockquote>
 <p>Is the following language Turing recognizable (recursively enumerable)
 ? </p>
 
... | habedi/stack-exchange-dataset |
109,562 | Efficiently deciding whether TM accepts all inputs in at most $k$ steps | <p>I want to decide if a deterministic TM <span class="math-container">$A=(Q, \varGamma, \delta, q_s, q_h)$</span> halts on every input in at most <span class="math-container">$k$</span> steps. If the TM <span class="math-container">$A$</span> stops after <span class="math-container">$k$</span> steps, then the positio... | turing machines finite automata | 1 | Efficiently deciding whether TM accepts all inputs in at most $k$ steps -- (turing machines finite automata)
<p>I want to decide if a deterministic TM <span class="math-container">$A=(Q, \varGamma, \delta, q_s, q_h)$</span> halts on every input in at most <span class="math-container">$k$</span> steps. If the TM <span c... | habedi/stack-exchange-dataset |
109,567 | Efficient Algorithms for Destroyed Document Reconstruction | <p>I am not certain this is the proper site for this question however I am mainly looking for resources on this topic (perhaps code). I was watching TV and one of the characters had a lawyer who destroyed his documents using a paper shredder. A lab tech said that the shredder was special. </p>

<p>I am not fami... | image processing | 1 | Efficient Algorithms for Destroyed Document Reconstruction -- (image processing)
<p>I am not certain this is the proper site for this question however I am mainly looking for resources on this topic (perhaps code). I was watching TV and one of the characters had a lawyer who destroyed his documents using a paper shredd... | habedi/stack-exchange-dataset |
109,581 | Spanning trees on disconnected graphs | <p>Can anyone please help me out with my query: can disconnected graphs have minimum spanning trees?</p>
 | graphs minimum spanning tree | 1 | Spanning trees on disconnected graphs -- (graphs minimum spanning tree)
<p>Can anyone please help me out with my query: can disconnected graphs have minimum spanning trees?</p>
 | habedi/stack-exchange-dataset |
109,599 | Does |xy| ≤ p in the pumping lemma count for all i? | <p>While learning about the pumping lemma, I came across the following question:</p>

<p>Given the language L is <span class="math-container">$ a^n(0|1)^* $</span> with <span class="math-container">$ c_0 \cdot c_1 = n $</span>, where <span class="math-container">$ c_0 $</span> indicates the amount of zeros pres... | formal languages regular languages pumping lemma | 1 | Does |xy| ≤ p in the pumping lemma count for all i? -- (formal languages regular languages pumping lemma)
<p>While learning about the pumping lemma, I came across the following question:</p>

<p>Given the language L is <span class="math-container">$ a^n(0|1)^* $</span> with <span class="math-container">$ c_0 \c... | habedi/stack-exchange-dataset |
109,606 | context-free grammar for comma-separated list with comments | <p>I'm trying to write a context-free grammar for a comma-separated list of statements with comments. It is trivial if the comma appears at the end of a statement. It is trivial if the comment is ignored. But I don't know how to include a comma in the middle of a statement (before the comment).</p>

