Abstract not found

Translation to Boolean satisfiability is an important approach for solving state-space reachability problems that arise in planning and verification. Many important problems, however, involve numeric variables; for example, C programs or planning with resources. Focussing on planning, we propose a method for translating such problems into propositional SAT, based on an approximation of reachable variable domains. We compare to a more direct translation into “SAT modulo theory” (SMT), that is, SAT extended with numeric variables and arithmetic constraints. Though translation to SAT generates much larger formulas, we show that it typically outperforms translation to SMT almost up to the point where the formulas don’t fit into memory any longer. We also show that, even though our planner is optimal, it tends to outperform state-of-the-art sub-optimal heuristic planners in domains with tightly constrained resources. Finally we present encouraging initial results on applying the approach to model checking. 1

This thesis studies the problem of determining the satisfiability of a Boolean combination of binary difference constraints of the form x − y ≤ c where x and y are numeric variables and c is a constant. In particular, we present an incremental and model-based interpreter for the theory of difference constraints in the context of a generic Boolean satisfiability checking procedure capable of incorporating interpreters for arbitrary theories. We show how to use the model based approach to efficiently make inferences with the option of complete inference.

Verification problems require to reason in theories of data structures and fragments of arithmetic. Thus, decision procedures for such theories are needed, to be embedded in, or interfaced with, proof assistants or software model checkers. Such decision procedures ought to be sound and complete, to avoid false negatives and false positives, efficient, to handle large problems, and easy to combine, because most problems involve multiple theories. The rewritebased approach to decision procedures aims at addressing these sometimes conflicting issues in a uniform way, by harnessing the power of general first-order theorem proving. In this article, we generalize the rewrite-based approach from deciding the satisfiability of sets of ground literals to deciding that of arbitrary ground formulæ in the theory. Next, we present polynomial rewrite-based satisfiability procedures for the theories of records with extensionality and integer offsets. The generalization of the rewrite-based approach to arbitrary ground formulæ and the polynomial satisfiability procedure for the theory of records with extensionality use the same key property – termed variable-inactivity – that allows one to combine theories in a simple way in the rewrite-based approach.

Abstract. Many domains of reasoning include a set of distinct objects. For general-purpose automated theorem provers, this property has to be specified explicitly, by including distinctness axioms. Since their number grows quadratically with the number of distinct objects, this results in large and clumsy specifications, that may affect performance adversely. We show that object distinctness can be handled directly by a modified superposition-based inference system, including additional inference rules. The new calculus is shown to be sound and complete. A preliminary implementation shows promising results in the theory of arrays. 1

Abstract. We extend the DPLL(T) framework for satisfiability modulo theories to address richer theories by means of increased flexibility in the interaction between the propositional and theory-specific solvers. We decompose a rich theory into a chain of increasingly more complex subtheories, and define a corresponding propagation strategy which favors the simpler subtheories using two mechanisms. First, subtheory propagation is prioritized so that more expensive propagation is avoided whenever possible. Second, constraints are filtered along the path from simpler to more complex propagation, thus easing the task of propagation for each subtheory. We present this strategy formally in a refined abstract DPLL(T) system and provide a concrete algorithmic skeleton with a proof of correctness. 1

The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifier-free formulæ. We propose an approach that decomposes the formula in such a way that its definitional part, including the theory, can be compiled by a rewrite-based firstorder theorem prover, and the residual problem can be decided by an SMT-solver, based on the Davis-Putnam-Logemann-Loveland procedure. The resulting decision by stages mechanism may unite the complementary strengths of first-order provers and SMT-solvers. We demonstrate its practicality by giving decision procedures for the theories of records, integer offsets and arrays, with or without extensionality, and for combinations including such theories.

Formal verification is the act of proving correctness of a hardware or software system using formal methods of mathematics. In the last decade formal hardware verification has seen an increasing usage of Satisfiability Modulo Theories (SMT) solvers. SMT solvers check satisfiability of first-order formulas, where certain symbols are interpreted according to background theories like integer or bit-vector arithmetic. Since the formulas used to encode correctness of hardware design are mostly quantifier-free, SMT solvers are built as theory-aware extensions of propositional satisfiability solvers. As a consequence, SMT solvers do not “naturally ” support quantified formulas, which are needed for verification of complex software systems. Thus, while SMT solvers are already an industrially viable tool for formal hardware verification, software applications are not as developed. This thesis focuses on both the software verification specific problems in the construction of SMT solvers, as well as SMT-specific parts of a software verification system. On the SMT side, we present algorithms for efficient non-ground reasoning through quantifier instantiation and techniques for proof generation and proof checking for quantifier-rich software verification problems. On the verification tool side, we present methods for transforming programs into formulas in a solver-friendly way, with particular emphasis on design of annotations guiding the SMT solver through the non-ground part of the problem. The theoretical developments presented here were experimentally validated in implementations of state-of-the-art tools: an SMT solver and a verifier for concurrent C programs. Systemy SMT w formalnej weryfikacji oprogramowania

Increasing interest towards property based design calls for effective satisfiability procedures for expressive temporal logics, e.g. the IEEE standard Property Specification Language (PSL). In this paper, we propose a new approach to the satisfiability of PSL formulae; we follow recent approaches to decision procedures for Satisfiability Modulo Theory, typically applied to fragments of First Order Logic. The underlying intuition is to combine two interacting search mechanisms: on one side, we search for assignments that satisfy the Boolean abstraction of the problem; on the other, we invoke a solver for temporal satisfiability on the conjunction of temporal formulae corresponding to the assignment. Within this framework, we explore two directions. First, given the fixed polarity of each constraint in the theory solver, aggressive simplifications can be applied. Second, we analyze the idea of conflict reconstruction: whenever a satisfying assignment at the level of the Boolean abstraction results in a temporally unsatisfiable problem, we identify inconsistent subsets that can be used to rule out possibly many other assignments. We propose two methods to extract conflict sets on conjunctions of temporal formulae (one based on BDD-based Model Checking, and one based on SAT-based Simple Bounded Model Checking). We analyze the limits and the merits of the approach with a thorough experimental evaluation.

Abstract not found