Handbook of Satisfiability

A review of the Statistical Mechanics approach to Random Optimization Problems

We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts. We also discuss how statistical mechanics methods can be used to investigate the behavior of local search and decima...

Random Satisfiability

Satisfiability has received a great deal of study as the canonical NP-complete problem. In the last twenty years a significant amount of this effort has been devoted to the study of randomly generated satisfiability instances and the performance of different algorithms on them. Historically, the motivation for studying random instances has been the desire to understand the hardness of “typical”...

Satisfiability Modulo Theories

Satisfiability Modulo Theories (SMT) refers to the problem of determining whether a first-order formula is satisfiable with respect to some logical theory. Solvers based on SMT are used as back-end engines in model checking applications such as bounded, interpolation-based, and predicate abstraction-based model checking. After a brief illustration of these uses, we survey the predominant techni...

Probabilistic Greedy Heuristics for Satisfiability Problems

We examine probabilistic greedy heuristics for maximization and minimization versions of the satisfiability problem. Like deterministic greedy algorithms, these heuristics construct a truth assignment one variable at a time. Unlike them, they set a variable true or false using a probabilistic mechanism, the probabilities of a true assignment depending on the incremental number of clauses satisf...

A Review on the International Handbook of Suicide Prevention: Research, Policy and Practice