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Author: ignougroup

[Solved]: Running time of CDCL compared to DPLL

February 8, 2017 ignougroup

Problem Detail: What’s the complexity of Conflict-Driven Clause Learning SAT solvers, compared to DPLL solvers? Was it proven that CDCL is faster in general? Are there instances of SAT that are hard for CDCL but easy for DPLL? Asked By : asd Read More …

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[Solved]: Example for the analysis of a recursive function

February 8, 2017March 27, 2017 ignougroup

Problem Detail:  l is a matrix of size [1…n, 1…n] function: rec(i,j) if (i*j == 0) return 1 else if (l[i,j] == 0) l[i,j] = 1 * rec(i-1,j) + 2 * rec(i,j-1) + 3 * rec(i-1,j-1) return l[i,j] end_function for Read More …

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[Solved]: A regular expression for a given formal language

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I wanted to ask if someone can help me to construct a regular expression over the alphabet ${a,b,x}$ for the language $L$ which is constituted by all strings containing an odd number of $a$’s, and in which between each Read More …

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[Solved]: Time Complexity of Regular Languages

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I wonder how I can go about proving that if a language L is decidable in o(nlog(n)) then L must be regular. I should probably mention that by “decidable” I mean “being decidable by single-tape deterministic turing machine”. Thanks Read More …

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[Solved]: $mathbf{NC}$ is closed under logspace reductions

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I am trying to solve the question 6.12 in Arora-Barak (Computational Complexity: A modern approach). The question asks you to show that the $mathsf{PATH}$ problem (decide whether a graph $G$ has a path from a given node $s$ to Read More …

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[Solved]: Double hashing – probe count probabilities

February 8, 2017March 27, 2017 ignougroup

Problem Detail: From TAoCP, Vol. 3 by Knuth we know that expected (mean) probe counts for hash tables with open adressing and double hashing collision-resolution are: $1 over 1 – alpha$ – for unsuccessful search ${1 over alpha} ln({1 over 1 Read More …

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[Solved]: Language independent software libraries

February 8, 2017March 27, 2017 ignougroup

Problem Detail: When trying to decide on the choice of a programming language for a specific task, people will often tell me: “use this language because it has the best library for the type of problems you are addressing”. I would Read More …

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[Solved]: Find the centre of a circle given two points lying on it and its radius

February 8, 2017March 27, 2017 ignougroup

Problem Detail: We have been given 2 points on a circle and its radius. Now I want to find out the centre point of such a circle. How can I code this efficiently without solving the quadratic equations? Asked By : Nikunj Read More …

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[Solved]: What is the difference between shortest distance and shortest path?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I am studying graph currently. I found a question, which asks for The List A[] which shows shortest distances between $V$ and every other vertex The List B[] which shows shortest paths between $V$ and every other vertex as Read More …

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[Solved]: Lazily computing a random permutation of the positive integers

February 8, 2017March 27, 2017 ignougroup

Problem Detail: Are there any existing efficient algorithms for lazily computing a random permutation of the positive integers in a given range (e.g. the range offered by an unsigned integer type in a CPU)? What I mean is this: An algorithm Read More …

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