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 |
|---|---|---|---|---|---|---|
77,364 | Searching a sorted array to find the $k$ closest values to a target value $T$ | <p>Let $A$ be a sorted array of $N$ values. I am interested in finding the index $j$ such that the elements $A_j, A_{j + 1}, ..., A_{j + k - 1}$ have the $k$ closest values to the given target value $T$. Assume that $k$ is comparable, in magnitude, to $N$; i.e. we <em>don't</em> have $k \ll N$.</p>

<p>One can ... | algorithms search algorithms binary search nearest neighbour | 1 | Searching a sorted array to find the $k$ closest values to a target value $T$ -- (algorithms search algorithms binary search nearest neighbour)
<p>Let $A$ be a sorted array of $N$ values. I am interested in finding the index $j$ such that the elements $A_j, A_{j + 1}, ..., A_{j + k - 1}$ have the $k$ closest values to ... | habedi/stack-exchange-dataset |
77,365 | How can I understand if reduction is Karp reduction? | <p>I have a reduction and can't understand if it is Karp reduction. I want understand if my reduction is Karp reduction as well as understand how to determine which one is so.</p>

<p>Let I have formula $\Phi = (l_{1,1}\lor l_{1,2}\lor...\lor l_{1,k_1})\land(l_{2,1}\lor...\lor l_{2,k_2})\land...\land(l_{n,1}\lo... | reductions | 1 | How can I understand if reduction is Karp reduction? -- (reductions)
<p>I have a reduction and can't understand if it is Karp reduction. I want understand if my reduction is Karp reduction as well as understand how to determine which one is so.</p>

<p>Let I have formula $\Phi = (l_{1,1}\lor l_{1,2}\lor...\lor ... | habedi/stack-exchange-dataset |
77,368 | Why do we try to maximize Lagrangian in SVMs? | <p>I was learning about support vector machines from MIT OpenCourseWare. I figured it out. I understand why we try to minimize $\frac{1}{2} w^2$. I just did not get why we try to maximize Lagrange expression like said at 35:56 in the <a href="https://www.youtube.com/watch?v=_PwhiWxHK8o" rel="noreferrer">YouTube video</... | optimization machine learning os kernel svm | 1 | Why do we try to maximize Lagrangian in SVMs? -- (optimization machine learning os kernel svm)
<p>I was learning about support vector machines from MIT OpenCourseWare. I figured it out. I understand why we try to minimize $\frac{1}{2} w^2$. I just did not get why we try to maximize Lagrange expression like said at 35:5... | habedi/stack-exchange-dataset |
77,376 | Space complexity of Chomsky Normal Form | <p>I'm trying to find sup of $\|\mathbb{G}\|$ where $\mathbb{G}$ is CFG in Chomsky Normal Form. So far i have done some work, but I'm really not sure in my proof. Let $G = \langle Q, N, S, R\rangle$ and
$$\alpha \rightarrow \beta \in R,\ |\beta| = n$$
$$\|\alpha\| \le \sum_{i=0}^{\log_{2}n}2^{n}\,.$$
I made... | formal languages context free | 1 | Space complexity of Chomsky Normal Form -- (formal languages context free)
<p>I'm trying to find sup of $\|\mathbb{G}\|$ where $\mathbb{G}$ is CFG in Chomsky Normal Form. So far i have done some work, but I'm really not sure in my proof. Let $G = \langle Q, N, S, R\rangle$ and
$$\alpha \rightarrow \beta \in R,\ |\b... | habedi/stack-exchange-dataset |
77,385 | Is there a faster algorithm for constructing the adjacency list of this graph? | <p>My problem is to find a better algorithm to fill the adjacency list.</p>

<p>specs:</p>

<pre><code>G = (V , E ) //the graph
V ={w} //vertex in this case each vertex is an array 
E={⟨u,v⟩| u,v ∈V ∧ u>v} // edge only if u > v
u > v only if foreach i u̸=v ∧ u[i]≥v[i]. // (u>... | algorithms complexity theory graphs | 1 | Is there a faster algorithm for constructing the adjacency list of this graph? -- (algorithms complexity theory graphs)
<p>My problem is to find a better algorithm to fill the adjacency list.</p>

<p>specs:</p>

<pre><code>G = (V , E ) //the graph
V ={w} //vertex in this case each vertex is an array... | habedi/stack-exchange-dataset |
77,389 | How to express modalities in lambda calculus - are some extensions required? | <p>Lambda calculus can be used for encoding semantics of natural language, e.g. <a href="http://yoavartzi.com/tutorial/" rel="nofollow noreferrer">http://yoavartzi.com/tutorial/</a> contains full details about semantic parsing of natural language: converting natural language texts into lambda expressions - Cornell Sema... | formal grammars lambda calculus semantics natural language processing modal logic | 1 | How to express modalities in lambda calculus - are some extensions required? -- (formal grammars lambda calculus semantics natural language processing modal logic)
<p>Lambda calculus can be used for encoding semantics of natural language, e.g. <a href="http://yoavartzi.com/tutorial/" rel="nofollow noreferrer">http://yo... | habedi/stack-exchange-dataset |
77,407 | CCS synchronization | <p>Within CSS we talk about binary interactions. Does this prevent synchronizing multiple processes in one step? Example:</p>

<p>$P_1 ::= a.D$</p>

<p>$P_2 ::= \overline{a}.D$</p>

<p>$P_3 ::= a.D$</p>

<p>Let's consider the following LTS: $(P_1 | P_2 | P_3)\restriction_a$</p>

... | transition systems ccs | 1 | CCS synchronization -- (transition systems ccs)
<p>Within CSS we talk about binary interactions. Does this prevent synchronizing multiple processes in one step? Example:</p>

<p>$P_1 ::= a.D$</p>

<p>$P_2 ::= \overline{a}.D$</p>

<p>$P_3 ::= a.D$</p>

<p>Let's consider the following LTS:... | habedi/stack-exchange-dataset |
77,413 | Which are the cases where the "pumping lemma" doesn't work? | <p>Are there some languages not regular and/or not context-free in which the proof by contradiction fails? Why we need a "more specific" version of pumping lemma?</p>
 | formal languages pumping lemma | 1 | Which are the cases where the "pumping lemma" doesn't work? -- (formal languages pumping lemma)
<p>Are there some languages not regular and/or not context-free in which the proof by contradiction fails? Why we need a "more specific" version of pumping lemma?</p>
 | habedi/stack-exchange-dataset |
77,419 | Prove that given a number we can find whether there're 2 elements in a red/black tree that their sum equals that number in $\Theta(n)$ time | <blockquote>
 <p>Prove that given a number we can find whether there're 2 elements in a red/black tree that their sum equals that number in $\Theta(n)$ time and <strong>constant</strong> space.</p>
</blockquote>

<p>The original problem appears <a href="http://www.geeksforgeeks.org/find-a-pair-with-giv... | algorithms trees balanced search trees | 1 | Prove that given a number we can find whether there're 2 elements in a red/black tree that their sum equals that number in $\Theta(n)$ time -- (algorithms trees balanced search trees)
<blockquote>
 <p>Prove that given a number we can find whether there're 2 elements in a red/black tree that their sum equals that n... | habedi/stack-exchange-dataset |
77,422 | Trouble understanding the master theorem, from Jeffrey Erickson's Notes | <p>I'm looking at <a href="http://jeffe.cs.illinois.edu/teaching/algorithms/notes/99-recurrences.pdf" rel="nofollow noreferrer">Jeffrey Erickson's Notes on the master theorem</a>
(page 10).</p>

<p>Part (b) of the theorem states that if $T(n) = aT(\frac{n}{b})+f(n)$, $af(\frac{n}{b}) = kf(n)$ and $k>1$ t... | recurrence relation | 1 | Trouble understanding the master theorem, from Jeffrey Erickson's Notes -- (recurrence relation)
<p>I'm looking at <a href="http://jeffe.cs.illinois.edu/teaching/algorithms/notes/99-recurrences.pdf" rel="nofollow noreferrer">Jeffrey Erickson's Notes on the master theorem</a>
(page 10).</p>

<p>Part (b) of t... | habedi/stack-exchange-dataset |
77,425 | Relevance of memory reads while calculating the time complexity of an algorithm | <p>Can there be a genuine algorithm in which number of memory reads far outnumber the 
no. of operations performed? For example, number of memory reads scale with n^2, while no. of operations scale with only n, where n is the input size.</p>

<p>If yes, then how will one decide the time complexity in such a... | algorithms algorithm analysis data structures asymptotics memory access | 1 | Relevance of memory reads while calculating the time complexity of an algorithm -- (algorithms algorithm analysis data structures asymptotics memory access)
<p>Can there be a genuine algorithm in which number of memory reads far outnumber the 
no. of operations performed? For example, number of memory reads scale w... | habedi/stack-exchange-dataset |
77,428 | What exactly is bigO notation? | <p>I've heard of bigO notation but I don't really understand how do I determine it for my code and what exactly does it represent?
I heard that there are two:</p>

<ol>
<li>RunTime</li>
<li>Memory Complexity</li>
</ol>

<p>How can I learn to use it?</p>
 | complexity theory asymptotics | 1 | What exactly is bigO notation? -- (complexity theory asymptotics)
<p>I've heard of bigO notation but I don't really understand how do I determine it for my code and what exactly does it represent?
I heard that there are two:</p>

