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A survey of recent advances in SATbased formal verification
 STTT
, 2005
"... Dramatic improvements in SAT solver technology over the last decade and the growing need for more efficient and scalable verification solutions have fueled research in verification methods based on SAT solvers. This paper presents a survey of the latest developments in SATbased formal verificatio ..."
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Cited by 67 (9 self)
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Dramatic improvements in SAT solver technology over the last decade and the growing need for more efficient and scalable verification solutions have fueled research in verification methods based on SAT solvers. This paper presents a survey of the latest developments in SATbased formal verification, including incomplete methods such as bounded model checking and complete methods for model checking. We focus on how the surveyed techniques formulate the verification problem as a SAT problem and how they exploit crucial aspects of a SAT solver, such as applicationspecific heuristics and conflictdriven learning. Finally,wesummarizethenoteworthy achievements in this area so far and note the major challenges in making this technology more pervasive in industrial design verification flows.
Simple and minimumcost satisfiability for goal models
, 2004
"... Abstract. Goal models have been used in Computer Science in order to represent software requirements, business objectives and design qualities. In previous work we have presented a formal framework for reasoning with goal models, in a qualitative or quantitative way, and we have introduced an algori ..."
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Cited by 62 (29 self)
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Abstract. Goal models have been used in Computer Science in order to represent software requirements, business objectives and design qualities. In previous work we have presented a formal framework for reasoning with goal models, in a qualitative or quantitative way, and we have introduced an algorithm for forward propagating values through goal models. In this paper we focus on the qualitative framework and we propose a technique and an implemented tool for addressing two much more challenging problems: (1) find an initial assignment of labels to leaf goals which satisfies a desired final status of root goals by upward value propagation, while respecting some given constraints; and (2) find an minimum cost assignment of labels to leaf goals which satisfies root goals. The paper also presents preliminary experimental results on the performance of the tool using the goal graph generated by a case study involving the Public Transportation Service of Trentino (Italy). 1
The Effect of Restarts on the Efficiency of Clause Learning
, 2007
"... Given the common use of restarts in today’s clause learning SAT solvers, the task of choosing a good restart policy appears to have attracted remarkably little interest. On the other hand, results have been reported on the use of different restart policies for combinatorial search algorithms. Such r ..."
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Cited by 51 (6 self)
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Given the common use of restarts in today’s clause learning SAT solvers, the task of choosing a good restart policy appears to have attracted remarkably little interest. On the other hand, results have been reported on the use of different restart policies for combinatorial search algorithms. Such results are not directly applicable to clause learning SAT solvers, as the latter are now understood as performing a form of resolution, something fundamentally different from search (in the sense of backtracking search for satisfying assignments). In this paper we provide strong evidence that a clause learning SAT solver could benefit substantially from a carefully designed restart policy (which may not yet be available). We begin by pointing out that the restart policy works together with other aspects of a SAT solver in determining the sequence of resolution steps performed by the solver, and hence its efficiency. In this spirit we implement a prototype clause learning SAT solver that facilitates restarts at arbitrary points, and conduct experiments on an extensive set of industrial benchmarks using various restart policies, including those used by wellknown SAT solvers as well as a universal policy proposed in 1993 by Luby et al. The results indicate a substantial impact of the restart policy on the efficiency of the solver, and provide motivation for the design of better restart policies, particularly dynamic ones.
Computing the Least Common Subsumer w.r.t. a Background Terminology
 Journal of Applied Logic
, 2004
"... Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to reuse concepts defined in such terminologies and still support the definition of new concepts ..."
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Cited by 50 (10 self)
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Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to reuse concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology.
Goaloriented requirements analysis and reasoning in the tropos methodology
 Engineering Applications of Artificial Intelligence
, 2005
"... Abstract. Tropos is an agentoriented software methodology proposed in [1, 2]. The methodology is founded on the notions of agent and goal, and goal analysis is used extensively to support software development during different phases. This paper adopts a formal goal model defined and analyzed in [9, ..."
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Cited by 34 (8 self)
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Abstract. Tropos is an agentoriented software methodology proposed in [1, 2]. The methodology is founded on the notions of agent and goal, and goal analysis is used extensively to support software development during different phases. This paper adopts a formal goal model defined and analyzed in [9, 15] to make the goal analysis process concrete through the use of forward and backward reasoning for goal models. The formal goal analysis is illustrated through examples, using an implemented goal reasoning tool.
Expressiveness + automation + soundness: Towards combining SMT solvers and interactive proof assistants
 IN TOOLS AND ALGORITHMS FOR CONSTRUCTION AND ANALYSIS OF SYSTEMS (TACAS
, 2006
"... Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proofproducing ..."
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Cited by 31 (5 self)
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Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proofproducing SMT (Satisfiability Modulo Theories) solver that contains a SAT engine and a decision procedure for quantifierfree firstorder logic with equality. As a result, a user benefits from the expressiveness of Isabelle/HOL when modeling a system, but obtains much better automation for those fragments of the proofs that fall within the scope of the (automatic) SMT solver. Soundness is not compromised because all proofs are submitted to the trusted kernel of Isabelle for certification. This architecture is straightforward to extend for other interactive proof assistants and proofproducing reasoners.