<p>This ... | context free formal grammars compilers parsers | 1 | context-free grammar for comma-separated list with comments -- (context free formal grammars compilers parsers)
<p>I'm trying to write a context-free grammar for a comma-separated list of statements with comments. It is trivial if the comma appears at the end of a statement. It is trivial if the comment is ignored. ... | habedi/stack-exchange-dataset |
109,607 | Time complexity of an algorithm: Is it important to state the base of the logarithm? | <p>Since there is only a constant between bases of logarithms, isn't it just alright to write <span class="math-container">$f(n) = \Omega(\log{n})$</span>, as opposed to <span class="math-container">$\Omega(\log_2{n})$</span>, or whatever the base might be?</p>
 | algorithms time complexity | 1 | Time complexity of an algorithm: Is it important to state the base of the logarithm? -- (algorithms time complexity)
<p>Since there is only a constant between bases of logarithms, isn't it just alright to write <span class="math-container">$f(n) = \Omega(\log{n})$</span>, as opposed to <span class="math-container">$\Om... | habedi/stack-exchange-dataset |
109,611 | Reliability of a service | <p>Assume that I need to determine the reliability of a service. The service includes component <strong>a</strong> (software reliability=0.95) and component <strong>b</strong> (software reliability=0.98). I have 2 computers: Computer <strong>A</strong> (hardware reliability=0.99) and Computer <strong>B</strong> (hardwa... | software engineering reliability | 1 | Reliability of a service -- (software engineering reliability)
<p>Assume that I need to determine the reliability of a service. The service includes component <strong>a</strong> (software reliability=0.95) and component <strong>b</strong> (software reliability=0.98). I have 2 computers: Computer <strong>A</strong> (har... | habedi/stack-exchange-dataset |
109,618 | How Fibonacci LFSR work | <p>What is "Fibonacci" about the <a href="https://en.wikipedia.org/wiki/Linear-feedback_shift_register#Fibonacci_LFSRs" rel="nofollow noreferrer">Fibonacci LFSR</a>?
If I read right, Fibonacci LFSR means that it depends on its two last states, but from the example in Wikipedia it doesn't look like two states are ta... | pseudo random generators | 1 | How Fibonacci LFSR work -- (pseudo random generators)
<p>What is "Fibonacci" about the <a href="https://en.wikipedia.org/wiki/Linear-feedback_shift_register#Fibonacci_LFSRs" rel="nofollow noreferrer">Fibonacci LFSR</a>?
If I read right, Fibonacci LFSR means that it depends on its two last states, but from the examp... | habedi/stack-exchange-dataset |
109,622 | What is the closed-form expression for $T_n = \left(\sum_{i=1}^{n-1}7 T_i\right) + 1$ where $T_1 = 1 ?$ | <p><strong>Problem:</strong></p>

<blockquote>
 <p>Find the closed-form expression for<span class="math-container">$$
T_n = \left(\sum_{i=1}^{n-1}7 T_i\right) + 1
\tag{1}
$$</span>where <span class="math-container">$T_1 = 1 .$</span></p>
</blockquote>

<p>Calculating this sum I came... | recurrence relation recursion | 1 | What is the closed-form expression for $T_n = \left(\sum_{i=1}^{n-1}7 T_i\right) + 1$ where $T_1 = 1 ?$ -- (recurrence relation recursion)
<p><strong>Problem:</strong></p>

<blockquote>
 <p>Find the closed-form expression for<span class="math-container">$$
T_n = \left(\sum_{i=1}^{n-1}7 T_i\right) + 1&#... | habedi/stack-exchange-dataset |
109,624 | Closure properties of a non-regular language under complement? | <ul>
<li>Assume I have L1 which is a regular language, so we know since regular language is closed under complement, the complement of L1 is also a regular language.</li>
<li>But let's say if the complement of L1 is a non-regular language, is it safe to conclude that L1 is a non-regular language as well?</li>&#... | formal languages regular languages pumping lemma | 1 | Closure properties of a non-regular language under complement? -- (formal languages regular languages pumping lemma)
<ul>
<li>Assume I have L1 which is a regular language, so we know since regular language is closed under complement, the complement of L1 is also a regular language.</li>
<li>But let's say if the... | habedi/stack-exchange-dataset |
109,629 | Proof emptiness for PDA is $\mathcal{O}(n^3)$ | <p>It is well known that the emptiness problem vor PDAs is in <span class="math-container">$\mathcal{O}(n^3)$</span>. I couldn't find a good paper proving this theorem. Furthermore a proof for VPAs would be fine for me as well if that is easier.</p>

