Generating 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 check- ing, 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, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories

The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for effective decision procedures, called Satisfiability Modulo Theory solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories, that applies to the Delayed Theory Combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state of the art algorithms for Satisfiability Modulo Theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.Comment: submitted to ACM Transactions on Computational Logic (TOCL

Interpolation Properties and SAT-based Model Checking

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking techniques based on interpolation require collections of interpolants to satisfy particular properties, to which we refer as "collectives"; they do not hold in general for all interpolation systems and have to be established for each particular system and verification environment. Nevertheless, no systematic approach exists that correlates the individual interpolation systems and compares the necessary collectives. This paper proposes a uniform framework, which encompasses (and generalizes) the most common collectives exploited in verification. We use it for a systematic study of the collectives and of the constraints they pose on propositional interpolation systems used in SAT-based model checking

A 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 arithmetic, and how SMT solvers are used in automated software analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. 201