From SAT to SAT-UNSAT using P systems with dissolution rules

The SAT-UNSAT transition in the adversarial SAT problem

Adversarial SAT (AdSAT) is a generalization of the satisfiability (SAT) problem in which two players try to make a boolean formula true (resp. false) by controlling their respective sets of variables. AdSAT belongs to a higher complexity class in the polynomial hierarchy than SAT and therefore the nature of the critical region and the transition are not easily paralleled to those of SAT and wor...

New Upper Bounds for the SAT / UNSAT Threshold for Shapes

Phase transitions not only occur in physics but also in many problems in computer science. Among the problems from computer science, there are many NP-complete ones. An especially important problem is the satisfiability problem, SAT, for Boolean formulas. When phase transitions of SAT problems are studied, the corresponding formulas are usually restricted to conjunctive normal form, i.e., the f...

From Parallel SAT to Distributed SAT

This tutorial will present an overview of parallelism in SAT. It will start with a presentation of classical divide and conquer techniques, discuss their ancient origin and compare them to more recent portfolio-based algorithms. It will then present the impact of clause-sharing on their performances and discuss various strategies used to control the communication overhead. A particular techniqu...

φ φ φ φ φ φ k From Max - SAT to Min - UNSAT : Insights and Applications

This report describes a strong connection between maximum satisfiability and minimally-unsatisfiable subfor-mulas of any constraint system, as well as techniques for exploiting it. Focusing on CNF formulas, we explore this relationship and present novel algorithms for extracting minimally-unsatisfiable subformulas, including one that finds all such subformulas. We present experimental results s...

SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems