A Scalable Method for Solving Satisfiability of Integer Linear Arithmetic Logic

The Satisfiability Modulo Theories Competition (SMT-COMP) is intended to spark further advances in the decision procedures field, especially for applications in hardware and software verification. Public competitions are a well-known means of stimulating advancement in automated reasoning. Evaluation of SMT solvers entered in SMT-COMP took place while CAV 2005 was meeting. Twelve solvers were entered; 1,352 benchmarks were collected in seven different divisions.

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“…ARIO competed in every division except for QF_AUFLIA. More information can be found in [30,31] and at http://www.eecs.umich.edu/~ario.…”

Section: Participantsmentioning

confidence: 99%

Design and Results of the First Satisfiability Modulo Theories Competition (SMT-COMP 2005)

2005

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“…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 (e.g., Ario [158], BarceLogic [133], CVCLite/CVC3 [17], DLSAT [123], haRVey [144], MathSAT [37], Sateen [108], SDSAT [83] Simplify [70], TSAT++ [6], UCLID [117], Yices [71], Verifun [79], Zapato [16]), Z3 [63]. An amount of benchmarks, mostly derived from verification problems, is available at the SMT-LIB official page [147,148].…”

Section: Satisfiability Modulo Theories -Smtmentioning

confidence: 99%

“…In many calls to T -solver, a general solver for T is not needed: very often, the unsatisfiability of the current assignment µ can be established in less expressive, but much easier, subtheories. Thus, T -solver may be organized in a layered hierarchy of solvers of increasing solving capabilities [9,37,158,55,43]. If a higher level solver finds a conflict, then this conflict is used to prune the search at the Boolean level; if it does not, the lower level solvers are activated.…”

Section: Layered T -Solversmentioning

confidence: 99%

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Lazy Satisfiability Modulo Theories

Sebastiani

2007

SAT

148

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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“…This may increase the complexity of the ILP decision procedures that already have an exponential worst-case complexity. A promising approach has been suggested by Sheini and Sakallah [32], where they integrate an UTVPI decision procedure in DPLL(T) framework and use the general ILP solver in a lazy framework. Currently, implementations based on DPLL(T) framework are most competitive on the SMT-LIB QFP benchmarks.…”

Section: Related Workmentioning

confidence: 99%

Interpolant based Decision Procedure for Quantifier-Free Presburger Arithmetic

Lahiri

Mehra

2007

SAT

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Recently, off-the-shelf Boolean SAT solvers have been used to construct ground decision procedures for various theories, including Quantifier-Free Presburger (QFP) arithmetic. One such approach (often called the eager approach) is based on a satisfiability-preserving translation to a Boolean formula. Eager approaches are usually based on encoding integers as bit-vectors and suffer from the loss of structure and sometime very large size for the bit-vectors. In this paper, we present a decision procedure for QFP that is based on alternately under and over-approximating a formula, where Boolean interpolants are used to compute the overapproximation. The novelty of the approach lies in using information from each phase (either underapproximation or overapproximation) to improve the other phase. Our preliminary experiments indicate that the algorithm consistently outperforms approaches based on eager and very lazy methods, on a set of verification benchmarks. In our experience, the use of interpolants results in better abstractions being generated compared to an earlier method based on proofs directly.

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A Scalable Method for Solving Satisfiability of Integer Linear Arithmetic Logic

Cited by 19 publications

References 21 publications

Design and Results of the First Satisfiability Modulo Theories Competition (SMT-COMP 2005)

Design and Results of the First Satisfiability Modulo Theories Competition (SMT-COMP 2005)

Lazy Satisfiability Modulo Theories

Interpolant based Decision Procedure for Quantifier-Free Presburger Arithmetic

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