Optimization and Physics: On the satisfiability of random Boolean formulae
Marc Mezard
TL;DR
This paper explores the intersection of optimization, physics, and computational complexity by analyzing the satisfiability of random Boolean formulas, demonstrating how physics concepts can yield new theoretical and practical insights.
Contribution
It introduces a physics-inspired approach to analyze satisfiability problems, bridging combinatorial optimization and statistical physics with novel theoretical and practical results.
Findings
New theoretical bounds on satisfiability thresholds
Practical algorithms inspired by physics methods
Deeper understanding of phase transitions in satisfiability
Abstract
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial optimization and computational complexity theory, is used as a guide to show the convergence between these fields and the statistical physics of disordered systems. New results on satisfiability, both on the theoretical and practical side, can be obtained thanks to the use of physics concepts and methods.
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