<ol>
<li>RunTime</li>
<li>Memory Complexity</li>
</ol>

<p... | habedi/stack-exchange-dataset |
77,435 | Why don't these 2 algorithms take the same time to detect duplicate lines in a file? | <p>I'm trying to write a small algorithm to detect and delete duplicate lines inside a subset of consecutive lines in a file.
I've come up with 2 similar solutions.
After some quick tests, I've noticed that one of them is much faster than the other, especially on large files.
But I don't understand why.</p>... | time complexity | 1 | Why don't these 2 algorithms take the same time to detect duplicate lines in a file? -- (time complexity)
<p>I'm trying to write a small algorithm to detect and delete duplicate lines inside a subset of consecutive lines in a file.
I've come up with 2 similar solutions.
After some quick tests, I've noticed that... | habedi/stack-exchange-dataset |
77,437 | Problems understanding the Union functionality of the Union-Find Algorithm | <p>I am currently doing a course based on algorithms (Coursera). I've come across an algorithm called quick find. The course does have reference to Big O Notation. Despite the fact that I do not have much knowledge of Big O, I have been doing some basic <a href="https://rob-bell.net/2009/06/a-beginners-guide-to-big-o-n... | algorithms asymptotics union find | 1 | Problems understanding the Union functionality of the Union-Find Algorithm -- (algorithms asymptotics union find)
<p>I am currently doing a course based on algorithms (Coursera). I've come across an algorithm called quick find. The course does have reference to Big O Notation. Despite the fact that I do not have much k... | habedi/stack-exchange-dataset |
77,441 | Can parameters other than $n$ be always ignored in big $O$ notation? | <p>The Bentley–Ottmann algorithm, for example, has time complexity of $O((n + k) \log n)$. Is the statement $O((n + k) \log n) = O(n \log n)$ true? I know that $k$ is there because it has big enough of an impact on the overall time complexity that it's relevant to include it. But can it be ignored, so that the pr... | algorithm analysis asymptotics landau notation | 1 | Can parameters other than $n$ be always ignored in big $O$ notation? -- (algorithm analysis asymptotics landau notation)
<p>The Bentley–Ottmann algorithm, for example, has time complexity of $O((n + k) \log n)$. Is the statement $O((n + k) \log n) = O(n \log n)$ true? I know that $k$ is there because it has big e... | habedi/stack-exchange-dataset |
77,448 | Constructing Turing Machine for division with 8 | <p>Can someone help me to construct a Turing Machine for this function:</p>

<p>$f(n) = \frac{n}{8}$. If $n \mod 8 = 0$, then
$f(n)$ is undefined.</p>

<p>So the machine should somehow first prove if the number (which is represented in binary) is divisible by $8$ . That means for numbers like $1000$... | turing machines | 1 | Constructing Turing Machine for division with 8 -- (turing machines)
<p>Can someone help me to construct a Turing Machine for this function:</p>

<p>$f(n) = \frac{n}{8}$. If $n \mod 8 = 0$, then
$f(n)$ is undefined.</p>

<p>So the machine should somehow first prove if the number (which is represente... | habedi/stack-exchange-dataset |
77,449 | the maximum value for which combination of merge sort and insertion sort works more efficiently than standard merge sort? | <p>I'm totally new in algorithms and I have a hard time studying how to calculate the time complexity of algorithms.</p>

<p>I'm studying <strong><em>Introduction to Algorithms, by Cormen</em></strong> on my own. Iam doing an exercise and I faced a problem that I couldn't solved it. first, the book asks for <em... | algorithms algorithm analysis time complexity | 1 | the maximum value for which combination of merge sort and insertion sort works more efficiently than standard merge sort? -- (algorithms algorithm analysis time complexity)
<p>I'm totally new in algorithms and I have a hard time studying how to calculate the time complexity of algorithms.</p>

<p>I'm studying <... | habedi/stack-exchange-dataset |
77,450 | Logic, "and" operator between a set of formulas and a formula | <p>Consider a set $S$ of formulas $\beta_i$ and a formula $\alpha$, if we have a condition such as <strong>$S \land \alpha$ is inconsistent</strong> what we have to calculate to check the inconsistency of $S \land \alpha$? In other words, what is the result of $S \land \alpha$? </p>

<p>For example, $S=\{\beta_... | logic sets propositional logic | 1 | Logic, "and" operator between a set of formulas and a formula -- (logic sets propositional logic)
<p>Consider a set $S$ of formulas $\beta_i$ and a formula $\alpha$, if we have a condition such as <strong>$S \land \alpha$ is inconsistent</strong> what we have to calculate to check the inconsistency of $S \land \alpha$?... | habedi/stack-exchange-dataset |
77,461 | MSTs in Christofides Algorithm | <p>I am implementing the Christofides algorithm for TSP problem and currently I have one issue with the MST result. Let's assume that I have one graph $G$, whereas I can get $MST_1$ and $MST_2$ where both are Minimum Spanning Trees, because $G$ contains more than one edge with the same weight.</p>

<p>In image ... | graphs traveling salesman minimum spanning tree | 1 | MSTs in Christofides Algorithm -- (graphs traveling salesman minimum spanning tree)
<p>I am implementing the Christofides algorithm for TSP problem and currently I have one issue with the MST result. Let's assume that I have one graph $G$, whereas I can get $MST_1$ and $MST_2$ where both are Minimum Spanning Trees, bec... | habedi/stack-exchange-dataset |
77,470 | Is this restricted promise-3SAT version coNPComplete? | <p>Given a $3SAT$ problem the decision version of the problem (if it has a solution or not) is $NPComplete$. Now, given that we consider the promise version of the $3SAT$ problem, the promise is every $3SAT$ problem provided always has at least 1 solution.</p>

<p><strong>Query</strong>: Does every solution of ... | complexity theory np complete | 1 | Is this restricted promise-3SAT version coNPComplete? -- (complexity theory np complete)
<p>Given a $3SAT$ problem the decision version of the problem (if it has a solution or not) is $NPComplete$. Now, given that we consider the promise version of the $3SAT$ problem, the promise is every $3SAT$ problem provided always... | habedi/stack-exchange-dataset |
77,471 | For any non-trivial $A,B$, finding a language which both are polynomially reducible to | <blockquote>
<p>Given two non-trivial (not <span class="math-container">$\emptyset$</span> or <span class="math-container">$\Sigma^*$</span>) languages <span class="math-container">$A$</span>, <span class="math-container">$B$</span> over an alphabet <span class="math-container">$\Sigma$</span>, which of the followi... | complexity theory time complexity reductions polynomial time | 1 | For any non-trivial $A,B$, finding a language which both are polynomially reducible to -- (complexity theory time complexity reductions polynomial time)
<blockquote>
<p>Given two non-trivial (not <span class="math-container">$\emptyset$</span> or <span class="math-container">$\Sigma^*$</span>) languages <span class... | habedi/stack-exchange-dataset |
77,473 | What is the complexity of Hamming nearest neighbor to a subspace ...? | <p>Suppose that $F_2$ denotes the field with $2$ elements. We are given $m$ vectors $\{x_1, \ldots, x_m\}$ in $F_2^d$ which are a basis for a subspace $W$. </p>

<p>Suppose we have a vector $v \in F_q^m$, and we want to find a $w \in W$ that is closest to $v$ in the Hamming metric.</p>

<p>What is the c... | complexity theory time complexity coding theory | 1 | What is the complexity of Hamming nearest neighbor to a subspace ...? -- (complexity theory time complexity coding theory)
<p>Suppose that $F_2$ denotes the field with $2$ elements. We are given $m$ vectors $\{x_1, \ldots, x_m\}$ in $F_2^d$ which are a basis for a subspace $W$. </p>

<p>Suppose we have a vector... | habedi/stack-exchange-dataset |
77,484 | If M is recognizing L in polynomial time, is it also deciding it in polynomial time? | <blockquote>
 <p>Assume that a given turing machine $M$ accepts words in the language
 in $n^k$ or less steps, but words that aren't in the language
 are rejected in unknown number of steps (the machine might even loop).</p>
 
 <p>$k$ is unknown.</p>
 
 <p>Is $L(M)\in P$?</p>
</bl... | turing machines time complexity decision problem polynomial time | 1 | If M is recognizing L in polynomial time, is it also deciding it in polynomial time? -- (turing machines time complexity decision problem polynomial time)
<blockquote>
 <p>Assume that a given turing machine $M$ accepts words in the language
 in $n^k$ or less steps, but words that aren't in the language
 ... | habedi/stack-exchange-dataset |
77,487 | Decidable properties of computable reals | <p>Is "Rice's theorem for the computable reals" -- that is, no nontrivial property of the number represented by a given computable real is decidable -- true?</p>

<p>Does this correspond in some direct way to the connectedness of the reals?</p>
 | computability real numbers computable analysis | 1 | Decidable properties of computable reals -- (computability real numbers computable analysis)
<p>Is "Rice's theorem for the computable reals" -- that is, no nontrivial property of the number represented by a given computable real is decidable -- true?</p>

<p>Does this correspond in some direct way to the connec... | habedi/stack-exchange-dataset |
77,512 | Minimum number of intersections to arrive at specific set | <p>Say I have a large number of sets (on the order of ~1000) with a smaller number of potential entries (~200), and a widely varying number of entries per set. An example:</p>

<p>$s_1 = \{1, 42, 133\}$</p>

<p>$s_2 = \{27, 283, 292, 172, 66, 62\}$</p>

<p>$s_3 = \{1, 42, 292, 66\}$</p>

... | sets | 1 | Minimum number of intersections to arrive at specific set -- (sets)
<p>Say I have a large number of sets (on the order of ~1000) with a smaller number of potential entries (~200), and a widely varying number of entries per set. An example:</p>

