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Percolation of satisfiability in finite dimensions

J. M. Schwarz·A. Alan Middleton
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Abstract

The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though there is a logical connectivity transition. In part of the disconnected phase, rare regions lead to a divergent running time for optimization algorithms. The thermodynamic ground state for the NP-hard two-dimensional maximum-satisfiability problem is typically unique. These results have implications for the computational study of disordered materials.

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J. M. Schwarz, A. Alan Middleton. 2003-09-10. Percolation of satisfiability in finite dimensions. https://doi.org/10.1103/physreve.70.035103

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