Accelerating Loops with Arrays

Abstract: We propose a novel acceleration technique for loops operating on arrays. The goal of acceleration is to characterize the transitive closure of loops in a logic which is suitable for automated reasoning. Using the new notion of inductive lvalues, our technique can handle loops where previous techniques fail, and it unifies acceleration for arrays and scalar variables by regarding scalars as arrays of dimension 0. Moreover, our approach uses λs instead of quantifiers. Then the resulting SMT problems can be solved via lemmas on demand. An empirical evaluation of our implementation in the tool LoAT shows the power of our approach.