<p>$s_1 = \{1, 42, 133\}$</p>

<p>$s_2 = \{27, 283, 292, 17... | habedi/stack-exchange-dataset |
77,513 | Solving consensus for a known number of processes | <p>I was given an object with exactly 2 operations <code>test-and-reset</code> that sets the value of the object to 0 only if it was previously set to 1 and does not return a value and <code>fetch-and-add(v)</code> which adds <code>v</code> to the value of the object and returns the previous value.</p>

<p>I am... | concurrency consensus | 1 | Solving consensus for a known number of processes -- (concurrency consensus)
<p>I was given an object with exactly 2 operations <code>test-and-reset</code> that sets the value of the object to 0 only if it was previously set to 1 and does not return a value and <code>fetch-and-add(v)</code> which adds <code>v</code> to... | habedi/stack-exchange-dataset |
77,517 | CFL Closure Properties prove or disprove for the following languages | <p>I have following statements which I must prove or disprove :</p>

<p>1) Let $L$ be a CFL and $k \in N$ then $L^k$ is also a CFL.<br>
2) $L_1 \subseteq L_2 \subseteq L_3$ are Languages, if $L_1$ and $L_3$ are DCFL, then $L_2$ is also a DCFL</p>

<p>The first one I have no idea how to start or whe... | formal languages context free closure properties | 1 | CFL Closure Properties prove or disprove for the following languages -- (formal languages context free closure properties)
<p>I have following statements which I must prove or disprove :</p>

<p>1) Let $L$ be a CFL and $k \in N$ then $L^k$ is also a CFL.<br>
2) $L_1 \subseteq L_2 \subseteq L_3$ are Languag... | habedi/stack-exchange-dataset |
77,518 | Is the complement of MAX-CLIQUE in NP? | <blockquote>
<p>Let <span class="math-container">$$MAX-CLIQUE = \{\ <G,k>\ |\ G\ is\ an\ undirected\ graph,\ and\ the\ largest\ clique\ of\ G\ has\ k\ vertices\}$$</span></p>
<ol>
<li>Does <span class="math-container">$MAX-CLIQUE\in coNP$</span>? If it does, can you think of a verifier?</li>
<li>I... | turing machines time complexity decision problem polynomial time p vs np | 1 | Is the complement of MAX-CLIQUE in NP? -- (turing machines time complexity decision problem polynomial time p vs np)
<blockquote>
<p>Let <span class="math-container">$$MAX-CLIQUE = \{\ <G,k>\ |\ G\ is\ an\ undirected\ graph,\ and\ the\ largest\ clique\ of\ G\ has\ k\ vertices\}$$</span></p>
<ol>
<li>D... | habedi/stack-exchange-dataset |
77,532 | What does it mean that HDLs "explicitly include the notion of time"? | <p>I got onto the topic of HDLs (Hardware Description Languages) from a <a href="https://cs.stackexchange.com/questions/539/visual-programming-languages#comment2020_545">comment elsewhere on this site</a>.</p>

<p>The <a href="https://en.wikipedia.org/wiki/Hardware_description_language" rel="nofollow noreferrer... | programming languages real time | 1 | What does it mean that HDLs "explicitly include the notion of time"? -- (programming languages real time)
<p>I got onto the topic of HDLs (Hardware Description Languages) from a <a href="https://cs.stackexchange.com/questions/539/visual-programming-languages#comment2020_545">comment elsewhere on this site</a>.</p>
... | habedi/stack-exchange-dataset |
77,534 | Complexity of $FP^{NP}$ | <p>what is the complexity of $FP^{NP}$ w.r.t. $FPSPACE$?</p>

<p>Also can someone please provide a few examples of Problems complete for $FP^{NP}$? If possible let the examples be natural.</p>
 | complexity theory | 1 | Complexity of $FP^{NP}$ -- (complexity theory)
<p>what is the complexity of $FP^{NP}$ w.r.t. $FPSPACE$?</p>

<p>Also can someone please provide a few examples of Problems complete for $FP^{NP}$? If possible let the examples be natural.</p>
 | habedi/stack-exchange-dataset |
77,547 | Give one example where it takes Non- deterministically exponential time to solve the problem? | <p>I am a starter in complexity theory though I have fair knowledge in Turing machine. I know what it means to be non-deterministically polynomial time solvable but I am trying to understand where the time goes beyond polynomial time even using non-deterministic concept. Is it possible or we can do everything in polyno... | complexity theory time complexity np | 1 | Give one example where it takes Non- deterministically exponential time to solve the problem? -- (complexity theory time complexity np)
<p>I am a starter in complexity theory though I have fair knowledge in Turing machine. I know what it means to be non-deterministically polynomial time solvable but I am trying to unde... | habedi/stack-exchange-dataset |
77,555 | Algorithm which finds the maxmal solution that satisfies the following constraints | <p>I have $a_1, a_2,\dots,a_n$ and $b_1,b_2,\dots,b_n$ and an upper bound $U$ and $n$ linear equations of the form:</p>

<p>$k_1 * a_1 + b_1 = x$</p>

<p>$k_2 * a_2 + b_2 = x$</p>

<p>$\dots$</p>

<p>$k_n * a_n + b_n = x$</p>

<p>Additional info where $r \in \{ 1,2,\dots , n \}$:... | algorithms number theory mathematical programming primes | 1 | Algorithm which finds the maxmal solution that satisfies the following constraints -- (algorithms number theory mathematical programming primes)
<p>I have $a_1, a_2,\dots,a_n$ and $b_1,b_2,\dots,b_n$ and an upper bound $U$ and $n$ linear equations of the form:</p>

<p>$k_1 * a_1 + b_1 = x$</p>

<p>$k_2 ... | habedi/stack-exchange-dataset |
77,556 | Classes of outer totalistic cellular automata | <p>I'm wondering if anyone knows of any place where the Wolfram classifications of many outer totalistic cellular automata have been catalogued. The classes of a few examples are given in <em>A New Kind of Science</em>, famously that of Rule 224 (Life) or more simply ones like Rule 0 which kills all of the cells. I'm w... | cellular automata data sets | 1 | Classes of outer totalistic cellular automata -- (cellular automata data sets)
<p>I'm wondering if anyone knows of any place where the Wolfram classifications of many outer totalistic cellular automata have been catalogued. The classes of a few examples are given in <em>A New Kind of Science</em>, famously that of Rule... | habedi/stack-exchange-dataset |
77,564 | How large would a database containing perfect knowledge of chess be? | <p>Assuming that a database entry schema contains two 64-bit hash IDs generated via the algorithm explained <a href="https://www.gamedev.net/articles/programming/artificial-intelligence/chess-programming-part-ii-data-structures-r1046" rel="nofollow noreferrer">here, in the section "Generating Hash Keys for Chess Boards... | data structures space complexity database theory databases space analysis | 1 | How large would a database containing perfect knowledge of chess be? -- (data structures space complexity database theory databases space analysis)
<p>Assuming that a database entry schema contains two 64-bit hash IDs generated via the algorithm explained <a href="https://www.gamedev.net/articles/programming/artificial... | habedi/stack-exchange-dataset |
77,570 | What is the reasoning behind magic constancs in hash code calculations found in programming practice? | <p>In real-world programming, we frequently need to compute hash codes for complicated objects. The main desired properties are that the values should </p>

<ul>
<li>be deterministic and</li>
<li>have few collisions.</li>
</ul>

<p>Let's assume we have access to robust hashing for basic data... | data structures hash | 1 | What is the reasoning behind magic constancs in hash code calculations found in programming practice? -- (data structures hash)
<p>In real-world programming, we frequently need to compute hash codes for complicated objects. The main desired properties are that the values should </p>

<ul>
<li>be determinist... | habedi/stack-exchange-dataset |
77,573 | Lower bound of degree of polynomial approximating parity | <p>Let $\text{MOD}_2 : \{0,1\}^n \rightarrow \{0,1\}$ be a parity function where $$\text{MOD}_2(x_1,\dots,x_n) = \sum_i x_i \bmod 2$$</p>

<p>It is known [See e.g. Lemma 5 of <a href="http://theory.stanford.edu/~trevisan/cs254-14/lecture11.pdf" rel="nofollow noreferrer">this lecture note</a>] that any polynomia... | complexity theory circuits lower bounds polynomials | 1 | Lower bound of degree of polynomial approximating parity -- (complexity theory circuits lower bounds polynomials)
<p>Let $\text{MOD}_2 : \{0,1\}^n \rightarrow \{0,1\}$ be a parity function where $$\text{MOD}_2(x_1,\dots,x_n) = \sum_i x_i \bmod 2$$</p>

<p>It is known [See e.g. Lemma 5 of <a href="http://theory.... | habedi/stack-exchange-dataset |
77,575 | Set cover problem with sets of size 2 | <p>I have a question about the Set Cover problem: If I get a universe $U$, and $m$ subsets of size exactly $2$, and an integer $k$. Is this problem is still NP-C or I can solve it on a polynomial time?</p>

<p>Thanks.</p>
 | np complete set cover | 1 | Set cover problem with sets of size 2 -- (np complete set cover)
<p>I have a question about the Set Cover problem: If I get a universe $U$, and $m$ subsets of size exactly $2$, and an integer $k$. Is this problem is still NP-C or I can solve it on a polynomial time?</p>

<p>Thanks.</p>
 | habedi/stack-exchange-dataset |
77,589 | What does it mean the norm symbol applied to a concept? | <p>I'm reading this paper:
<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.14" rel="nofollow noreferrer">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.14</a>
or
<a href="http://www.jmlr.org/papers/volume10/kontorovich09a/kontorovich09a.pdf" rel="nofollow noreferrer">http:/... | formal languages automata regular languages notation learning theory | 1 | What does it mean the norm symbol applied to a concept? -- (formal languages automata regular languages notation learning theory)
<p>I'm reading this paper:
<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.14" rel="nofollow noreferrer">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.... | habedi/stack-exchange-dataset |
77,593 | Where have I gone wrong in "proving" this big-O identity? | <p>(From CLRS -- 3-4,d)</p>

