Rewrite-Based Satisfiability Procedures for Recursive Data Structures

Bonacina, Maria Paola; Echenim, Mnacho

doi:10.1016/j.entcs.2006.11.039

Cited by 13 publications

(19 citation statements)

References 5 publications

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“…In BV terms indicate fixed-width bit vectors, and are built from variables (e.g., x [32] indicates a bit vector x of 32 bits) and constants (e.g., 0 [16] denotes a vector of 16 0's) by means of interpreted functions representing standard RTL operators: word concatenation (e.g., 0 [16] • z [16] ), sub-word selection (e.g., (x [32] [20 : 5]) [16] ), modulo-n sum and multiplication (e.g., x [32] + 32 y [32] and x [16] • 16 y [16] ), bitwise-operators and n , or n , xor n , not n (e.g.,…”

Section: Bit Vectorsmentioning

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: Bit Vectorsmentioning

confidence: 99%

“…x [16] and 16 y [16] ), left and right shift << n , >> n (e.g., x [32] << 4 ). Atomic expressions can be built from terms by applying interpreted predicates like ≤ n , < n (e.g., 0 [32] ≤ 32 x [32] ) and equality.…”

Section: Bit Vectorsmentioning

confidence: 99%

Lazy Satisfiability Modulo Theories

Sebastiani

2007

SAT

149

106

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“…Available surveys include [10,48,56]. A standard superposition-based inference system was proved to terminate and hence to be a satisfiability procedure for several theories of data structures, including arrays and recursive data structures, and their combinations [3][4][5]15].…”

Section: Introductionmentioning

confidence: 99%

On Deciding Satisfiability by Theorem Proving with Speculative Inferences

2010

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Applications in software verification often require determining the satisfiability of first-order formulae with respect to background theories. During development, conjectures are usually false. Therefore, it is desirable to have a theorem prover that terminates on satisfiable instances. Satisfiability Modulo Theories (SMT) solvers have proven to be highly scalable, efficient and suitable for integrated theory reasoning. Inference systems with resolution and superposition are strong at reasoning with equalities, universally quantified variables, and Horn clauses. We describe a theorem-proving method that tightly integrates superposition-based inference system and SMT solver. The combination is refutationally complete if background theory symbols only occur in ground formulae, and non-ground clauses are variable-inactive. Termination is enforced by introducing additional axioms as hypotheses. The system detects any unsoundness introduced by these speculative inferences and recovers from it.

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“…Such inference systems are at the heart of theorem provers for first-order logic with equality (e.g., [47,57,60]), and also yield decision procedures for theories relevant to program verification (e.g., [2,3,8,9]). As a byproduct, we discuss interpolation for DPLL( +T ) [13], a theorem-proving method that integrates in the DPLL(T ) framework for satisfiability modulo theories (SMT) [26,55], to unite the strengths of resolution-based theorem provers, such as the automatic treatment of quantifiers, with those of DPLL(T )-based SMT-solvers, such as built-in theories and scalability of performance on large sets of very long ground clauses.…”

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confidence: 99%

On Interpolation in Automated Theorem Proving

Bonacina

Johansson

2014

J Autom Reasoning

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Given two inconsistent formulae, a (reverse) interpolant is a formula implied by one, inconsistent with the other, and only containing symbols they share. Interpolation finds application in program analysis, verification, and synthesis, for example, towards invariant generation. An interpolation system takes a refutation of the inconsistent formulae and extracts an interpolant by building it inductively from partial interpolants. Known interpolation systems for ground proofs use colors to track symbols. We show by examples that the color-based approach cannot handle non-ground refutations by resolution and paramodulation/superposition. We present a two-stage approach that works by tracking literals, computes a provisional interpolant, which may contain non-shared symbols, and applies lifting to replace non-shared constants by quantified variables. We obtain an interpolation system for non-ground refutations, and we prove that it is complete, if the only non-shared symbols in provisional interpolants are constants.

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Rewrite-Based Satisfiability Procedures for Recursive Data Structures

Cited by 13 publications

References 5 publications

Lazy Satisfiability Modulo Theories

Lazy Satisfiability Modulo Theories

On Deciding Satisfiability by Theorem Proving with Speculative Inferences

On Interpolation in Automated Theorem Proving

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