Linear Pseudo-Boolean (LPB) constraints denote inequalities between arithmetic sums of weighted Boolean functions and provide a significant extension of the modeling power of purely propositional constraints. They can be used to compactly describe many discrete EDA problems with constraints on linearly combined, parameterized weights, yet also offer efficient search strategies for proving or disproving whether a satisfying solution exists. Furthermore, corresponding decision procedures can easily be extended for minimizing or maximizing an LPB objective function, thus providing a core optimization method for many problems in logic and physical synthesis. In this paper we review how recent advances in satisfiability (SAT) search can be extended for pseudo-Boolean constraints and describe a new LPB solver that is based on generalized constraint propagation and conflict-based learning. We present a comparison with other, state-of-the-art LPB solvers which demonstrates the overall efficiency of our method.

For the last ten years, a significant amount of work in the constraint community has been devoted to the improvement of complete methods for solving soft constraints networks. We wanted to see how recent progress in the weighted CSP (WCSP) field could compete with other approaches in related fields.

Artificial Intelligence, to appear Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most competitive exact algorithms for solving max-SAT. In this paper, we propose and investigate a number of strategies for max-SAT. The first strategy is a set of unit propagation or unit resolution rules for max-SAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max-SAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a a binary-clause first rule and a dynamicweighting variable ordering rule, which are motivated by a thorough analysis of two existing well-known variable orderings. Based on the analysis of these strategies, we develop an exact solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from the max-SAT libraries show that our new solver outperforms most of the existing exact max-SAT solvers, with orders of magnitude of improvement in many cases.

This paper introduces a new hybrid method for efficiently integrating Pseudo-Boolean (PB) constraints into generic SAT solvers in order to solve PB satisfiability and optimization problems. To achieve this, we adopt the cutting-plane technique to draw inferences among PB constraints and combine it with generic implication graph analysis for conflictinduced learning. Novel features of our approach include a light-weight and efficient hybrid learning and backjumping strategy for analyzing PB constraints and CNF clauses in order to simultaneously learn both a CNF clause and a PB constraint with minimum overhead and use both to determine the backtrack level. Several techniques for handling the original and learned PB constraints are introduced. Overall, our method benefits significantly from the pruning power of the learned PB constraints, while keeping the overhead of adding them into the problem low. In this paper, we also address two other methods for solving PB problems, namely Integer Linear Programming (ILP) and pre-processing to CNF SAT, and present a thorough comparison between them and our hybrid method. Experimental comparison of our method against other hybrid approaches is also demonstrated. Additionally, we provide details of the MiniSAT-based implementation of our solver Pueblo to enable the reader to construct a similar one.

We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of propositional logic facilitates modeling search problems and often results in very concise encodings. We propose two "native" local-search solvers for theories in the extended language.

search problems

We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M , if M C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudo-boolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the one-step provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.

Many important tasks in circuit design and verification can be performed in practice via reductions to Boolean Satisfiability (SAT), making SAT a fundamental EDA problem. However such reductions often leave out application-specific structure, thus handicapping EDA tools in their competition with creative engineers. Successful attempts to represent and utilize additional structure on Boolean variables include recent work on 0-1 Integer Linear Programming (ILP) and on symmetries in SAT. Those extensions gracefully...

Recent algorithmic advances in Boolean satisfiability (SAT), along with highly efficient solver implementations, have enabled the successful deployment of SAT technology in a wide range of applications domains, and particularly in electronic design automation (EDA). SAT is increasingly being used as the underlying model for a number of applications in EDA. This paper describes how to formulate two problems in power estimation of CMOS combinational circuits as SAT problems or 0–1 integer linear programming (ILP). In these circuits, it was proven that maximizing dissipation is equivalent to maximizing gate output activity, appropriately weighted to account for differing load capacitances. The first problem in this work deals with identifying an input vector pair that maximizes the weighted circuit activity. In the second application we attempt to find an estimate for the maximum power-up current in circuits where power cut-off or gating techniques are used to reduce leakage current. Both problems were successfully formulated as SAT problems. SAT-Based and generic Integer Linear Programming (ILP) solvers are then used to find a solution. The experimental results obtained on a large number of benchmark circuits provide promising evidence that the proposed complete approach is both viable and useful and outperforms the random approach.

Abstract. We propose and study a technique to improve the performance of those local-search SAT solvers that proceed by executing a prespecified number of tries, each starting with an element of the space of all truth assignments and performing a prespecified number of local-search steps (flips). Based on the input theory T, our method first constructs a collection of its relaxations, that is, theories whose models are easy to compute and “almost ” satisfy T. It then uses a local-search algorithm to compute models of the relaxed theories and, finally, uses these models as starting points for tries when executing the local search algorithm on T. To construct relaxations our method takes advantage of high-level representation of search problems, which separate the specification of a search problem from the description of its particular instances. The method is general. We applied it to WSAT, a local-search SAT solver for CNF theories, and to WSAT(cc), a local-search SAT algorithm for theories in the language of propositional logic with cardinality constraints. Experimental results demonstrate its effectiveness for both local-search algorithms we studied. 1