SMT Interpolants
نویسندگان
چکیده
The linear arithmetic solver in Yices was specifically designed for SMT provers, providing fast support for operations like adding and deleting constraints. We give a procedure for developing interpolants based on the results of the Yices arithmetic solver. For inequalities over real numbers, the interpolant is computed directly from the one contradictory equation and associated bounds. For integer inequalities, a formula is computed from the contradictory equation, the bounds, and the Gomory cuts. The formula is not exactly an interpolant because it may contain local variables. But local variables only arise from Gomory cuts, so there will not be many local variables, and the formula should thereby be useful for applications like predicate abstraction. For integer equalities, we designed a new procedure. It accepts equations and congruence equations, and returns an interpolant. We have implemented our method and give experimental results.
منابع مشابه
Proof Tree Preserving Interpolation
Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in the presence of mixed literals. Contrary to existing approaches, this scheme neither limits the inferences done by the SMT solver, nor does it t...
متن کاملEfficient Interpolant Generation in Satisfiability Modulo Theories
The problem of computing Craig Interpolants for propositional (SAT) formulas has recently received a lot of interest, mainly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Although some w...
متن کاملGenerating Non-linear Interpolants by Semidefinite Programming
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model checking, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, litt...
متن کاملVinter: A Vampire-Based Tool for Interpolation
This paper describes the Vinter tool for extracting interpolants from proofs and minimising such interpolants using various measures. Vinter takes an input problem written in either SMT-LIB or TPTP syntax, generates so called local proofs and then uses a technique of playing in the grey areas of proofs to find interpolants minimal with respect to various measures. Proofs are found using either ...
متن کاملA Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative “natural domain” approaches. We also cover quantifiers, Craig interpolants, polynomial...
متن کاملThe MathSAT 4 SMT Solver ( Tool Paper )
We present MathSAT 4, a state-of-the-art SMT solver. MathSAT 4 handles several useful theories: (combinations of) equality and uninterpreted functions, difference logic, linear arithmetic, and the theory of bit-vectors. It was explicitly designed for being used in formal verification, and thus provides functionalities which extend the applicability of SMT in this setting. In particular: model g...
متن کامل