Many applications of SAT solving can profit from minimal models—a partial variable assignment that is still a witness for satisfiability. Examples include software verification, model checking, and counterexample-guided abstraction refinement. In this paper, we examine how a given model can be minimized for SAT instances that have been obtained by Tseitin encoding of a full propositional logic ...

Alloy [Jac02a] is a widely adopted relational modeling language. Its appealing syntax and the support provided by the Alloy Analyzer [Jac02b] tool make model analysis accessible to a public of non-specialists. A model and property are translated to a propositional formula, which is fed to a SAT-solver to search for counterexamples. The translation strongly depends on user-provided bounds for da...

SAT solving has gained tremendous interest. On the practical side there have been considerable performance improvements, due to new highly efficient algorithms, new heuristics, and optimized data structures. There are new applications and reformulations of important classical problems, mainly in the context of formal methods, where SAT solving is also applied successfully in an industrial setti...

A long range frustration index R is introduced to the finite connectivity Viana–Bray ±J spin glass model as a new order parameter. This order parameter is then applied to the random K-satisfiability (K-SAT) problem to understand its satisfiability transition and to evaluate its global minimum energy. Associated with a jump in R from zero to a finite value, SAT-UNSAT transition in random 3-SAT o...

Model checking is a formal technique for automatically verifying that a finite-state model satisfies a temporal property. In model checking, generally Binary Decision Diagrams (BDDs) are used to efficiently encode the transition relation of the finite-state model. Recently model checking algorithms based on Boolean satisfiability (SAT) procedures have been developed to complement the traditiona...

The relationship between insulin sensitivity and overall obesity is well established. However, there remains debate as to which of the fat depots, visceral abdominal tissue (VAT) or subcutaneous abdominal tissue (SAT), is of greater importance. Also, the relationship between fat distribution and insulin secretion is largely unknown. We studied SI, acute insulin response (AIR), and disposition i...

The success of portfolio approaches in SAT solving relies on the observation that different SAT solvers may dramatically change their performance depending on the class of SAT instances they are trying to solve. In these approaches, a set of features of the problem is used to build a prediction model, which classifies instances into classes, and computes the fastest algorithm to solve each of t...

In recent years there has been signi1cant interest in the study of random k-SAT formulae. For a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct, non-complementary literals from its variables (k-clauses). A random k-SAT formula Fk(n; m) is formed by selecting uniformly and independently m clauses from Bk and taking their conjunction. Motivated b...

The parameterized satisfiability problem over a set of Boolean relations Γ (SAT(Γ)) is the problem of determining whether a conjunctive formula over Γ has at least one model. Due to Schaefer’s dichotomy theorem the computational complexity of SAT(Γ), modulo polynomial-time reductions, has been completely determined: SAT(Γ) is always either tractable or NP-complete. More recently, the problem of...

This paper addresses the problem of counting models in integer linear programming (ILP) using Boolean Satisfiability (SAT) techniques, and proposes two approaches to solve this problem. The first approach consists of encoding ILP instances into pseudo-Boolean (PB) instances. Moreover, the paper introduces a model counter for PB constraints, which can be used for counting models in PB as well as...