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Exact enumeration of satisfiable 2-SAT formulae
[article]

2021
*
arXiv
*
pre-print

We obtain

arXiv:2108.08067v1
fatcat:kxuoquwxz5gobldqg3zw5rtehy
*exact*expressions counting the*satisfiable**2*-*SAT**formulae*and describe the structure*of*associated implication digraphs. Our approach is based on generating function manipulations. ... We expect these*exact**formulae*to be amenable to rigorous asymptotic analysis using complex analytic tools, leading to a more detailed picture*of*the*2*-*SAT*phase transition in the future. ... Having*exact*expressions for*2*-*SAT**formulae*potentially opens many new possibilities to describe the properties*of*a typical*2*-*SAT**formula*. ...##
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MAX-SAT for Formulas with Constant Clause Density Can Be Solved Faster Than in $\mathcal{O}(2^n)$ Time
[chapter]

2006
*
Lecture Notes in Computer Science
*

We give an

doi:10.1007/11814948_26
fatcat:jybmdhppwfatvdp7tqn765wpgi
*exact*deterministic algorithm for MAX-*SAT*. ... Worst-case upper bounds for MAX-*SAT*less than O(*2*n ) were previously known only for k-CNF*formulas*and for CNF*formulas*with small clause density. where |F | is the size*of*input*formula*F , m is the ... There is an*exact*deterministic algorithm that solves MAX-*SAT*for*formulas*with constant clause density inO(c n ) time where c <*2*. ...##
###
Enumerative counting is hard

1989
*
Information and Computation
*

An n-variable Boolean

doi:10.1016/0890-5401(89)90063-1
fatcat:bgvpotvtqnchxheic32ny77hpe
*formula*may have anywhere from 0 to*2*"*satisfying*assignments. ... Can a polynomial-time machine, given such a*formula*, reduce this exponential number*of*possibilities to a small number*of*possibilities? ... We have r new leaves, where 26r=*2*ISI <2k.*2*. COMBINE*FORMULAS*and RUN*ENUMERATOR*. Combine f ...##
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Enumerative counting is hard

1988
*
[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
*

An n-variable Boolean

doi:10.1109/sct.1988.5279
dblp:conf/coco/CaiH88
fatcat:mzratsooqjg5riutgc6x2inpua
*formula*may have anywhere from 0 to*2*"*satisfying*assignments. ... Can a polynomial-time machine, given such a*formula*, reduce this exponential number*of*possibilities to a small number*of*possibilities? ... We have r new leaves, where 26r=*2*ISI <2k.*2*. COMBINE*FORMULAS*and RUN*ENUMERATOR*. Combine f ...##
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Satisfiability on Mixed Instances

2016
*
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
*

We show that there is an algorithm which for any such

doi:10.1145/2840728.2840768
dblp:conf/innovations/ChenS16
fatcat:pkhlcnd75beernitffblimhuvm
*formula*with a constant number*of*quantifier blocks and*of*size n c , where c < 5/4, solves*satisfiability*in time*2*n−n Ω(1) . ... The study*of*the worst-case complexity*of*the Boolean*Satisfiability*(*SAT*) problem has seen considerable progress in recent years, for various types*of*instances including CNFs [16, 15, 20, 21] , Boolean ... Introduction Boolean*Satisfiability*(*SAT*) is the canonical NP-complete problem. Much effort has gone into designing and analyzing*exact*algorithms for*SAT*. ...##
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Smallest MUS Extraction with Minimal Hitting Set Dualization
[chapter]

2015
*
Lecture Notes in Computer Science
*

An unsatisfiable

doi:10.1007/978-3-319-23219-5_13
fatcat:q2qlgjswybe2fnypjqnczktyty
*formula*can have multiple MUSes, some*of*which provide more insights than others. Different criteria can be considered in order to identify a good minimal explanation. ... Among these, the size*of*an MUS is arguably one*of*the most intuitive. ... Call a*SAT*solver on the resulting*formula*, requesting an MHS*of*size k. If the*formula*is*satisfiable*, then we have a new MHS*of*size k that also hits C. ...##
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Computing the Density of States of Boolean Formulas
[chapter]

2010
*
Lecture Notes in Computer Science
*

In this paper we consider the problem

doi:10.1007/978-3-642-15396-9_6
fatcat:ba4b72rtbzayhg2bc3bfugse5i
*of*computing the density*of*states*of*a Boolean*formula*in CNF, a generalization*of*both MAX-*SAT*and model counting. ... Using this method, we show the first known results on the density*of*states*of*several widely used*formulas*and we provide novel insights about the behavior*of*random 3-*SAT**formulas*around the phase transition ... The true density is computed by*exact**enumeration*. ...##
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Paradigms for Parameterized Enumeration
[article]

2013
*
arXiv
*
pre-print

First we define formally different notions

arXiv:1306.2171v1
fatcat:632mpnrbofcstbad5plje2vle4
*of*efficient*enumeration*in the context*of*parameterized complexity. ... The aim*of*the paper is to examine the computational complexity and algorithmics*of**enumeration*, the task to output all solutions*of*a given problem, from the point*of*view*of*parameterized complexity. ...*Enumeration*classification for MaxOnes-*SAT*The self-reducibility technique was in particular applied in order to*enumerate*all*satisfying*assignments*of*a generalized CNF-*formula*[1] , thus allowing to ...##
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An Exact Algorithm for the Boolean Connectivity Problem for k-CNF
[chapter]