<p>Let $f(n)$ and $g(n)$ be asymptotically positive functions.</p>

<p>I tried to prove that $$f(n) = O(g(n)) \implies 2^{f(n)} = O\left(2^{g(n)}\right) .$$</p>

<p>I know that the above statement is false, so where have I gone wrong in my proof?:</p>

<block... | asymptotics | 1 | Where have I gone wrong in "proving" this big-O identity? -- (asymptotics)
<p>(From CLRS -- 3-4,d)</p>

<p>Let $f(n)$ and $g(n)$ be asymptotically positive functions.</p>

<p>I tried to prove that $$f(n) = O(g(n)) \implies 2^{f(n)} = O\left(2^{g(n)}\right) .$$</p>

<p>I know that the above state... | habedi/stack-exchange-dataset |
77,596 | Variant of bipartite matching, with real capacities from source and to sink, all others unlimited | <p>I've got a variant of bipartite graph matching and I can't find any literature about it.</p>

<p>We have bipartite graph with real capacity edges from source to left vertices (the sum of which is 1), real capacity edges from right vertices to sink (also summing to 1), and unlimited capacity edges between lef... | algorithms graphs network flow bipartite matching | 1 | Variant of bipartite matching, with real capacities from source and to sink, all others unlimited -- (algorithms graphs network flow bipartite matching)
<p>I've got a variant of bipartite graph matching and I can't find any literature about it.</p>

<p>We have bipartite graph with real capacity edges from sourc... | habedi/stack-exchange-dataset |
77,597 | Check if a binary tree is a perfect tree | <p>I'm trying to write an algorithm to check if a given binary tree is a perfect binary tree, and of course with the lowest complexity.</p>

<p>I was thinking to calculate the height of the tree $h$ and the number of the nodes $n$, then if $2^{h+1} -1 = n$, it's a perfect tree.
But then again, it's not very... | algorithms binary trees | 1 | Check if a binary tree is a perfect tree -- (algorithms binary trees)
<p>I'm trying to write an algorithm to check if a given binary tree is a perfect binary tree, and of course with the lowest complexity.</p>

<p>I was thinking to calculate the height of the tree $h$ and the number of the nodes $n$, then if $2... | habedi/stack-exchange-dataset |
77,598 | Equivalent definitions of big O | <blockquote>
 <p>Let $A = \{ g(n) \mid \exists c,n_0 \, \forall n \ge n_0\colon g(n) \le cf(n) \}$, and $B = \{ g(n) \mid \exists c,n_0 \, \forall n \geq n_0 \colon g(n) < cf(n) \}$.</p>
 
 <p>Prove $A = B$.</p>
</blockquote>

<p>My solution:</p>

<ul>
<li>Let $f(n)$ and $g(n)$... | asymptotics landau notation | 1 | Equivalent definitions of big O -- (asymptotics landau notation)
<blockquote>
 <p>Let $A = \{ g(n) \mid \exists c,n_0 \, \forall n \ge n_0\colon g(n) \le cf(n) \}$, and $B = \{ g(n) \mid \exists c,n_0 \, \forall n \geq n_0 \colon g(n) < cf(n) \}$.</p>
 
 <p>Prove $A = B$.</p>
</blockquote>
&#x... | habedi/stack-exchange-dataset |
77,608 | Datastructure for insertion and scored extraction | <p>I have a simple program (assume a shop) that is actually just returning the $m$ most active customers from a total list of $n$ users (so $m \leq n$). I only use this program on one machine with one process, so assume no distribution of data to be necessary.</p>

<p>I require a data structure storing $\mathrm... | data structures | 1 | Datastructure for insertion and scored extraction -- (data structures)
<p>I have a simple program (assume a shop) that is actually just returning the $m$ most active customers from a total list of $n$ users (so $m \leq n$). I only use this program on one machine with one process, so assume no distribution of data to be... | habedi/stack-exchange-dataset |
77,610 | Transitive Amstrong Rules | <p>I have R={A,B,C,D,E} with functional dependencies ABCD → E and AC → ABCD,with Axiom of transitivity rule is AC → E a transitive dependency? Thanks before and sorry for this simple question</p>
 | database theory | 1 | Transitive Amstrong Rules -- (database theory)
<p>I have R={A,B,C,D,E} with functional dependencies ABCD → E and AC → ABCD,with Axiom of transitivity rule is AC → E a transitive dependency? Thanks before and sorry for this simple question</p>
 | habedi/stack-exchange-dataset |
77,611 | Does this problem offer any insight into $P$ vs $NP$ | <blockquote>
 <p>What is the input of a given hash? </p>
</blockquote>

<p>The problem can be verified in polynomial time (using a hash that executed in polynomial time), and I suspect that it may be possible to prove that there is no algorithm that can solve it in polynomial time. </p>&#... | complexity theory hash p vs np | 1 | Does this problem offer any insight into $P$ vs $NP$ -- (complexity theory hash p vs np)
<blockquote>
 <p>What is the input of a given hash? </p>
</blockquote>

<p>The problem can be verified in polynomial time (using a hash that executed in polynomial time), and I suspect that it may be possibl... | habedi/stack-exchange-dataset |
77,621 | Use machine learning algorithms data structure to store information (memory) | <blockquote>
 <p>DISCLAIMER : I'm pretty new to machine learning field, so forgive me
 if my questions are somehow naive ... I already searched on Internet
 about this topic and find nothing interesting so I am asking here ....</p>
</blockquote>

<p>I wonder if a ML algorithm can be consider ... | machine learning artificial intelligence neural networks | 1 | Use machine learning algorithms data structure to store information (memory) -- (machine learning artificial intelligence neural networks)
<blockquote>
 <p>DISCLAIMER : I'm pretty new to machine learning field, so forgive me
 if my questions are somehow naive ... I already searched on Internet
 about thi... | habedi/stack-exchange-dataset |
77,633 | Finding all edges of an undirected graph which are in some cycle in linear time | <p>As a reduction from another problem, I am trying to deal with finding all edges which are part of some cycle in an undirected graph $G=(V,E)$ in time $O(|V|+|E|)$.</p>

<p>My first idea is to use DFS and search for back edges closing cycles, but then the issue is how to add all edges found to the cycle, if w... | graphs search algorithms | 1 | Finding all edges of an undirected graph which are in some cycle in linear time -- (graphs search algorithms)
<p>As a reduction from another problem, I am trying to deal with finding all edges which are part of some cycle in an undirected graph $G=(V,E)$ in time $O(|V|+|E|)$.</p>

<p>My first idea is to use DFS... | habedi/stack-exchange-dataset |
77,645 | Rules of converting a weighted digraph to an undirected graph? | <p>What are the rules of converting a weighted digraph to a weighted, undirected graph? </p>

<p>I understand that the edges should go in both directions from vertex to vertex. However, do the weights of each edge to/from other edges need to be the same? If not, how does one decide which weight to attach to the... | graphs weighted graphs | 1 | Rules of converting a weighted digraph to an undirected graph? -- (graphs weighted graphs)
<p>What are the rules of converting a weighted digraph to a weighted, undirected graph? </p>

<p>I understand that the edges should go in both directions from vertex to vertex. However, do the weights of each edge to/from... | habedi/stack-exchange-dataset |
77,650 | Alternative definitions of ZPP and probabilistic Turing Machines | <p>There are two ways to define a probabilistic Turing Machine:</p>

<ol>
<li>A Turing Machine that can toss coins during its computation.</li>
<li>A deterministic Turing Machine that takes two inputs: $(x,r)$, where $x$ is the original input and $r$ is taken from a distribution of coin tosses.</li>
... | complexity theory turing machines computation models randomized algorithms | 1 | Alternative definitions of ZPP and probabilistic Turing Machines -- (complexity theory turing machines computation models randomized algorithms)
<p>There are two ways to define a probabilistic Turing Machine:</p>

<ol>
<li>A Turing Machine that can toss coins during its computation.</li>
<li>A determini... | habedi/stack-exchange-dataset |
77,653 | why the big-oh of a linear function is n^2? | <p>I know the <strong><em>definitions and differences</em></strong> of <em>big-theta, big-oh, and big-omega</em> in finding time complexity of algorithms. what I can't understand is that why the big-oh of a linear function cannot be O(n).</p>

<p>$0 \le an + b \le cn \Rightarrow c = a + \frac b {n_0}$</p>
... | algorithms time complexity asymptotics | 1 | why the big-oh of a linear function is n^2? -- (algorithms time complexity asymptotics)
<p>I know the <strong><em>definitions and differences</em></strong> of <em>big-theta, big-oh, and big-omega</em> in finding time complexity of algorithms. what I can't understand is that why the big-oh of a linear function cannot be... | habedi/stack-exchange-dataset |
77,659 | Why do derivation tree not make sense for context-sensitive grammars? | <p>I don't understand the line in the paper "Mappings and Grammars on Trees" by William C. Rounds, the passage:</p>

<blockquote>
 <p>Transformational theory, as developed by Chomsky
 [7] and many others, deals with the notion of phrase-structure grammar, and with certain mappings defined on derivatio... | formal languages formal grammars context sensitive | 1 | Why do derivation tree not make sense for context-sensitive grammars? -- (formal languages formal grammars context sensitive)
<p>I don't understand the line in the paper "Mappings and Grammars on Trees" by William C. Rounds, the passage:</p>

