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, New Mexico/ Santa Fe Institute, Santa Fe, New Mexico;CCS-5, Los Alamos National Laboratory, Los Alamos, New Mexico;Archimedean Academy, 12425 SW Sunset Drive, Miami, Florida;Department of Computer Science, Rice University, Houston, Texas
Venue:
Random Structures & Algorithms
Year:
2007

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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 is continuous but its derivative diverges. This is the first case in which a phase transition of this type has been rigorously established for a random constraint satisfaction problem. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007