We consider the following problem. Given a 2-cnf formula, is it possible to remove at most k clauses so that the resulting 2-cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-k 2-SAT, 2-cnf deletion, and 2-SAT deletion. The status of the fixed-parameter tractability of this problem is a long-...

The success of portfolio approaches in SAT solving relies on the observation that different SAT solving techniques perform better on different SAT instances. The Algorithm Selection Problem faces the problem of choosing, using a prediction model, the best algorithm from a predefined set, to solve a particular instance of a problem. Using Machine Learning techniques, this prediction is performed...

We present Regular-SAT, an extension of Boolean Satisfiability based on a class of many-valued CNF formulas. Regular-SAT shares many properties with Boolean SAT, which allows us to generalize some of the best known SAT results and apply them to Regular-SAT. In addition, Regular-SAT has a number of advantages over Boolean SAT. Most importantly, it produces more compact encodings that capture pro...

Constraint satisfaction deals with developing automated techniques for solving computationally hard problems in a declarative fashion. This note summarizes a dissertation that focuses on search-based methods for the propositional satisfiability problem (SAT). As methods for propositional satisfiability checking have rapidly progressed during the last 15 years, implementations of decision proced...

In the maximum 2-satisfiability problem (abbreviated as Max 2-Sat), one is given a Boolean formula in conjunctive normal form, such that each clause contains at most two literals. The task is to find an assignment to the variables of the formula such that a maximum number of clauses is satisfied. Max 2-Sat is a classic optimization problem. Its decision version was proved NP-complete by Garey, ...

Recently, edge matching puzzles, an NP-complete problem, have received, thanks to money-prized contests, considerable attention from wide audiences. We consider these competitions not only a challenge for SAT/CSP solving techniques but also as an opportunity to showcase the advances in the SAT/CSP community to a general audience. This paper studies the NP-complete problem of edge matching puzzl...

Max-SAT is an extensively studied optimization problem and variations of Max-SAT (like Partial Max-SAT and Weighted Max-SAT) can be used for computing minimal diagnoses. In this report we (1) describe a family of algorithms for computing minimal diagnoses based on Max-SAT and (2) experimentally evaluate the performance and optimality of these algorithms on a benchmark consisting of 74XXX/ISCAS8...

Consider SAT, the prototypical example of an NP-complete problem. An instance of this problem consists of a Boolean function f (x1, . . . ,xn) = c1 ∧ . . .∧ cm; the SAT problem asks you to determine whether there exists a satisfying assignment—that is, an input (a1, . . . ,an) such that f (a1, . . . ,an) = 1. UNIQUE-SAT is a variant of SAT that poses the same problem with the restriction that f...

Advances in SAT solver technology have enabled many automated analysis and reasoning tools to reduce their input problem to a SAT problem, and then to use an efficient SAT solver to solve the underlying analysis or reasoning problem. The solving time for SAT solvers can vary substantially for semantically identical SAT problems depending on how the problem is expressed. This property motivates ...