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Proving NP-complete problem

Suppose the following problem: Given an undirected graph G=(V,E), is it possible to choose a subset V' of vertex set V, such that deleting it removes all triangles (cycles of length 3), where |V'| is ...
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votes
1answer
271 views

NP-completeness of one generalized subset sum problem (target sum belongs to interval) [closed]

I need to prove that decision problem: for a given set of positive integers $a_1, ..., a_n$, does it exist a subset that sums up to a value within interval $[\frac{1}{2}\sum a_i; \frac{1}{2}\sum a_i+...
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votes
1answer
108 views

Temporal Logic - Until [closed]

I have a doubt, in Linear Temporal Logic LTL, does the Until operator require that the first occurrence is the first term of the formula? ex: a U b does require ...
-4
votes
1answer
1k views

Time complexity of finding the shortest path in DAG [closed]

I apologize for seemingly basic question: I saw numerous times that the time complexity of finding the shortest path in directed acyclic graph is O(|V| + |E|). ...
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votes
2answers
459 views

Covering Codes with Game Theory Application

Here is a question I came up with and i have been pondering for a while. It relates to covering codes, a subset of coding theory. I could not come up with an adequate solution, so here I am, asking ...
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1answer
1k views

Subset-Sum modulo small primes

I was thinking about the strategy of solving Subset-Sum (with a set of size n and integers having n bits each) by using Dynamic Programming (described here: http://en.wikipedia.org/wiki/...
-4
votes
1answer
2k views

Find sentences with similar relative meaning from a list of sentences against an example one

I want to be able to find sentences with the same meaning. I have a query sentence, and a long list of millions of other sentences. Sentences are words, or a special type of word called a symbol which ...
-4
votes
2answers
92 views

Is it possible to have a sorting algorithm that computes faster than QuickSort? [closed]

Given an unsorted array, QuickSort has to touch each source element it is trying to sort multiple times before it declares an array as sorted. (notice how many times the 2 is touched [circled in red ...
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1answer
603 views

Proving NP-hardness of scheduling problem (total weighted completion time)

Consider the problem $P \mid \mid \sum w_j C_j$. I want to prove that this problem is (strongly) NP-hard by reducing from $3$-Partition, but I am not really sure how to do this. Just to be precise, ...
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votes
1answer
205 views

What exactly is a search space? [closed]

I am new to CS so excuse my question if it seems very rudimentary. I just want to make sure I understand the terminology 100% correct as I go along. Is a "search space" the total amount of all the ...
-4
votes
1answer
231 views

How to reduce LCS from Vertex-Cover [closed]

I am trying to understand the demostration of intractability of the LCS problem, as stated as a reduction from Vertex-Cover problem, and so far, i'm stuck with the demostration of the problem in this ...
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votes
1answer
132 views

Is there an algorithm for 3x3 sudokus without backtracking? [closed]

From what I can see on Wikipedia and the Internet at large, all sudoku solving algorithms (including human ones) employ some kind of EXPTIME backtracking search for some sudokus. Are there any SAT ...
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votes
1answer
915 views

What is the complexity of the fastest method of k-coloring any graph? [closed]

I heard brute-force is the only method. Is there any other way? Is there a way to prove that the complexity cannot be exponential?
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votes
1answer
2k views

Developing A Perfect Tic-Tac-Toe Player - AI [closed]

I'm interested in AI as an area to study on in MSc. I don't have much prior knowledge. So, I decided to develop an AI that plays Tic-Tac-Toe perfectly, as an introduction. I've made some progress that ...
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votes
1answer
315 views

Solving a system of linear inequations

Consider the following system of inequalities: $Ax=b$; $x\geq 0$; A is a $m\times n$ (non-square) and sparse matrix in which some part of entries are rational. a) How feasibility of this system can ...
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votes
1answer
123 views

What do you think of Bokov's “CNF-SAT is in P” proof? [closed]

There are now several versions of G. V. Bokov's paper "Complexity of the CNF-satisfiability problem", cf. https://arxiv.org/abs/1804.02478 In the most recent version of his paper, the proof is only ...
-5
votes
1answer
177 views

Should GCT focus on $PSPACE\not\subseteq P/poly$?