<p>Do you maybe have a book or paper I should investigate?</p... | formal languages reference request pushdown automata | 1 | Proof emptiness for PDA is $\mathcal{O}(n^3)$ -- (formal languages reference request pushdown automata)
<p>It is well known that the emptiness problem vor PDAs is in <span class="math-container">$\mathcal{O}(n^3)$</span>. I couldn't find a good paper proving this theorem. Furthermore a proof for VPAs would be fine for ... | habedi/stack-exchange-dataset |
109,634 | Reduce 4-SAT to 5-SAT | <p>given is a reduction from 4-SAT to 5-SAT.
How is it possible to describe such a function? 
I found some informations about reduction 3-SAT to 4-SAT <a href="https://cs.stackexchange.com/questions/92888/to-prove-4-sat-cnf-is-np-complete">here</a>, but it can't help me so much. </p>
 | time complexity np complete np hard satisfiability polynomial time | 1 | Reduce 4-SAT to 5-SAT -- (time complexity np complete np hard satisfiability polynomial time)
<p>given is a reduction from 4-SAT to 5-SAT.
How is it possible to describe such a function? 
I found some informations about reduction 3-SAT to 4-SAT <a href="https://cs.stackexchange.com/questions/92888/to-prove-4-sa... | habedi/stack-exchange-dataset |
109,640 | Turing recognizable language between languages that aren't recognizable? | <p>Let <span class="math-container">$L_{1},L_{2}$</span> be languages that are not Turing recognizable, and let <span class="math-container">$L$</span> be a language such that <span class="math-container">$L_{1} \subseteq L \subseteq L_{2}$</span>. </p>

<p>Is <span class="math-container">$L$</span> also not Tu... | turing machines | 1 | Turing recognizable language between languages that aren't recognizable? -- (turing machines)
<p>Let <span class="math-container">$L_{1},L_{2}$</span> be languages that are not Turing recognizable, and let <span class="math-container">$L$</span> be a language such that <span class="math-container">$L_{1} \subseteq L \s... | habedi/stack-exchange-dataset |
109,646 | Is it reasonable to consider a book's table of contents as a hierarchical collection? if yes, what does the root node represent? | <p>this book "Fundamentals of Python: Data Structures 1st Edition" says</p>

<blockquote>
 <p>data items in hierarchical collections are ordered in a structure
 resembling an upside-down tree. Each data item except the one at the
 top has just one predecessor
 ...
 A file directory syst... | data structures | 1 | Is it reasonable to consider a book's table of contents as a hierarchical collection? if yes, what does the root node represent? -- (data structures)
<p>this book "Fundamentals of Python: Data Structures 1st Edition" says</p>

<blockquote>
 <p>data items in hierarchical collections are ordered in a structu... | habedi/stack-exchange-dataset |
109,647 | AVL Tree - Print ascending using in-order | <p>Trying to understand how to write proof of correctness.
Searched over the internet on how to write proof of correctness but can't find a good solution for it.</p>

<p>The following sorting algorithm is proposed using the AVL tree: AVL input of all elements, and printing them in order.</p>

<p><st... | data structures sorting avl trees | 1 | AVL Tree - Print ascending using in-order -- (data structures sorting avl trees)
<p>Trying to understand how to write proof of correctness.
Searched over the internet on how to write proof of correctness but can't find a good solution for it.</p>

<p>The following sorting algorithm is proposed using the AVL... | habedi/stack-exchange-dataset |
109,648 | Guided Backpropagation in Deep Neural Networks | <p>I am reading about a method called guided backpropagation. 
<a href="https://ramprs.github.io/2017/01/21/Grad-CAM-Making-Off-the-Shelf-Deep-Models-Transparent-through-Visual-Explanations.html#deconv-and-guided-backprop" rel="nofollow noreferrer">https://ramprs.github.io/2017/01/21/Grad-CAM-Making-Off-the-Shelf-D... | neural networks | 1 | Guided Backpropagation in Deep Neural Networks -- (neural networks)
<p>I am reading about a method called guided backpropagation. 
<a href="https://ramprs.github.io/2017/01/21/Grad-CAM-Making-Off-the-Shelf-Deep-Models-Transparent-through-Visual-Explanations.html#deconv-and-guided-backprop" rel="nofollow noreferrer"... | habedi/stack-exchange-dataset |
109,662 | Divide two strings to form palindrome | <p>Given two strings, A and B, of the same length <span class="math-container">$n$</span>, find whether it is possible to cut both strings at a common point such that the first part of A and the second part of B form a palindrome.</p>

