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Typical random 3-SAT formulae and the satisfiability threshold
[article]
2002
arXiv
pre-print
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We present a new structural (or syntatic) approach for estimating the satisfiability threshold of random 3-SAT formulae. ...
The method combines well with other techniques, and also applies to other problems, such as the 3-colourability of random graphs. ...
Experiments strongly suggest that satisfiability of random 3-SAT formulae (the 3-SAT problem) exhibits a sharp threshold or a phase transition as a function of a control parameter, the ratio c of the number ...
arXiv:cs/0211036v1
fatcat:o522jarxcnhvjcgnvcfs33qnny
Phase Transitions for Scale-Free SAT Formulas
2017
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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Similar to the uniform model, on formulas with k>=3, we find that the phase transition regime corresponds to a set of formulas that are difficult to solve by backtracking search. ...
Recently, a number of non-uniform random satisfiability models have been proposed that are closer to practical satisfiability problems in some characteristics. ...
The study of random SAT formulas is concerned with characterizing probability distributions over satisfiability formulas. ...
doi:10.1609/aaai.v31i1.11133
fatcat:64b4xw3zuba3re3oqtxuhuxtem
Why almost all satisfiable $k$-CNF formulas are easy
2007
Discrete Mathematics & Theoretical Computer Science
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We rigorously analyze the structure of the space of satisfying assignments of a random formula in that distribution, showing that basically all satisfying assignments are clustered in one cluster, and ...
International audience Finding a satisfying assignment for a $k$-CNF formula $(k \geq 3)$, assuming such exists, is a notoriously hard problem. ...
As we already mentioned, the event of a random formula in P n,m being satisfiable, when m/n is some constant above the satisfiability threshold, is very unlikely. ...
doi:10.46298/dmtcs.3538
fatcat:gx5iozuryffi7nfoqc7mxrzxiy
Solution space heterogeneity of the randomK-satisfiability problem: Theory and simulations
2010
Journal of Physics, Conference Series
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The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity ...
In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem. ...
This work was partially supported by the National Science Foundation of China (Grant numbers 10774150 and 10834014) and the China 973-Program (Grant number 2007CB935903). ...
doi:10.1088/1742-6596/233/1/012011
fatcat:k2j54j47afgajcfscj3euzpee4
Random k-SAT and the Power of Two Choices
[article]
2013
arXiv
pre-print
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We study an Achlioptas-process version of the random k-SAT process: a bounded number of k-clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a ...
In particular, while a rule to delay the 2-SAT threshold was known previously, this is the first proof of a rule to shift the threshold of k-SAT for k >= 3. ...
A second central open question in this area is whether or not random k-SAT formulae (k ≥ 3) at or near the satisfiability threshold are computationally hard (2-SAT is solvable in polynomial time in the ...
arXiv:1209.5313v2
fatcat:a3v2gx46rjgdhh4oc7mlggqxp4
Glassy behavior and jamming of a random walk process for sequentially satisfying a constraint satisfaction formula
2010
European Physical Journal B : Condensed Matter Physics
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2009 pre-print arXiv:0907.0295v1 fatcat:fb7e2m46cfddtel23jql5lsfveOther Versions
Random K-satisfiability (K-SAT) is a model system for studying typical-case complexity of combinatorial optimization. ...
For random 3-SAT, the jamming transition point α_j is larger than the solution space clustering transition point α_d, and its value can be predicted by a long-range frustration mean-field theory. ...
As a comparison, the satisfiability threshold of the random 3-SAT problem is α s ≈ 4.27 [7, 19] , and that of the random 4-SAT problem is α s ≈ 9.93 [19] . ...
doi:10.1140/epjb/e2010-00021-x
fatcat:ajfvop7pfjfvjc5gjzadlpwlm4
Satisfiability Threshold of the Skewed Random k-SAT
[chapter]
2005
Lecture Notes in Computer Science
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We also prove an upper bound on the satisfiability threshold and a linear lower bound on the number of literals in satisfying partial assignments of skewed random k-SAT formulas. ...
The essential feature of the random k-SAT is that positive and negative literals occur with equal probability in a random formula. ...
We proved an upper bound on the satisfiability threshold and a lower bound on the number of literals in satisfying partial assignments for a skewed random k-SAT formula. ...
doi:10.1007/11527695_21
fatcat:tpxrhql54bhsdi4agldswhdxoy
Regular Random k-SAT: Properties of Balanced Formulas
2006
Journal of automated reasoning
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We consider a model for generating random k-SAT formulas, in which each literal occurs approximately the same number of times in the formula clauses (regular random k-SAT). ...
We will show that for α > 3.78 w.h.p. 1 random Regular 3-SAT formulas are unsatisfiable. ...
