The Potential of Restarts for ProbSAT

This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.Comment: Eurocast 201

Survey-propagation decimation through distributed local computations

We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the "SP diffusion algorithm", diffuses as dynamical information the maximum bias over the system, so that variable nodes can decide to freeze in a self-organized way, each variable making its decision on the basis of purely local information. The second solver, called the "SP reinforcement algorithm", makes use of time-dependent external forcing messages on each variable, which let the variables get completely polarized in the direction of a solution at the end of a single convergence. Both methods allow us to find a solution of the random 3-SAT problem in a range of parameters comparable with the best previously described serialized solvers. The simulated time of convergence towards a solution (if these solvers were implemented on a distributed device) grows as log(N).Comment: 18 pages, 10 figure

The Fractal Dimension of SAT Formulas

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the structure of these formulas in terms of complex networks, with the long-term aim of explaining the success of these SAT solving techniques, and possibly improving them. We study the fractal dimension of SAT formulas, and show that most industrial families of formulas are self-similar, with a small fractal dimension. We also show that this dimension is not affected by the addition of learnt clauses. We explore how the dimension of a formula, together with other graph properties can be used to characterize SAT instances. Finally, we give empirical evidence that these graph properties can be used in state-of-the-art portfolios.Comment: 20 pages, 11 Postscript figure

Proceedings of SAT Competition 2021 : Solver and Benchmark Descriptions

Non peer reviewe

Proceedings of SAT Competition 2020 : Solver and Benchmark Descriptions

Non peer reviewe