<blockquote>
 <p>Transformational theory, as developed by Chomsk... | habedi/stack-exchange-dataset |
77,664 | What does $\sigma(t_0, \ldots, t_{n-1}) \in \mathcal{T}_{\Sigma}^{0}$ in this paper mean? | <p>The paper is "Mappings and Grammars on Trees" by William C. Rounds. There was a definition of ranked alphabet in page 3 and I can't understand the second part of the definition.</p>
<blockquote>
<p>Definition. A ranked alphabet is a pair <span class="math-container">$(\Sigma, r)$</span> where <span... | finite automata | 1 | What does $\sigma(t_0, \ldots, t_{n-1}) \in \mathcal{T}_{\Sigma}^{0}$ in this paper mean? -- (finite automata)
<p>The paper is "Mappings and Grammars on Trees" by William C. Rounds. There was a definition of ranked alphabet in page 3 and I can't understand the second part of the definition.</p>
<blockquot... | habedi/stack-exchange-dataset |
77,667 | Why is CVAL a P-Complete problem? | <p>We've learned in class that CVAL is P-complete. CVAL is the language of all $\langle C,x\rangle$ where $C$ is a formula (a circuit which outputs $0$ or $1$) and $x$ is some input for $C$ such that $C(x) = 1$.</p>

<p>We've done this in the same fashion Michael Sipser does in this <a href="http://courses.csai... | complexity theory reductions space complexity | 1 | Why is CVAL a P-Complete problem? -- (complexity theory reductions space complexity)
<p>We've learned in class that CVAL is P-complete. CVAL is the language of all $\langle C,x\rangle$ where $C$ is a formula (a circuit which outputs $0$ or $1$) and $x$ is some input for $C$ such that $C(x) = 1$.</p>

<p>We've d... | habedi/stack-exchange-dataset |
77,670 | Convolutional Neural Network with constant kernels | <p>I'm starting to learn about CNNs, and I have this question that I haven't been able to answer. Sorry if it is too basic.</p>

<p>I know that in a CNN, the network learns to extract relevant features of images in order to classify them. My question is: <strong>if I just update the weights of the fully-connect... | machine learning neural networks image processing clustering | 1 | Convolutional Neural Network with constant kernels -- (machine learning neural networks image processing clustering)
<p>I'm starting to learn about CNNs, and I have this question that I haven't been able to answer. Sorry if it is too basic.</p>

<p>I know that in a CNN, the network learns to extract relevant fe... | habedi/stack-exchange-dataset |
77,671 | Estimating run time in the absence of knowledge | <p>I’ve always wondered how to make a best guess in the absence of any knowledge.</p>

<p>Let’s say you have a computation running, and you don’t know when it will complete (just that it will). Can you make any estimate when it will be finished just based on the elapsed time without any further knowledge? For e... | statistics | 1 | Estimating run time in the absence of knowledge -- (statistics)
<p>I’ve always wondered how to make a best guess in the absence of any knowledge.</p>

<p>Let’s say you have a computation running, and you don’t know when it will complete (just that it will). Can you make any estimate when it will be finished jus... | habedi/stack-exchange-dataset |
77,672 | Closure of regular languages under non-contiguous subsequence | <p>Suppose there is a language $L$ on alphabet $Σ$.
Now consider the language </p>

<p>$$ S(L) = \{x : wxy ∈ L, w, y ∈ Σ^*\} ∪ \{x : w ∈ L,\text{ and $x$ is a subsequence of $w$}\}. $$</p>

<p>How to prove that if $L$ is regular then $S(L)$ is also regular?</p>

<p>For first part I think if ... | automata finite automata closure properties | 1 | Closure of regular languages under non-contiguous subsequence -- (automata finite automata closure properties)
<p>Suppose there is a language $L$ on alphabet $Σ$.
Now consider the language </p>

<p>$$ S(L) = \{x : wxy ∈ L, w, y ∈ Σ^*\} ∪ \{x : w ∈ L,\text{ and $x$ is a subsequence of $w$}\}. $$</p>

... | habedi/stack-exchange-dataset |
77,681 | General Number Field Sieve Big O Clarification | <p><a href="https://dx.doi.org/10.1134/S1063739711040032" rel="nofollow noreferrer">This paper</a> states that the general number field sieve is of order:</p>

<p>$$L\approx\exp\left((64/9)^{1/3}\,n^{1/3}\,(\ln(n))^{2/3}\right)$$</p>

<p>However several sources (e.g. <a href="http://mathworld.wolfram.co... | complexity theory asymptotics | 1 | General Number Field Sieve Big O Clarification -- (complexity theory asymptotics)
<p><a href="https://dx.doi.org/10.1134/S1063739711040032" rel="nofollow noreferrer">This paper</a> states that the general number field sieve is of order:</p>

<p>$$L\approx\exp\left((64/9)^{1/3}\,n^{1/3}\,(\ln(n))^{2/3}\right)$$<... | habedi/stack-exchange-dataset |
77,683 | Where to start on SJF Cpu schedualing homework problem? | <p>So the question is;</p>

<p>For the following three jobs:
P1: 10 (3,2,5); P2: 4 (2,2); P3: 16 (2,3,5,6)
Execute the three jobs using Exp Ave Alpha =0.6, default=2</p>

<p>I know the formula to get the exponential average for a process is </p>

<p>Pn+1 = (alpha) * Tn + (1-alpha * Pn)</... | process scheduling | 1 | Where to start on SJF Cpu schedualing homework problem? -- (process scheduling)
<p>So the question is;</p>

<p>For the following three jobs:
P1: 10 (3,2,5); P2: 4 (2,2); P3: 16 (2,3,5,6)
Execute the three jobs using Exp Ave Alpha =0.6, default=2</p>

<p>I know the formula to get the exponential ... | habedi/stack-exchange-dataset |
77,686 | Asserting Run Time From Big O Function | <p>Related to <a href="https://cs.stackexchange.com/questions/77681/general-number-field-sieve-big-o-clarification">this</a>, but I felt it was more appropriate to ask as a separate question:</p>

<p>The complexity of Shor's algorithm is of order</p>

<p>$$O\left(n^2\,\log(n)\,\log(\log(n))\right)$$</p>... | asymptotics complexity classes quantum computing | 1 | Asserting Run Time From Big O Function -- (asymptotics complexity classes quantum computing)
<p>Related to <a href="https://cs.stackexchange.com/questions/77681/general-number-field-sieve-big-o-clarification">this</a>, but I felt it was more appropriate to ask as a separate question:</p>

<p>The complexity of S... | habedi/stack-exchange-dataset |
77,687 | Devising algorithm for an A.I. to solve the Wumpus game | <h2>Background</h2>

<p>I am currently coding an AI in C++ to solve a game called Hunt the Wumpus. You can try the game out <a href="https://jayisgames.com/games/hunt-the-wumpus/" rel="nofollow noreferrer">here</a>. My implementation of the game is based on a Graph template which I use to model the caves and th... | algorithms graphs optimization | 1 | Devising algorithm for an A.I. to solve the Wumpus game -- (algorithms graphs optimization)
<h2>Background</h2>

<p>I am currently coding an AI in C++ to solve a game called Hunt the Wumpus. You can try the game out <a href="https://jayisgames.com/games/hunt-the-wumpus/" rel="nofollow noreferrer">here</a>. My i... | habedi/stack-exchange-dataset |
77,696 | Minimum Number of People Such That No Two People Know the Same Two People | <p>In a population of $n$ people, each person knows $k$ other people and each person is known by the same $k$ people. However, no two people, p1 and p2, know the same two people p3 and p4. What is the minimum $n$ such that this is possible for a given $k$? Or, in other words, what's the minimum number of nodes that ... | graphs trees | 1 | Minimum Number of People Such That No Two People Know the Same Two People -- (graphs trees)
<p>In a population of $n$ people, each person knows $k$ other people and each person is known by the same $k$ people. However, no two people, p1 and p2, know the same two people p3 and p4. What is the minimum $n$ such that thi... | habedi/stack-exchange-dataset |
77,703 | Lower bound on multiplication | <p>I was told that the fastest possible algorithm for integer multiplication is $O\left(n{\log}(n)\right)$. Why would this so?<br>
 <br>
Can you please show why the fastest multiplication algorithm would have such a time complexity?</p>
 | algorithms runtime analysis multiplication | 1 | Lower bound on multiplication -- (algorithms runtime analysis multiplication)
<p>I was told that the fastest possible algorithm for integer multiplication is $O\left(n{\log}(n)\right)$. Why would this so?<br>
 <br>
Can you please show why the fastest multiplication algorithm would have such a time complexi... | habedi/stack-exchange-dataset |
77,709 | Primal-dual schema in approximation algorithms | <p>I was studying Set Cover via the Primal–Dual Schema on my own that I faced a problem in the following paragraph:
Consider an LP-relaxation for an NP-hard problem. In general, the relaxation
will not have an optimal solution that is integral(why?? when we relax an LP we can choose the variables from the inter... | algorithms approximation linear programming | 1 | Primal-dual schema in approximation algorithms -- (algorithms approximation linear programming)
<p>I was studying Set Cover via the Primal–Dual Schema on my own that I faced a problem in the following paragraph:
Consider an LP-relaxation for an NP-hard problem. In general, the relaxation
will not have an optima... | habedi/stack-exchange-dataset |
77,714 | Is $\Omega^\infty (g(n)$ a more general version of $\Omega(g(n))$? | <p>In CLRS, one question defines $\Omega^\infty(g(n))$ such that:
$$f(n) = \Omega^\infty (g(n)) \iff \exists c \in \mathbb{R}^+ : \text{for infinitely many integers } n, 0 \leq cg(n) \leq f(n) \ .$$</p>

