A Practical Decision Procedure for Arithmetic with 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...

Modular Arithmetic Decision Procedure

All integer data types in programs (such as int, short, byte) have an underlying finite representation in hardware. This finiteness can result in subtle integer-overflow errors that are hard to reason about both for humans and analysis tools alike. As a first step towards finding such errors automatically, we will describe two modular arithmetic decision procedures for reasoning about bounded i...

Analyzing Automata with Presburger Arithmetic and Uninterpreted Function Symbols

A Proof-Producing Decision Procedure for Real Arithmetic

We present a fully proof-producing implementation of a quantifier elimination procedure for real closed fields. To our knowledge, this is the first generally useful proof-producing implementation of such an algorithm. While many problems within the domain are intractable, we demonstrate convincing examples of its value in interactive theorem proving. 1 Overview and related work Arguably the fir...