A continuous-discontinuous second-order transition in the satisfiability of random Horn-SAT formulas

Authors:
Cristopher Moore;Gabriel Istrate;Demetrios Demopoulos;Moshe Y. Vardi
Affiliations:
Department of Computer Science, University of New Mexico, Albuquerque, NM;CCS-5, Los Alamos National Laboratory, Los Alamos, NM;Archimedean Academy, Miami, FL;Department of Computer Science, Rice University, Houston, TX
Venue:
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Year:
2005

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Abstract

We compute the probability of satisfiability of a class of random Horn-SAT formulae, motivated by a connection with the nonemptiness problem of finite tree automata. In particular, when the maximum clause length is three, this model displays a curve in its parameter space along which the probability of satisfiability is discontinuous, ending in a second-order phase transition where it becomes continuous. This is the first case in which a phase transition of this type has been rigorously established for a random constraint satisfaction problem.