<p>My question:
What does it mean by "infinitely many integers"? Does it mean $\{n : n \in \mathbb{Z... | asymptotics | 1 | Is $\Omega^\infty (g(n)$ a more general version of $\Omega(g(n))$? -- (asymptotics)
<p>In CLRS, one question defines $\Omega^\infty(g(n))$ such that:
$$f(n) = \Omega^\infty (g(n)) \iff \exists c \in \mathbb{R}^+ : \text{for infinitely many integers } n, 0 \leq cg(n) \leq f(n) \ .$$</p>

<p>My question:
... | habedi/stack-exchange-dataset |
77,721 | Lower Bound for Sorted 2-Sum | <blockquote>
 <p>Given a sorted array of integers $x$ and a target value $t$, determine if there exists a pair $x_i, x_j \in x \wedge i \neq j$ such that $x_i + x_j = t$.</p>
</blockquote>

<p>What is the lower bound for this problem?</p>

<hr>

<p>I know for the generalized $k$-sum (un... | lower bounds | 1 | Lower Bound for Sorted 2-Sum -- (lower bounds)
<blockquote>
 <p>Given a sorted array of integers $x$ and a target value $t$, determine if there exists a pair $x_i, x_j \in x \wedge i \neq j$ such that $x_i + x_j = t$.</p>
</blockquote>

<p>What is the lower bound for this problem?</p>

<hr>
... | habedi/stack-exchange-dataset |
77,736 | Meaning of $NL$ Complexity Class | <p>I am aware of the complexity classes $P$, $NP$ and $L$. But I am not clear what $NL$ or Non-deterministic Log Space intuitively means. The part what I am unclear about is what is the meaning of Non-deterministic Space?</p>

<p>A Turing machine in a $L$ case would read an input, read/write on the work tape th... | complexity theory | 1 | Meaning of $NL$ Complexity Class -- (complexity theory)
<p>I am aware of the complexity classes $P$, $NP$ and $L$. But I am not clear what $NL$ or Non-deterministic Log Space intuitively means. The part what I am unclear about is what is the meaning of Non-deterministic Space?</p>

<p>A Turing machine in a $L$ ... | habedi/stack-exchange-dataset |
77,739 | Proving the given language isn't context free using Pumping Lemma | <p>i want to prove that the following Language isn't CF</p>

<p>$L=\{a^kba^kba^k|k\in \mathbb{N}\}$</p>

<p>Let $z=a^nba^nba^n$ be a String from $L$</p>

<p>$n$ is the pumping length and
$|z|=3n+2 > n$</p>

<p>and $z=uvwxy$ with $|vx|\geqslant 1$, $|vwx|\leqslant n$</p>

<... | formal languages context free pumping lemma | 1 | Proving the given language isn't context free using Pumping Lemma -- (formal languages context free pumping lemma)
<p>i want to prove that the following Language isn't CF</p>

<p>$L=\{a^kba^kba^k|k\in \mathbb{N}\}$</p>

<p>Let $z=a^nba^nba^n$ be a String from $L$</p>

<p>$n$ is the pumping lengt... | habedi/stack-exchange-dataset |
77,740 | Determine the optimal strategy and maximize the reward | <p>Given an array of length <code>n</code> filled with objects which contain 2 ints (<code>size</code> and <code>reward</code>). </p>

<p>Now 2 players are taking turns, each player has an int value we call <code>strength</code>. Let's call them player A and player B, player A goes first. </p>

<p>Playe... | algorithms optimization dynamic programming | 1 | Determine the optimal strategy and maximize the reward -- (algorithms optimization dynamic programming)
<p>Given an array of length <code>n</code> filled with objects which contain 2 ints (<code>size</code> and <code>reward</code>). </p>

<p>Now 2 players are taking turns, each player has an int value we call <... | habedi/stack-exchange-dataset |
77,749 | Is it possible to implement a WeakMap with primitive keys and weak values? | <h3>Theory</h3>

<p>Basically, I have a use-case where I would like to use primitives to store weak references to non-primitive values. If the value is no longer referenced anywhere else, then the entry should be GC'd from the WeakMap and checking the primitive key for an existing value would return false.</p>&... | data structures programming languages efficiency garbage collection | 1 | Is it possible to implement a WeakMap with primitive keys and weak values? -- (data structures programming languages efficiency garbage collection)
<h3>Theory</h3>

<p>Basically, I have a use-case where I would like to use primitives to store weak references to non-primitive values. If the value is no longer re... | habedi/stack-exchange-dataset |
77,753 | Complexity of determining whether three points are collinear from a set of points | <p>Let $S \subseteq \mathbb{R}^2$ be a finite set of points. Do there exists three collinear points $p, q, r \in S$?</p>

<p>I wan't to know the complexity of this decision problem and present my approach as following.</p>

<p><strong>SOLUTIONS</strong>. Let $n = |S|$. A naive brute-force takes time $\m... | algorithms time complexity computational geometry lower bounds | 1 | Complexity of determining whether three points are collinear from a set of points -- (algorithms time complexity computational geometry lower bounds)
<p>Let $S \subseteq \mathbb{R}^2$ be a finite set of points. Do there exists three collinear points $p, q, r \in S$?</p>

<p>I wan't to know the complexity of thi... | habedi/stack-exchange-dataset |
77,754 | Grid covering by rectangles | <p>We have a $N_1 \times N_2$ grid.
We have a collection of rectangles on this grid, each rectangle can be represented as a $N_1$-by-$N_2$ binary matrix $R$. We want to cover the grid with those rectangles.</p>

<p>Is the decision version of this set cover problem NP-complete ?</p>

<ul>
<li>Inp... | complexity theory np complete set cover | 1 | Grid covering by rectangles -- (complexity theory np complete set cover)
<p>We have a $N_1 \times N_2$ grid.
We have a collection of rectangles on this grid, each rectangle can be represented as a $N_1$-by-$N_2$ binary matrix $R$. We want to cover the grid with those rectangles.</p>

<p>Is the decision vers... | habedi/stack-exchange-dataset |
77,763 | How to compare/cluster millions of strings? | <p>I have around 1,000,000 of strings of variable length (from 200 to 50000) that can contain 5 characters (A, B, C, D, E).</p>

<p>What I actually want is to cluster them together if they are similar enough. By similar enough I mean they have an edit distance < $t$. This $t$ should be dependent on the lengt... | algorithms reference request strings clustering | 1 | How to compare/cluster millions of strings? -- (algorithms reference request strings clustering)
<p>I have around 1,000,000 of strings of variable length (from 200 to 50000) that can contain 5 characters (A, B, C, D, E).</p>

<p>What I actually want is to cluster them together if they are similar enough. By sim... | habedi/stack-exchange-dataset |
77,764 | Clarification of definition of class $DisNP$ | <p>I an trying to learn about $DisNP$ Complexity class. I couldn't find this class in any book. But, regarding it, I found this definition in a paper:</p>

<p>Definition: A disjoint NP-pair (NP-pair for short) is a pair of nonempty sets $A$ and $B$ such that $A, B \in NP$ and $A \cap B = Empty$. $DisNP$ denote ... | complexity theory | 1 | Clarification of definition of class $DisNP$ -- (complexity theory)
<p>I an trying to learn about $DisNP$ Complexity class. I couldn't find this class in any book. But, regarding it, I found this definition in a paper:</p>

<p>Definition: A disjoint NP-pair (NP-pair for short) is a pair of nonempty sets $A$ and... | habedi/stack-exchange-dataset |
77,765 | "Implied atomic propositions" in propositional boolean formula | <p>Suppose we have a propositional boolean formula F and let M be the set of all models of that formula.</p>

<p>I am wondering if there is an efficient way to find all atomic propositions that are implied by the formula. Informally, this means that they can only have one specific value in all models M.</p>
... | propositional logic | 1 | "Implied atomic propositions" in propositional boolean formula -- (propositional logic)
<p>Suppose we have a propositional boolean formula F and let M be the set of all models of that formula.</p>

<p>I am wondering if there is an efficient way to find all atomic propositions that are implied by the formula. In... | habedi/stack-exchange-dataset |
77,773 | Halting problem with Proof of The Immerman-Szelepcenyi Theorem (knowledge of the theorem might not be necessary to clear my doubt) | <p>So, I was reading <a href="http://www.math.ru.nl/~terwijn/teaching/complexitytheory.pdf" rel="nofollow noreferrer">this pdf</a> on complexity theory. On page 18 pf pdf (Page 12 of book) The Immerman-Szelepcsenyi Theorem is mentioned with proof. The following lines are from the book :</p>

<blockquote>
 ... | turing machines halting problem | 1 | Halting problem with Proof of The Immerman-Szelepcenyi Theorem (knowledge of the theorem might not be necessary to clear my doubt) -- (turing machines halting problem)
<p>So, I was reading <a href="http://www.math.ru.nl/~terwijn/teaching/complexitytheory.pdf" rel="nofollow noreferrer">this pdf</a> on complexity theory.... | habedi/stack-exchange-dataset |
77,774 | Unrecognizable languages relationship to NP-hard languages | <p>I would like to know if there exists an NP-hard language which is also a member of co-RE\R?
I think it depends if P=NP or not, but i'm not sure.</p>

<p>Can I simply assume NP-hard is in R?</p>

<p>Can you direct me how to think about it?</p>
 | complexity theory computability np hard semi decidability | 1 | Unrecognizable languages relationship to NP-hard languages -- (complexity theory computability np hard semi decidability)
<p>I would like to know if there exists an NP-hard language which is also a member of co-RE\R?
I think it depends if P=NP or not, but i'm not sure.</p>

