Abstract

1 Introduction Linear-relations analysis discovers linear relationships among the variables of aprogram that hold in all the reachable program states. Such relationships are called linear invariants. Invariants are useful in the verification of both safetyand liveness properties. Many existing techniques rely on the presence of these invariants to prove properties of interest. Some types of analysis, e.g., variable-bounds analysis, can be viewed as specializations of linear-relations analysis. Traditionally, this analysis is framed as an abstract interpretation in the domainof polyhedra [6, 7]. The analysis is carried out using a propagation-based technique, wherein increasingly accurate polyhedral iterates, converging towards thefinal result, are computed. This convergence is ensured through the use of widening, or extrapolation, operators. Such techniques are popular in the domains ofdiscrete and hybrid programs, motivating tools like

Citations