GCT tries to show $P$ is not $NP$ by showing $NP$ is not in $P/poly$. Could it be useful in showing $\Sigma_{i+1}\not\subseteq P^{\Sigma_i}/Poly$ at every $i>0$? Suppose if it turns out that $\...
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votes
1answer
1k views

why is a Turing machine defined as a 5-tuple? [closed]

[Edited to provide better context.] In a comment on meta, JɛffE suggested that this would be a good topic for a question to ask here. why is a Turing machine defined as a 5-tuple?
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1answer
623 views

Is 3SAT problem APX-hard or not?

Could you point me a reference, an answer or it is an open question?
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votes
1answer
256 views

Does a Non deterministic TM halt after the same number of steps on the same input? [closed]

Let $M$ be a Turing Machine (TM) which decides a certain language. Enter an input $x$ to $M$ and let the machine compute on $x$. After some time, $M$ will halt. If $M$ is a deterministic TM, it will ...
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1answer
382 views

Theoretical Computer Science or Sensor Networks

I am a first year PhD student in computer science. The major areas my supervisor is working with are: Theoretical Computer Science (knowledge representation, uncertainty, etc.) and wireless sensor ...
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votes
1answer
3k views

Proof that DFA that accepts string has NFA that accepts reversal of string

I have seen descriptions for an algorithm that can take a regular deterministic finite automata and create a non-deterministic finite automata that is guaranteed to generate the reverse of string ...
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votes
1answer
1k views

Alternative Turing Machine Proofs

I am asking this question again. I am aware of, and have read the other similar "alternative proof TM" questions, but unfortunately, they do help me. I am looking for a TM Halting Problem proof that ...
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votes
1answer
76 views

We know that X3C is NP-complete with |X|=3q and |C|=m. Is this problem still remains NP-complete if |C|<2q? [closed]

Exact-Cover-by-3Sets (X3C) is NP-complete. If the number of classes i.e. |C|<2q then whether this is version of X3C is NP-complete or not?
-5
votes
2answers
4k views

Minimum-weight feedback edge set in undirected graph - how to find it? Is it NP hard problem?

Let G = (V,E) be an undirected graph. A set F ⊆ E of edges is called a feedback-edge set if every cycle of G has at least one edge in F. Suppose that G is a weighted undirected graph with positive ...
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votes
1answer
745 views

Self-avoiding walk in Graph [closed]

Short question: How many self-avoiding-filling-polygons are there in a grid-graph of $n×n$? Long question: Edit: This question is not about p = np. I am searching for a way to calculate the numbers ...
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votes
1answer
314 views

whats the difference between nondeterminism and parallelism? [closed]

pondering another Q/A & the responses on here[1] leads to this question: whats the difference between nondeterminism and parallelism? am aware of basic answers. have some of my own ideas on ...
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votes
2answers
981 views

Proof of correctness of in-place Quick sort

I have found proof of correctness of Quick sort (not in-place version), Please refer me a proof of correctness of in-place Quick sort, or provide proof here is very appropriated. a typical ...
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votes
2answers
659 views

Is halting that hard? [Yes] [closed]

I want to make a modification to the halting problem. The output now has two possibilities: This program halts and it does not have the crossing structure (defined below); This program does not halt ...
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votes
1answer
990 views

Polynomial time algorithm to solve the TSP on an m by n solid grid

Is there a polynomial algorithm to solve TSP (or Ham Cycle) on an m by n solid grid graph whose points are at unit distance apart? I've heard about Umans and Lenhart research paper but reading such ...
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votes
2answers
199 views

A sandwich Algorithm / Data Structure [closed]

$O(n^c)$ is asymptotically greater than $O(\log^d n) $ for all possible pair of values of $c$ and $d$. Can you give an example of a problem (or data structure) which has running time (or query/...
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votes
1answer
126 views

NP hard? Maximize the average for a subset of numbers

Given a set of real numbers, choose a subset to maximize the average subject to the average not exceeding a given threshold. Is it NP hard? I think so, but I cannot come out with a proof. Thanks a ...
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votes
1answer
143 views

Are there proofs which show that AIs are bound to be “worse” than the human brain? [closed]

