A randomized satisfiability procedure for arithmetic and uninterpreted function symbols

A Randomized Satisfiability Procedure for Arithmetic and Uninterpreted Function Symbols

We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., i...

A Randomized Satisfability Procedure for Arithmetic and Uninterpreted Function Symbols

We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., i...

Analyzing Automata with Presburger Arithmetic and Uninterpreted Function Symbols

The Bernays-Schönfinkel-Ramsey Fragment with Bounded Difference Constraints over the Reals Is Decidable

First-order linear real arithmetic enriched with uninterpreted predicate symbols yields an interesting modeling language. However, satisfiability of such formulas is undecidable, even if we restrict the uninterpreted predicate symbols to arity one. In order to find decidable fragments of this language, it is necessary to restrict the expressiveness of the arithmetic part. One possible path is t...

Path-Sensitive Analysis for Linear Arithmetic and Uninterpreted Functions

We describe data structures and algorithms for performing a path-sensitive program analysis to discover equivalences of expressions involving linear arithmetic or uninterpreted functions. We assume that conditionals are abstracted as boolean variables, which may be repeated to reflect equivalent conditionals. We introduce free conditional expression diagrams (FCEDs), which extend binary decisio...