2010
*
Lecture Notes in Computer Science
*

We present an

doi:10.1007/978-3-642-14186-7_15
fatcat:uywyeojbbbgnfinv7zkgae57ca
*exact*algorithm for a PSPACE-complete problem, denoted by CONNkSAT, which asks if the solution space for a given k-CNF*formula*is connected on the n-dimensional hypercube. ... that the*SAT*problem (with no restriction to the clause length) is not solvable in time O((*2*− ) n ) for any constant > 0. ... number*of*vertices*of*a graph for the traveling salesman problem, or the number*of*variables*of*a*formula*for the*satisfiability*problem) is there an*exact*algorithm for the problem in time O(*2*n ), or ...##
###
An exact algorithm for the Boolean connectivity problem for k-CNF

2011
*
Theoretical Computer Science
*

We present an

doi:10.1016/j.tcs.2011.04.041
fatcat:jc65muc7cvfcfnstkind7uc4mu
*exact*algorithm for a PSPACE-complete problem, denoted by CONNkSAT, which asks whether the solution space for a given k-CNF*formula*is connected on the ndimensional hypercube. ... > 0, provided that the*SAT*problem (with no restriction to the clause length) is not solvable in time O((*2*− ϵ) n ) for any constant ϵ > 0. ... number*of*vertices*of*a graph for the traveling salesman problem, or the number*of*variables*of*a*formula*for the*satisfiability*problem) is there an*exact*algorithm for the problem in time O(*2*n ), or ...##
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An Approximation Algorithm for #k-SAT

2012
*
Symposium on Theoretical Aspects of Computer Science
*

We present a simple randomized algorithm that approximates the number

doi:10.4230/lipics.stacs.2012.78
dblp:conf/stacs/Thurley12
fatcat:375aoaw36nclvckyjuip4bv4kq
*of**satisfying*assignments*of*Boolean*formulas*in conjunctive normal form. ... fastest*exact*algorithms for the problem. ...*Formulas*with few solutions For*formulas*with few solutions we will now present an algorithm relying on a simple*enumeration**of*solutions by using a k-*SAT*algorithm as a subroutine. ...##
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Generating functions and the satisfiability threshold

2004
*
Discrete Mathematics & Theoretical Computer Science
*

Although the threshold has been proved to exist for the

doi:10.46298/dmtcs.325
fatcat:tes7p725vncadciwxncc75mu6i
*2*-*SAT**formulæ*and for closely related problems like 3-XORSAT, there is still no proof for the 3-*sat*problem. ... International audience The 3-*SAT*problem consists in determining if a boolean*formula*with 3 literals per clause is*satisfiable*. ... Acknowledgements I want to thank Olivier Dubois for all the time he took to explain his articles to me, and Philippe Flajolet for pointing to generating functions as a useful tool for*enumeration*in threshold ...##
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An Approximation Algorithm for #k-SAT
[article]

2011
*
arXiv
*
pre-print

We present a simple randomized algorithm that approximates the number

arXiv:1107.2001v1
fatcat:4ti42kporvef7kgmm2qhlqotli
*of**satisfying*assignments*of*Boolean*formulas*in conjunctive normal form. ... fastest*exact*algorithms for the problem. ...*Formulas*with few solutions For*formulas*with few solutions we will now present an algorithm relying on a simple*enumeration**of*solutions by using a k-*SAT*algorithm as a subroutine. ...##
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Towards backbone computing: A Greedy-Whitening based approach

2018
*
AI Communications
*

Computing a part

doi:10.3233/aic-180763
fatcat:tjrrzv7hvne5hbs2v6d54ipcbq
*of*backbone efficiently could guide the following searching in*SAT*solving and accelerate the process, which is widely used in fault localization, product configuration, and*formula*simplification ... Backbone computing is accelerated since*SAT*testings*of*literals in BL ( ) are saved. ... Acknowledgements This work is supported the by the program*of*Theoretical and Practical Research about Linear Time Logic (LTL)*Satisfiability*(61572197) from National Natural Science Foundation*of*China ...##
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Exact sat-based toffoli network synthesis

2007
*
Proceedings of the 17th great lakes symposium on Great lakes symposium on VLSI - GLSVLSI '07
*

Our iterative algorithm formulates the synthesis problem with d Toffoli gates as a sequence

doi:10.1145/1228784.1228812
dblp:conf/glvlsi/GrosseCDD07
fatcat:mm3iiizrn5dz3glfrbjh4q52cu
*of*Boolean*Satisfiability*(*SAT*) instances. ... In this paper, we present the first*exact*synthesis algorithm for reversible functions using generalized Toffoli gates. ... In this paper we present the first*exact*algorithm for Toffoli synthesis*of*a reversible function 1 . Our method uses an iterative algorithm that is based on Boolean*Satisfiability*(*SAT*). ...
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