<p>I've tried bruteforce, and this can be achieved in <span class="math-cont... | algorithms strings | 1 | Divide two strings to form palindrome -- (algorithms strings)
<p>Given two strings, A and B, of the same length <span class="math-container">$n$</span>, find whether it is possible to cut both strings at a common point such that the first part of A and the second part of B form a palindrome.</p>

<p>I've tried ... | habedi/stack-exchange-dataset |
109,665 | What is an array that can be iterated circularly an infinite amount of times called? | <p>I have a feeling that the answer is either a "circular linked list" or a finite state machine, but the answer is probably a circular linked list.</p>
 | arrays loops lists | 1 | What is an array that can be iterated circularly an infinite amount of times called? -- (arrays loops lists)
<p>I have a feeling that the answer is either a "circular linked list" or a finite state machine, but the answer is probably a circular linked list.</p>
 | habedi/stack-exchange-dataset |
109,668 | Matrix covering by squares | <p>I wonder about the following decision problem :</p>

<p>Instance: We consider a <span class="math-container">$n\times p$</span> matrix <span class="math-container">$M$</span> of zeros and ones, and two integers <span class="math-container">$N$</span> and <span class="math-container">$k$</span>.</p>

... | complexity theory np complete np matrices | 1 | Matrix covering by squares -- (complexity theory np complete np matrices)
<p>I wonder about the following decision problem :</p>

<p>Instance: We consider a <span class="math-container">$n\times p$</span> matrix <span class="math-container">$M$</span> of zeros and ones, and two integers <span class="math-contai... | habedi/stack-exchange-dataset |
109,670 | In which reference can I find a definition for the equivalence of DFAs? | <p>How is the equivalence of DFA defined? I found the equivalence of states --- James Hein, section 5.3, page 301. But he doesn't define equivalence between entire automata. (Ullman and Hopcropft seem to define neither.)</p>
 | finite automata reference request | 1 | In which reference can I find a definition for the equivalence of DFAs? -- (finite automata reference request)
<p>How is the equivalence of DFA defined? I found the equivalence of states --- James Hein, section 5.3, page 301. But he doesn't define equivalence between entire automata. (Ullman and Hopcropft seem to de... | habedi/stack-exchange-dataset |
109,682 | Minimize number of DFS searches in a graph | <p>I got a weird homework question about graph.</p>

<p>A helicopter is going to land on an island to check the n houses after an earthquake. Some of the two-way roads connecting the houses are destroyed however the helicopter won't know beforehand. Once the the helicopter lands on a house u, they can drive to ... | algorithms graphs graph traversal | 1 | Minimize number of DFS searches in a graph -- (algorithms graphs graph traversal)
<p>I got a weird homework question about graph.</p>

<p>A helicopter is going to land on an island to check the n houses after an earthquake. Some of the two-way roads connecting the houses are destroyed however the helicopter won... | habedi/stack-exchange-dataset |
109,691 | Quicksort where element comparison outcome is random. Probability of element being in a certain position | <p>So we have this block of pseudocode:</p>

<pre><code>Monsters = [M1,M2,M3,M4,M5,M6,M7,M8];
qsort(Monsters,rand_compare);
</code></pre>

<blockquote>
 <p><code>qsort()</code> sorts the array via quicksort where we use the last element
 as pivot. To compare two elements it uses <code>... | sorting probability theory quicksort | 1 | Quicksort where element comparison outcome is random. Probability of element being in a certain position -- (sorting probability theory quicksort)
<p>So we have this block of pseudocode:</p>

<pre><code>Monsters = [M1,M2,M3,M4,M5,M6,M7,M8];
qsort(Monsters,rand_compare);
</code></pre>

<blockquot... | habedi/stack-exchange-dataset |
109,697 | Karp-Rabin - what is the input for the worst case time complexity? | <p>I'm trying to determine the input for the worst case time complexity of Karb-Rabin regardless of the used hash function. However, I'm seeing both of these answers on the Internet:</p>

