On Superposition-Based Satisfiability Procedures and Their Combination

Kirchner, Hélène; Ranise, Silvio; Ringeissen, Christophe; Tran, Duc Khanh

doi:10.1007/11560647_39

Cited by 16 publications

(8 citation statements)

References 10 publications

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“…bunch of theories. [4,109,33,110] extended these results to some more theories and, more importantly, showed how to apply the methods also to combinations of theories. These termination results show that, at least in principle, rewrite-based theorem provers could be used off-the-shelf as validity checkers.…”

Section: The Rewrite-based Approach For Building T -Solversmentioning

confidence: 83%

“…A relatively-recent and promising approach for building T -solvers is that referred as rewritebased 58. approach [8,144,4,109,33,110]. The main idea is that of producing T i -solvers for finitely-axiomatizable theories T i and for their combinations by customizing an equational FOL theorem prover, in particular one based on the superposition calculus 59. .…”

Section: The Rewrite-based Approach For Building T -Solversmentioning

confidence: 99%

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Lazy Satisfiability Modulo Theories

Sebastiani

2007

SAT

149

106

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Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some decidable first-order theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingly important due to its applications in many domains in different communities, in particular in formal verification. An amount of papers with novel and very efficient techniques for SMT has been published in the last years, and some very efficient SMT tools are now available. Typical SMT (T) problems require testing the satisfiability of formulas which are Boolean combinations of atomic propositions and atomic expressions in T , so that heavy Boolean reasoning must be efficiently combined with expressive theory-specific reasoning. The dominating approach to SMT (T), called lazy approach, is based on the integration of a SAT solver and of a decision procedure able to handle sets of atomic constraints in T (T-solver), handling respectively the Boolean and the theory-specific components of reasoning. Unfortunately, neither the problem of building an efficient SMT solver, nor even that of acquiring a comprehensive background knowledge in lazy SMT, is of simple solution. In this paper we present an extensive survey of SMT, with particular focus on the lazy approach. We survey, classify and analyze from a theory-independent perspective the most effective techniques and optimizations which are of interest for lazy SMT and which have been proposed in various communities; we discuss their relative benefits and drawbacks; we provide some guidelines about their choice and usage; we also analyze the features for SAT solvers and T-solvers which make them more suitable for an integration. The ultimate goals of this paper are to become a source of a common background knowledge and terminology for students and researchers in different areas, to provide a reference guide for developers of SMT tools, and to stimulate the cross-fertilization of techniques and ideas among different communities.

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Section: The Rewrite-based Approach For Building T -Solversmentioning

confidence: 83%

Section: The Rewrite-based Approach For Building T -Solversmentioning

confidence: 99%

Lazy Satisfiability Modulo Theories

Sebastiani

2007

SAT

149

106

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“…e.g. [2,19,1]. Our approach allows us to consider, in addition, situations in which the saturated sets are not finite, by giving finite representations for them.…”

Section: Introductionmentioning

confidence: 99%

Obtaining Finite Local Theory Axiomatizations via Saturation

Horbach

Sofronie-Stokkermans

2013

Frontiers of Combining Systems

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In this paper we present a method for obtaining local sets of clauses from possibly non-local ones. For this, we follow the work of Basin and Ganzinger and use saturation under a version of ordered resolution. In order to address the fact that saturation can generate infinite sets of clauses, we use constrained clauses and show that a link can be established between saturation and locality also for constrained clauses: This often allows us to give a finite representation of possibly infinite saturated sets of clauses

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“…First, combination techniques allow us to incorporate theories which are difficult to handle using rewriting techniques, such as Linear Arithmetics. Second, rewriting techniques are of prime interest to design satisfiability procedures which can be efficiently plugged into the disjoint combination framework [11]. In some particular cases, the rewriting approach is an alternative to the combination approach by allowing us to build superposition-based satisfiability procedures for combinations of finitely axiomatized theories, including the theory of Integer Offsets [1,3], but these theories must be over disjoint signatures.…”

Section: Introductionmentioning

confidence: 99%

Satisfiability Procedures for Combination of Theories Sharing Integer Offsets

Nicolini

Ringeissen

Rusinowitch

2009

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We present a novel technique to combine satisfiability procedures for theories that model some data-structures and that share the integer offsets. This procedure extends the Nelson-Oppen approach to a family of non-disjoint theories that have practical interest in verification. The result is derived by showing that the considered theories satisfy the hypotheses of a general result on non-disjoint combination. In particular, the capability of computing logical consequences over the shared signature is ensured in a non trivial way by devising a suitable complete superposition calculus.

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On Superposition-Based Satisfiability Procedures and Their Combination

Cited by 16 publications

References 10 publications

Lazy Satisfiability Modulo Theories

Lazy Satisfiability Modulo Theories

Obtaining Finite Local Theory Axiomatizations via Saturation

Satisfiability Procedures for Combination of Theories Sharing Integer Offsets

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