<p>Can I simply assume NP-hard is... | habedi/stack-exchange-dataset |
77,776 | Run time of a Simple Recurrence | <p>Given the recurrence $T(n) = T(\sqrt{n}) + \theta(lglgn)$, provide an asymptotically tight bound on it's run time.</p>

<p>My solution was to let $m = 2\sqrt{n}$, which leads to the recurrence $S(m) = S(m/2) + \theta(lg(2lg(m) + lg4)) = S(m/2) + \theta(lglgm)$. </p>

<p>By case 3 of the master rule, ... | asymptotics recurrence relation master theorem | 1 | Run time of a Simple Recurrence -- (asymptotics recurrence relation master theorem)
<p>Given the recurrence $T(n) = T(\sqrt{n}) + \theta(lglgn)$, provide an asymptotically tight bound on it's run time.</p>

<p>My solution was to let $m = 2\sqrt{n}$, which leads to the recurrence $S(m) = S(m/2) + \theta(lg(2lg(m... | habedi/stack-exchange-dataset |
77,786 | Given regular grammars (each is either left or right linear), does exist word/string so it can be derived from all regular grammars? | <p>Given regular grammars (each is either left or right linear), does exist word/string so it can be derived from all regular grammars, i.e. a word/string that can be derived from each regular grammar.</p>

<p>Suppose that S<sub>1</sub>, ... , S<sub>n</sub> are regular grammars. Then is the following statement ... | algorithms complexity theory formal languages regular languages formal grammars | 1 | Given regular grammars (each is either left or right linear), does exist word/string so it can be derived from all regular grammars? -- (algorithms complexity theory formal languages regular languages formal grammars)
<p>Given regular grammars (each is either left or right linear), does exist word/string so it can be d... | habedi/stack-exchange-dataset |
77,799 | safe edge for Minimum spanning tree | <p>I know this question is posted many times, but i am still posting this because i have my own doubt which pulls me out to move forward to kruskal and prim's algorithm.So Please do help me out $-:$</p>

<h2>Question</h2>

<blockquote>
 <p>Let $G=\left(V,E\right)$ be a be a <strong>connected, undir... | algorithms graphs spanning trees minimum spanning tree | 1 | safe edge for Minimum spanning tree -- (algorithms graphs spanning trees minimum spanning tree)
<p>I know this question is posted many times, but i am still posting this because i have my own doubt which pulls me out to move forward to kruskal and prim's algorithm.So Please do help me out $-:$</p>

<h2>Question... | habedi/stack-exchange-dataset |
77,809 | Complexity of simplifying two-variable algebraic expression | <p>Given algebraic expression of two variables x and y, I want to simplify this algebraic expression until it cannot be simplified anymore. What algorithm can I use for this?</p>

<p>For instance:</p>

<p>x+x+y+y = 2•x+2•y = 2•(x+y)</p>

<p>x•x+y•y=x<sup>2</su... | algorithms complexity theory time complexity space complexity | 1 | Complexity of simplifying two-variable algebraic expression -- (algorithms complexity theory time complexity space complexity)
<p>Given algebraic expression of two variables x and y, I want to simplify this algebraic expression until it cannot be simplified anymore. What algorithm can I use for this?</p>

<p>F... | habedi/stack-exchange-dataset |
77,810 | construct a TM decides in linear time, if valid bracket | <p>I want to construct a 2-tape Turing Machine, which decides in linear time if the input string over $\Sigma^* := \{(, [, ], )\}$ is a valid bracket.</p>

<p>I have not constructed too many TM's yet, this is why I need your help.</p>
 | turing machines decision problem | 1 | construct a TM decides in linear time, if valid bracket -- (turing machines decision problem)
<p>I want to construct a 2-tape Turing Machine, which decides in linear time if the input string over $\Sigma^* := \{(, [, ], )\}$ is a valid bracket.</p>

<p>I have not constructed too many TM's yet, this is why I nee... | habedi/stack-exchange-dataset |
77,815 | What advantage do quadratic basis functions have over gaussian basis functions in RBF implementations? | <p>I've been reading up recently on radial basis functions, and I've recently moved from Gaussian basis functions of the form $\phi(x)=\exp(-\alpha||x-x_i||)$ to multiquadratic basis functions. My source is <a href="https://www.researchgate.net/profile/Edward_Kansa/publication/222180584_Improved_accuracy_of_multiquadri... | algorithms approximation | 1 | What advantage do quadratic basis functions have over gaussian basis functions in RBF implementations? -- (algorithms approximation)
<p>I've been reading up recently on radial basis functions, and I've recently moved from Gaussian basis functions of the form $\phi(x)=\exp(-\alpha||x-x_i||)$ to multiquadratic basis func... | habedi/stack-exchange-dataset |
77,816 | 2-tape TM that accepts words from $L := \{bin(n)$#$w \in \Sigma^* | n \in \mathbb N \land w \in \{0,1\}^* \land |w| \le n\}$ in $O(n)$ | <p>Let $\Sigma := \{0,1,$#$\}$ be the input-alphabet and $L := \{bin(n)$#$w \in \Sigma^* | n \in \mathbb N \land w \in \{0,1\}^* \land |w| \le n\}$ the alphabet. $|w|$ means the length of the word $w$ and $bin(n)$ the binary representation of $n$.</p>

<p>I need to construct a 2-tape TM which has $O(n)$ complex... | formal languages turing machines | 1 | 2-tape TM that accepts words from $L := \{bin(n)$#$w \in \Sigma^* | n \in \mathbb N \land w \in \{0,1\}^* \land |w| \le n\}$ in $O(n)$ -- (formal languages turing machines)
<p>Let $\Sigma := \{0,1,$#$\}$ be the input-alphabet and $L := \{bin(n)$#$w \in \Sigma^* | n \in \mathbb N \land w \in \{0,1\}^* \land |w| \le n\}$... | habedi/stack-exchange-dataset |
77,824 | Is there an existing data structure that is of fixed size, and will push the oldest/last element out if a new element is inserted? | <p>I'm looking for a data structure that will push its oldest/last element out if a new element is inserted. For example, let <code>D</code> represent the structure. <code>D</code> contains 3 elements of the type <code>Number</code> <code>D</code>'s default values will be initialized to <code>1, 2</code> and <code>3</c... | data structures arrays queues | 1 | Is there an existing data structure that is of fixed size, and will push the oldest/last element out if a new element is inserted? -- (data structures arrays queues)
<p>I'm looking for a data structure that will push its oldest/last element out if a new element is inserted. For example, let <code>D</code> represent the... | habedi/stack-exchange-dataset |
77,837 | How to prove the outcome of both segment of code are equal | <p><a href="https://i.stack.imgur.com/6e5bU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/6e5bU.png" alt="enter image description here"></a></p>

<p>Is it possible to prove using induction? If possible what would be the steps to proof A=B?</p>

<p>Main thing i want to proof is outco... | algorithms correctness proof | 1 | How to prove the outcome of both segment of code are equal -- (algorithms correctness proof)
<p><a href="https://i.stack.imgur.com/6e5bU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/6e5bU.png" alt="enter image description here"></a></p>

<p>Is it possible to prove using induction? If possi... | habedi/stack-exchange-dataset |
77,840 | Can quantum computer compute the minimal intersection DFA of numerous minimal DFAs in polynomial time using polynomial number of qubits? | <p>Can <strong>quantum</strong> computer compute the <strong>minimal</strong> intersection DFA of numerous <strong>minimal</strong> DFAs in polynomial time using polynomial number of <strong>qu</strong>bits, where the language of each given <strong>minimal</strong> DFA is finite and it's alphabet is Σ={0,1} and a... | complexity theory formal languages finite automata quantum computing | 1 | Can quantum computer compute the minimal intersection DFA of numerous minimal DFAs in polynomial time using polynomial number of qubits? -- (complexity theory formal languages finite automata quantum computing)
<p>Can <strong>quantum</strong> computer compute the <strong>minimal</strong> intersection DFA of numerous <s... | habedi/stack-exchange-dataset |
77,842 | Efficient algorithm to translate/shift polynomials | <p>I have a polynomial $P(x)$, and given some constant $d$, I need to find the polynomial $P(x+d)$. For example, if $P(x)=x^2$ and $d=1$, then the result would be $P(x+1)=(x+1)^2=x^2+2x+1$ (with the coefficients stored in an array/vector).</p>

<p>I know the algorithm with $O(n^2)$ time complexity, which is bas... | algorithms polynomials | 1 | Efficient algorithm to translate/shift polynomials -- (algorithms polynomials)
<p>I have a polynomial $P(x)$, and given some constant $d$, I need to find the polynomial $P(x+d)$. For example, if $P(x)=x^2$ and $d=1$, then the result would be $P(x+1)=(x+1)^2=x^2+2x+1$ (with the coefficients stored in an array/vector).</... | habedi/stack-exchange-dataset |
77,844 | how does a harddisk work? block / sector | <p>Can someone explain me the way harddisks work? :/</p>
<p>The size of a block is specified in the filesystem, am I right? As you can see in the picture from wikipedia, the disk is divided into circle sectors. But the blocks on the outer tracks are obviously larger (physically)...</p>
<p><a href="https://i.sta... | computer architecture storage | 1 | how does a harddisk work? block / sector -- (computer architecture storage)
<p>Can someone explain me the way harddisks work? :/</p>
<p>The size of a block is specified in the filesystem, am I right? As you can see in the picture from wikipedia, the disk is divided into circle sectors. But the blocks on the outer t... | habedi/stack-exchange-dataset |
77,847 | Maximum sum difference between two sorted array elements under one condition | <p>We're given two arrays $A$ and $B$ with size $N$ and $M$ respectively. We want to find a set $P = \{(a_1, b_1), \dots, (a_s,b_s)\}$ such that</p>

