Automatic decidability

Lynch, Christopher S.; Morawska, Barbara

doi:10.1109/lics.2002.1029813

Cited by 19 publications

(23 citation statements)

References 9 publications

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“…Results of this nature were obtained in [Armando et al 2003]: a refutationally complete rewrite-based inference system, named SP (from superposition), was shown to generate finitely many clauses on satisfiability problems in the theories of non-empty lists, arrays with or without extensionality, encryption, finite sets with extensionality, homomorphism, and the combination of lists and arrays. This work was extended in [Lynch and Morawska 2002], by using a meta-saturation procedure to add complexity characterizations 3 . Since the inference system SP reduces to ground completion on a set of ground equalities and inequalities, it terminates and represents a decision procedure also for the quantifier-free theory of equality 4 .…”

Section: ·mentioning

confidence: 99%

New results on rewrite-based satisfiability procedures

Armando

Bonacina

Ranise

et al. 2009

ACM Trans. Comput. Logic

133

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Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T . If a sound and complete inference system for first-order logic is guaranteed to terminate on T -satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T -satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.

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Section: ·mentioning

confidence: 99%

New results on rewrite-based satisfiability procedures

Armando

Bonacina

Ranise

et al. 2009

ACM Trans. Comput. Logic

133

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show abstract

“…It uses constrained equations between arrays to capture when arrays are equal except possibly on a finite set of indices. Rewriting approaches in the context of super-position are presented in [7] and [8]. An approach that also uses constrained equations is developed in [9].…”

Section: A Related Workmentioning

confidence: 99%

Generalized, efficient array decision procedures

Moura

Bjørner

2009

2009 Formal Methods in Computer-Aided Design

102

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The theory of arrays is ubiquitous in the context of software and hardware verification and symbolic analysis. The basic array theory was introduced by McCarthy and allows to symbolically representing array updates. In this paper we present combinatory array logic, CAL, using a small, but powerful core of combinators, and reduce it to the theory of uninterpreted functions. CAL allows expressing properties that go well beyond the basic array theory. We provide a new efficient decision procedure for the base theory as well as CAL. The efficient procedure serves a critical role in the performance of the stateof-the-art SMT solver Z3 on array formulas from applications.

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“…Other theory-generic satisfiability approaches include: (i) the superpositionbased one, e.g., [17,2,18,1,27], where it is proved that a superposition theorem proving inference system terminates for a given first-order theory together with any given set of ground clauses representing a satisfiability problem; and (ii) that of decidable theories defined by means of formulas with triggers [10], that allows a user to define a new theory with decidable QF satisfiability by axiomatizing it according to some requirements, and then making an SMT solver extensible by such a user-defined theory. While not directly comparable to the present one, these approaches (discussed in more detail in [20]) can be seen as complementary ones, further enlarging the repertoire of theory-generic satisfiability methods.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Variant-Based Decidable Satisfiability in Initial Algebras with Predicates

Gutiérrez

Meseguer

2018

Logic-Based Program Synthesis and Transformation

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Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free satisfiability in the initial algebra of an ordersorted equational theory pΣ, E Y Bq under two conditions: (i) E Y B has the finite variant property and B has a finitary unification algorithm; and (ii) pΣ, E Y Bq protects a constructor subtheory pΩ, EΩ Y BΩq that is OS-compact. These conditions apply to many user-definable theories, but have a main limitation: they apply well to data structures, but often do not hold for user-definable predicates on such data structures. We present a theory-generic satisfiability decision procedure, and a prototype implementation, extending variant-based satisfiability to initial algebras with user-definable predicates under fairly general conditions. Keywords: finite variant property (FVP), OS-compactness, user-definable predicates, decidable validity and satisfiability in initial algebras.

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Automatic decidability

Cited by 19 publications

References 9 publications

New results on rewrite-based satisfiability procedures

New results on rewrite-based satisfiability procedures

Generalized, efficient array decision procedures

Variant-Based Decidable Satisfiability in Initial Algebras with Predicates

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