<ul>
<li><p>String "AAAAAAAA" and pattern "AAA"</p></li>
<li><p>String "AAAAAAAB" and pattern "AAB"</p></li>
</u... | time complexity runtime analysis search algorithms | 1 | Karp-Rabin - what is the input for the worst case time complexity? -- (time complexity runtime analysis search algorithms)
<p>I'm trying to determine the input for the worst case time complexity of Karb-Rabin regardless of the used hash function. However, I'm seeing both of these answers on the Internet:</p>

<... | habedi/stack-exchange-dataset |
109,707 | Subset with modified condition, is it still NP-complete? | <p>So I know the conditions required for a problem to be NP-Complete is that it has to lie within NP and has to be NP-hard. </p>

<p>The given problem I have is subset sum. </p>

<p>However, the conditions have been change to sum ≤ M and sum ≥ M from sum = M. To be more specific: </p>

<ol>
... | np complete np hard decision problem | 1 | Subset with modified condition, is it still NP-complete? -- (np complete np hard decision problem)
<p>So I know the conditions required for a problem to be NP-Complete is that it has to lie within NP and has to be NP-hard. </p>

<p>The given problem I have is subset sum. </p>

<p>However, the conditions... | habedi/stack-exchange-dataset |
109,708 | Algorithm for factoring elements of permutation groups? | <p>You can solve a Rubik's cube by factoring its permutation into a sequence of "elementary" permutations (a subset of permutations that is sufficient to construct every other permutation in the group). There are several algorithms for solving Rubik's cubes. Are there any algorithms for the general problem of factoring... | algorithms permutations group theory | 1 | Algorithm for factoring elements of permutation groups? -- (algorithms permutations group theory)
<p>You can solve a Rubik's cube by factoring its permutation into a sequence of "elementary" permutations (a subset of permutations that is sufficient to construct every other permutation in the group). There are several a... | habedi/stack-exchange-dataset |
109,711 | R-tree insertion procedure when leaf is full | <p>I am implementing an R-tree with the quadratic splitting method. </p>

<p>However in most articles I have read there a piece of information that is missing or misleading (or the most probably case, I completely misunderstood something).</p>

<p>R-trees are supposed to be balanced, yet you need to fin... | search trees | 1 | R-tree insertion procedure when leaf is full -- (search trees)
<p>I am implementing an R-tree with the quadratic splitting method. </p>

<p>However in most articles I have read there a piece of information that is missing or misleading (or the most probably case, I completely misunderstood something).</p>
&... | habedi/stack-exchange-dataset |
109,714 | Can all regular tree types be expressed as $\mu$ types? | <p>In "Types and Programming Languages", Pierce gives a translation from recursive types (<span class="math-container">$\mu$</span> types) to types expressed as regular trees: possibly infinite trees, but with finitely many distinct subtrees.</p>

<p>I'm wondering, is the converse true? Can every regular tree t... | programming languages lambda calculus type theory tree automata | 1 | Can all regular tree types be expressed as $\mu$ types? -- (programming languages lambda calculus type theory tree automata)
<p>In "Types and Programming Languages", Pierce gives a translation from recursive types (<span class="math-container">$\mu$</span> types) to types expressed as regular trees: possibly infinite t... | habedi/stack-exchange-dataset |
109,723 | Prove disprove an existence of mapping reduction between 2 sets | <p>I am currently studying mapping reduction in computational theory and finding it hard to grasp the concept fully. </p>

<p>For reference, consider the following given WHILE-Prog sets:</p>

<p>A = { (p.d) | p doesn't halt on input d } = Complementary HALT set.
B = { p | p halts on exactly one inpu... | complexity theory reductions | 1 | Prove disprove an existence of mapping reduction between 2 sets -- (complexity theory reductions)
<p>I am currently studying mapping reduction in computational theory and finding it hard to grasp the concept fully. </p>

<p>For reference, consider the following given WHILE-Prog sets:</p>

<p>A = { (p.d)... | habedi/stack-exchange-dataset |
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