I was talking with two PhDs (both teach IT related subjects) about artificial intelligence the other day. They were in agreement that an AI can never reach the level of the human brain, but failed to ...
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votes
1answer
148 views

Do irrational number contain infinate/every patterns of sequences? [closed]

I guess the question is "does an 'infinite' number of patterns imply 'every' number of patterns?" For instance, if you could quickly calculate the decimal sequence of π, could you not (in ...
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votes
2answers
1k views

Deterministic CFL closure Property Homomorphism [closed]

I tried to research the following question with no results: Can you find one example where the following holds true: Let L = {xxxxxxx} be a deterministic-context-free Language and Let h(...) = xxxxx ...
-5
votes
1answer
23 views

Help find algorithm for array-based task

Given array if numbers a[1..n]. Pair of numbers (i, j) is interesting, if i < j и a[i] > 2a[j]. How to count number of interesting pairs in O(nlogn)? What is the solution? My solution is not ...
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votes
1answer
120 views

Is mathematical proof itself NP-hard?

At the 8:00 mark of this video, he claims that proving things is itself an NP problem. I'm looking for more insight into this. Could someone help explain this concept to me and also provide a link to ...
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votes
1answer
26 views

Polynomial-time reducibility of Primality and 3-SAT

Is 3-SAT $\leq_{p}$ Primality? And/or is Primality $\leq_{p}$ 3-SAT? I think the answer is no and yes, respectively, but I'm not sure. Any help would be appreciated. Thank you.
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votes
1answer
374 views

Does any DAG can be topologically sorted? [closed]

I am not good enough in computer science. My intention is to solve some programming problem in terms of DAG's. The key point is that before getting them into database, I need run "topological sort" in ...
-5
votes
1answer
160 views

Dance Partner Problem NP-completeness [closed]

I really can't think of a concise way to phrase this problem, which makes it hard to search for, so forgive me if this is a duplicate question. I've come across a problem and I would like to know if ...
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votes
1answer
129 views

non deterministic algorithm always find the right solution? [closed]

i'm confused since i see some books mention the NP time algorithms as "very lucky" that means it always finds the right path? also can someone explain the coming points to me please... A ...
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votes
1answer
130 views

A simple challenge

Consider the following problem: given a number $n$, an alphabet $\Sigma$, and a finite language $L$, how many strings of length $n$ in $\Sigma^*$ contain at least one word $w\in L$? E.g. ...
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votes
1answer
241 views

Some questions (still) unresolved about braids?

I was looking for interesting questions pertaining to braid theory. I don't know if the following are considered important, but I'd like to ask: (1) in relation with the following link, is it true ...
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votes
1answer
251 views

Can on every instance P = NP? [closed]

I want to ask a question concerning some aspects of the P vs. NP problem. NOTE: Possibly by "popular" standards i am a crank (i tend towards P=NP), but lets focus on the issue (please with a grain of ...
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votes
2answers
691 views

open problems on $NP$-complete? [closed]

How can we find the list of open problems on $NP$-comlpete?
-5
votes
1answer
332 views

Attacking TSP via small nonintersecting circuits

Consider the problem of finding smaller "non-intersecting" circuits or paths in graphs embedded in the euclidean plane (visiting all vertices) in the sense of geometric intersections of edges plotted ...
-6
votes
3answers
372 views

How can I call functions that are not “first-class functions”?

I mean, is there an antonym for "first-class function"?
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5answers
27k views

Application of calculus in computer science

Where are derivatives and integrals used in the field of Computer Science? What are their applications?
-6
votes
1answer
356 views

What function has the signature $ A \times \left ( B + C \right ) \rightarrow \left ( A \times B \right ) + \left ( A \times C \right ) $?

$ A \times \left ( B + C \right ) $ is isomorphic to $ \left ( A \times B \right ) + \left ( A \times C \right ) $, right? That means there's a function from one to the other and another function back....
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votes
1answer
207 views

Is the sub-bit model of quantum computation equivalent to other models? [closed]

In a comment to this question Peter Shor asked me for a reference about the third described in the question point of view, namely, that quantum computers can be described as computers that can ...

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