<ul>
<li>for each $i\in\{1, \dots, s\}$, $a_i\in A$, $b_i\in B$ and $a_i>b_i$ and $a_i,b_i$ musn't be chosen before;</li>
<li>$\sum_{i=1}^s (a_i-b_i)$ ... | sorting arrays greedy algorithms | 1 | Maximum sum difference between two sorted array elements under one condition -- (sorting arrays greedy algorithms)
<p>We're given two arrays $A$ and $B$ with size $N$ and $M$ respectively. We want to find a set $P = \{(a_1, b_1), \dots, (a_s,b_s)\}$ such that</p>

<ul>
<li>for each $i\in\{1, \dots, s\}$, $a... | habedi/stack-exchange-dataset |
77,855 | Can I say is lossy compression to discard data having a way to recover it? | <p>I'm working on a compression algorithm for a specific kind of data. I have found a way to discard (important) parts of the data during compression as I have also found a way to recover the missing parts during decompression. </p>

<p>The decompression algorithm most of the times will infer the data equal to ... | data compression | 1 | Can I say is lossy compression to discard data having a way to recover it? -- (data compression)
<p>I'm working on a compression algorithm for a specific kind of data. I have found a way to discard (important) parts of the data during compression as I have also found a way to recover the missing parts during decompress... | habedi/stack-exchange-dataset |
77,859 | $L = \{ w \in \{0, 1, 2\}^*: |0| + |2| = |1| \}$ where |0| denotes number of 0s in the string w | <p>I have come up with:</p>

<pre><code>S→0SX | 1SY | 2SZ | SS | ϵ
X→1
Y→0 | 2
Z→1
</code></pre>

<p>I think I am wrong. Any directions?</p>
 | automata context free formal grammars | 1 | $L = \{ w \in \{0, 1, 2\}^*: |0| + |2| = |1| \}$ where |0| denotes number of 0s in the string w -- (automata context free formal grammars)
<p>I have come up with:</p>

<pre><code>S→0SX | 1SY | 2SZ | SS | ϵ
X→1
Y→0 | 2
Z→1
</code></pre>

<p>I think I am wrong. Any directions?</p>
 | habedi/stack-exchange-dataset |
77,867 | Lower bound on competitive ratio of $m$-machine scheduling | <p>Given a sequence of positive reals $a_1, a_2, \dots, a_n$ and an integer $m$, for each $j$ assign $a_j$ to a machine $i$, $1< i < m$, so as to minimize the maximum, over $i$, of the sum of all reals assigned to machine $i$. </p>

<p>Theorem: There is no randomized $m$-machine scheduling algorithm wi... | algorithms scheduling online algorithms competitive ratio | 1 | Lower bound on competitive ratio of $m$-machine scheduling -- (algorithms scheduling online algorithms competitive ratio)
<p>Given a sequence of positive reals $a_1, a_2, \dots, a_n$ and an integer $m$, for each $j$ assign $a_j$ to a machine $i$, $1< i < m$, so as to minimize the maximum, over $i$, of the sum of ... | habedi/stack-exchange-dataset |
77,874 | What is the best Approximation algorithm to schedule a task graph? | <p>If I have a task graph T and want a schedule to optimize the make-span, what is currently the best approximation algorithm for this problem? Are there any constant approximation algorithms?</p>
 | approximation scheduling process scheduling | 1 | What is the best Approximation algorithm to schedule a task graph? -- (approximation scheduling process scheduling)
<p>If I have a task graph T and want a schedule to optimize the make-span, what is currently the best approximation algorithm for this problem? Are there any constant approximation algorithms?</p>
 | habedi/stack-exchange-dataset |
77,876 | CFG for palindromes containing atleast 3 c's | <p>Input alphabet = {a,b,c}</p>

<p>I tried with the following grammar :-</p>

<p>S -> aSa / bSb / T <br>
T -> cTc / cSc / cBc <br>
B -> c / cXc <br>
X -> a / b / aXa / bXb / epsilon <br></p>

<p>This grammar is not able to generate 'cacac' .Is there any way to write this grammar wi... | context free | 1 | CFG for palindromes containing atleast 3 c's -- (context free)
<p>Input alphabet = {a,b,c}</p>

<p>I tried with the following grammar :-</p>

<p>S -> aSa / bSb / T <br>
T -> cTc / cSc / cBc <br>
B -> c / cXc <br>
X -> a / b / aXa / bXb / epsilon <br></p>

<p>This grammar is not able... | habedi/stack-exchange-dataset |
77,883 | If we can simulate $NP$-machines why isn't it trivial that $NP=coNP$? | <p>I'm looking at some proof that shows $NP^{NP\cap coNP} = NP$.</p>

<p>Let's consider the non-trivial direction. Consider $L\in NP^{NP\cap coNP}$. Then, there's an $A\in NP\cap coNP$ such that $L\in NP^A$.</p>

<p>Since $A\in NP\cap coNP$, there're two machines $M_A$ and $M_{\overline A}$ to decide $A... | complexity theory | 1 | If we can simulate $NP$-machines why isn't it trivial that $NP=coNP$? -- (complexity theory)
<p>I'm looking at some proof that shows $NP^{NP\cap coNP} = NP$.</p>

<p>Let's consider the non-trivial direction. Consider $L\in NP^{NP\cap coNP}$. Then, there's an $A\in NP\cap coNP$ such that $L\in NP^A$.</p>
&#x... | habedi/stack-exchange-dataset |
77,892 | Efficiency of 0-1 linear programming w.r.t. number of binary variables | <p>I am working on a problem in which I have to solve 0-1 linear programs, that is linear programs where some of the variables are binary, i.e. either 1 or 0.</p>

<p>Lets say I have a fixed number of $n$ variables in my program of which $k \leq n$ are binary. The other $n-k$ variables are continuous. My questi... | efficiency linear programming integer programming | 1 | Efficiency of 0-1 linear programming w.r.t. number of binary variables -- (efficiency linear programming integer programming)
<p>I am working on a problem in which I have to solve 0-1 linear programs, that is linear programs where some of the variables are binary, i.e. either 1 or 0.</p>

<p>Lets say I have a f... | habedi/stack-exchange-dataset |
77,897 | Time complexity of this while loop | <p>So, i would like to know the time complexity of the following codes:</p>

<pre><code>x = (float) rand() / rand(); // T(4)

while (x >= 0.01) // T(?)
{
 x *= 0.8; // T(?) x T(2)
}
</code></pre>

<p>Assuming that all the basic operations are perfomed once, is the best... | algorithm analysis runtime analysis randomness average case | 1 | Time complexity of this while loop -- (algorithm analysis runtime analysis randomness average case)
<p>So, i would like to know the time complexity of the following codes:</p>

<pre><code>x = (float) rand() / rand(); // T(4)

while (x >= 0.01) // T(?)
{
 x *= 0.8; // T(?) x T(2)
}... | habedi/stack-exchange-dataset |
77,899 | What graph problems are hard to solve even for a small number of verticies? | <p>The only graph problem that I worked with is TSP. It is exponentially hard, but there are tons of heuristics which allows to find near to optimum solution.</p>

<p>So I was wondering, is there any graph problems (or optimization problems which could be mapped onto graph) that are exponentially hard and can n... | graphs optimization np complete np hard | 1 | What graph problems are hard to solve even for a small number of verticies? -- (graphs optimization np complete np hard)
<p>The only graph problem that I worked with is TSP. It is exponentially hard, but there are tons of heuristics which allows to find near to optimum solution.</p>

<p>So I was wondering, is t... | habedi/stack-exchange-dataset |
77,901 | proving $IP^\star = NP$ | <blockquote>
 <p>Consider the following complexity class $IP^\star$, a variant of $IP$.
 A language $L$ is in $IP^\star$ if there's a proof system $(P,V)$ s.t.
 $V$ is a verifier runs for a polynomial time and:</p>
 
 <p>$$x\in L \implies Pr[(P,V)(x) = 1] \ge 3/4 \\ x\not\in L \implies
>... | complexity theory probabilistic algorithms interactive proof systems | 1 | proving $IP^\star = NP$ -- (complexity theory probabilistic algorithms interactive proof systems)
<blockquote>
 <p>Consider the following complexity class $IP^\star$, a variant of $IP$.
 A language $L$ is in $IP^\star$ if there's a proof system $(P,V)$ s.t.
 $V$ is a verifier runs for a polynomial time a... | habedi/stack-exchange-dataset |
77,908 | Find an upper bound for $T(n)=T(\sqrt{n})+10\log\log n$ | <p>I need to find an upper bound for $T(n)=T(\sqrt{n})+10\log\log n$.</p>

<p>I thought first to make a substitution: $m=\log n$. Then:
$$
T(2^m)=T(2^{m \over 2})+10\log m
$$
Let $S(m)=T(2^m)$:
$$
S(m)=S\big({m \over 2}\big)+10\log m
$$</p>

<p>Now we can use Master theorem. ... | asymptotics recurrence relation check my answer | 1 | Find an upper bound for $T(n)=T(\sqrt{n})+10\log\log n$ -- (asymptotics recurrence relation check my answer)
<p>I need to find an upper bound for $T(n)=T(\sqrt{n})+10\log\log n$.</p>

<p>I thought first to make a substitution: $m=\log n$. Then:
$$
T(2^m)=T(2^{m \over 2})+10\log m
$$
Let $S(m)=T(... | habedi/stack-exchange-dataset |
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