Lockstep Composition for Unbalanced Loops

Abstract

Equivalence checking of two programs is often reduced to the safety verification of a so-called product program that aligns the programs in lockstep. However, this strategy is not applicable when programs have arbitrary loop structures, e.g., the numbers of loops vary. We introduce an automatic iterative abstraction-refinement-based technique for checking equivalence of a single-loop program and a program which has a series of consecutive loops. Our approach decomposes the single loop into a sequence of separate loops thus reducing the main problem to a series of equivalence-checking problems for pairs of loops. Since due to the decomposition, these problems become abstract, our approach iteratively refines the decomposed loops and lifts useful information across them. Our second contribution is a procedure for the alignment of loops with counters and explicit bounds that cannot be composed in lockstep. We have implemented the approach and successfully evaluated it on two suites, one with benchmarks containing different numbers of loops and the other containing benchmarks that need alignment.