Abstraction Refinement of Linear Programs with Arrays

摘要

In previous work we presented a model checking procedure for linear programs, i.e. programs in which variables range over a numeric domain and expressions involve linear combinations of the variables. In this paper we lift our model checking procedure for linear programs to deal with arrays via iterative abstraction refinement. While most approaches are based on predicate abstraction and therefore the abstraction is relative to sets of predicates, in our approach the abstraction is relative to sets of variables and array indexes, and the abstract program can express complex correlations between program variables and array elements. Thus, while arrays are problematic for most of the approaches based on predicate abstraction, our approach treats them in a precise way. This is an important feature as arrays are ubiquitous in programming. We provide a detailed account of both the abstraction and the refinement processes, discuss their implementation in the EUREKA tool, and present experimental results that confirm the effectiveness of our approach on a number of programs of interest.