An incremental and layered procedure for the satisfiability of linear arithmetic logic
 In Tools and Algorithms for the Construction and Analysis of Systems, 11th Int. Conf., (TACAS
, 2005
"... Abstract. In this paper we present a new decision procedure for the satisfiability of Linear Arithmetic Logic (LAL), i.e. boolean combinations of propositional variables and linear constraints over numerical variables. Our approach is based on the well known integration of a propositional SAT proce ..."
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Cited by 31 (14 self)
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Abstract. In this paper we present a new decision procedure for the satisfiability of Linear Arithmetic Logic (LAL), i.e. boolean combinations of propositional variables and linear constraints over numerical variables. Our approach is based on the well known integration of a propositional SAT procedure with theory deciders, enhanced in the following ways. First, our procedure relies on an incremental solver for linear arithmetic, that is able to exploit the fact that it is repeatedly called to analyze sequences of increasingly large sets of constraints. Reasoning in the theory of LA interacts with the boolean top level by means of a stackbased interface, that enables the top level to add constraints, set points of backtracking, and backjump, without restarting the procedure from scratch at every call. Sets of inconsistent constraints are found and used to drive backjumping and learning at the boolean level, and theory atoms that are consequences of the current partial assignment are inferred. Second, the solver is layered: a satisfying assignment is constructed by reasoning at different levels of abstractions (logic of equality, real values, and integer
Symbolic Decision Procedures for QBF
 Proceedings of 10th Int. Conf. on Principles and Practice of Constraint Programming (CP 2004
, 2004
"... Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symb ..."
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Cited by 28 (1 self)
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Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decisiondiagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multiresolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive searchbased solvers. We show that QBDD is not competitive, but QMRES compares favorably with searchbased solvers on various benchmarks consisting of nonrandom formulas.
Delayed theory combination vs. NelsonOppen for satisfiability modulo theories: A comparative analysis
 IN PROC. LPAR’06, VOLUME 4246 OF LNAI
, 2006
"... Many approaches for Satisfiability Modulo Theory (SMT(T)) rely on the integration between a SAT solver and a decision procedure for sets of literals in the background theory T (Tsolver). When T is the combination T1 ∪ T2 of two simpler theories, the approach is typically handled by means of Nelson ..."
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Cited by 25 (7 self)
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Many approaches for Satisfiability Modulo Theory (SMT(T)) rely on the integration between a SAT solver and a decision procedure for sets of literals in the background theory T (Tsolver). When T is the combination T1 ∪ T2 of two simpler theories, the approach is typically handled by means of NelsonOppen’s (NO) theory combination schema in which two specific Tsolvers deduce and exchange (disjunctions of) interface equalities. In recent papers we have proposed a new approach to SMT(T1 ∪ T2), called Delayed Theory Combination (DTC). Here part or all the (possibly very expensive) task of deducing interface equalities is played by the SAT solver itself, at the potential cost of an enlargement of the boolean search space. In principle this enlargement could be up to exponential in the number of interface equalities generated. In this paper we show that this estimate was too pessimistic. We present a comparative analysis of DTC vs. NO for SMT(T1 ∪T2), which shows that, using stateoftheart SATsolving techniques, the amount of boolean branches performed by DTC can be upper bounded by the number of deductions and boolean branches performed by NO on the same problem. We prove the result for different deduction capabilities of the Tsolvers and for both convex and nonconvex theories.
MathSAT: Tight integration of SAT and mathematical decision procedures
 JOURNAL OF AUTOMATED REASONING
, 2005
"... Recent improvements in propositional satisfiability techniques (SAT) made it possible to tackle successfully some hard realworld problems (e.g. modelchecking, circuit testing, propositional planning) by encoding into SAT. However, a purely boolean representation is not expressive enough for many o ..."
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Cited by 24 (2 self)
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Recent improvements in propositional satisfiability techniques (SAT) made it possible to tackle successfully some hard realworld problems (e.g. modelchecking, circuit testing, propositional planning) by encoding into SAT. However, a purely boolean representation is not expressive enough for many other realworld applications, including the verification of timed and hybrid systems, of proof obligations in software, and of circuit design at RTL level. These problems can be naturally modeled as satisfiability in Linear Arithmetic Logic (LAL), i.e., the boolean combination of propositional variables and linear constraints over numerical variables. In this paper we present MATHSAT, a new, SATbased decision procedure for LAL, based on the (known approach) of integrating a stateoftheart SAT solver with a dedicated mathematical solver for LAL. We improve MATHSAT in two different directions. First, the top level procedure is enhanced, and now features a tighter integration between the boolean search and the mathematical solver. In particular, we allow for theorydriven backjumping and learning, and theorydriven deduction; we use static learning in order to reduce the number of boolean models that are mathematically inconsistent; we exploit problem clustering in order to partition