A Comparative Study of Arithmetic Constraints on Integer Intervals

A Comparative Study of Arithmeti Constraints on Integer Intervals

A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a...

An Automata - Theoretic Approach toPresburger Arithmetic Constraints

This paper introduces a nite-automata based representation of Presburger arithmetic deenable sets of integer vectors. The representation consists of concurrent automata operating on the binary en-codings of the elements of the represented sets. This representation has several advantages. First, being automata-based it is operational in nature and hence leads directly to algorithms, for instance...

Applying Interval Arithmetic to Real, Integer, and Boolean Constraints

We present in this paper a uni ed processing for Real, Integer and Boolean Constraints based on a general narrowing algorithm which applies to any n-ary relation on <. The basic idea is to de ne, for every such relation , a narrowing function ! based on the approximation of by a Cartesian product of intervals whose bounds are oating point numbers. We then focus on non-convex relations and estab...

On the Satisfiability of Modular Arithmetic Formula

Modular arithmetic is the underlying integer computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of modular arithmetic formulae over the finite ring Z2ω . Although an upper bound of 2 2 4) can be obtained by solving alternation-free Presburger arithmetic, it is easy to see that the problem is in fact NP-complete. Further, we give an effi...