To sum up the probability that T satisfies a random Reg-3-SAT formula is : Pr(T satisfies F ) = 3αn/2 ! ( 3α/2 + 1)! µn 3α/2 ! (1−µ)n 2 ( 3α/2 + 1)! 2µn 3α/2 ! 2(1−µ)n (3αn)! ...
doi:10.1007/s10817-005-9012-z
fatcat:ba6yzzc655fu5dwaqtjyfrniqu
Hiding Solutions in Random Satisfiability Problems: A Statistical Mechanics Approach
2002
Physical Review Letters
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On the basis of statistical mechanics results, we propose random generators of hard and satisfiable instances for the 3-satisfiability problem (3SAT). ...
The design of the hardest problem instances is based on the existence of a first order ferromagnetic phase transition and the glassy nature of excited states. ...
The transition point moves towards the random 3-SAT threshold a c , and the computational complexity increases with p 0 . ...
doi:10.1103/physrevlett.88.188701
pmid:12005728
fatcat:lbqrp62sgjhlrjf5bhnamgzgyi
Communities of solutions in single solution clusters of a randomK-satisfiability formula
2009
Physical Review E
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2009 pre-print arXiv:0903.2908v2 fatcat:g4geywabq5dwninypzti5wolkaOther Versions
This paper explores single solution clusters of random 3- and 4-SAT formulas through unbiased and biased random walk processes and the replica-symmetric cavity method of statistical physics. ...
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips ...
Results for random 3-SAT.-As an example, Fig. 1 (a) shows the simulation results for a random 3-SAT formula of N = 10 6 and α = 4.25. ...
doi:10.1103/physreve.80.066108
pmid:20365232
fatcat:dh5ui33oozahlgw7hxdmtqj62m
A review of the Statistical Mechanics approach to Random Optimization Problems
[article]
2008
arXiv
pre-print
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We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. ...
We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts. ...
random 3-SAT [55, 56] and XORSAT [33] . ...
arXiv:0802.1829v1
fatcat:wv65adl4v5cmzjxon6unr7mg6q
Faster Random k-CNF Satisfiability
2020
International Colloquium on Automata, Languages and Programming
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We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly. We build upon the algorithms of Schöning 1999 and Dantsin et al. in 2002. ...
The Schöning algorithm works by trying many possible random assignments, and for each one searching systematically in the neighborhood of that assignment for a satisfying solution. ...
Preliminaries In this section we will give the definition of random k-CNF Satisfiability (random k-CNF SAT) at the threshold. ...
doi:10.4230/lipics.icalp.2020.78
dblp:conf/icalp/LincolnY20
fatcat:v6lxpmxk2nge3n6qt6rpuos72m
On the Empirical Time Complexity of Scale-Free 3-SAT at the Phase Transition
[chapter]
2019
Lecture Notes in Computer Science
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The hardness of formulas at the solubility phase transition of random propositional satisfiability (SAT) has been intensely studied for decades both empirically and theoretically. ...
The main contribution of this paper utilizes the scale-free random 3-SAT model to isolate heterogeneity as an important factor in the scaling discrepancy between complete and SLS solvers at the uniform ...
are typically recognized for their performance on uniform random k-SAT, do not benefit much (if at all) from heterogeneity. (3) Random instances (even heterogeneous ones) close to the satisfiability threshold ...
doi:10.1007/978-3-030-17462-0_7
fatcat:tgbcl5pbjffipgrgxvu7xhjjvy
Critical behavior in the computational cost of satisfiability testing
1996
Artificial Intelligence
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There are intriguing similarities and differences between these effects and kinetic phenomena studied in statistical physics, in glasses and in spin glasses. Fig. 1. (a) Threshold for random 3-SAT. ...
In previous work, we employed finite-size scaling, a method from statistical mechanics, to explore the crossover from the SAT regime of k-SAT, where almost all randomly generated expressions are satisfiable ...
We also thank Jimi Crawford, Ian Gent, Tad Hogg, Robert Schrag, Toby Walsh, and Colin Williams for useful comments and discussions. ...
doi:10.1016/0004-3702(95)00056-9
fatcat:nwmqyvj7wbbwxedbbzfarlpj2q
Reweighted Belief Propagation and Quiet Planting for Random K-SAT
2014
Journal on Satisfiability, Boolean Modeling and Computation
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We are hence able to generate at the same time a typical random SAT instance and one of its solutions. ...
region of parameters in the random K-satisfiability problem. ...
Most importantly we give further theoretical justification for why the λ * -planted random 3-SAT formulas are (together with benchmarks from [16] ) the hardest satisfiable formulas on the market of hard ...
doi:10.3233/sat190096
fatcat:locashkltngn5cixxepvnxh6va
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