Verification by parallelization of parametric code

Loops and other unbound control structures constitute a major bottleneck in formal software verification, because correctness proofs over such control structures generally require user interaction: typically, induction hypotheses or invariants must be found or modified by hand. Such interaction involves expert knowledge of the underlying calculus and proof engine. We show that one can replace interactive proof techniques, such as induction, with automated first-order reasoning in order to deal with parallelizable loops. A loop can be parallelized, whenever the execution of a generic iteration of its body depends only on the step parameter and not on other iterations. We use a symbolic dependence analysis that ensures parallelizability. This guarantees soundness of a proof rule that transforms a loop into a universally quantified update of the state change information effected by the loop body. This rule makes it possible to employ automatic first-order reasoning techniques to deal with loops. The method has been implemented in the KeY verification tool. We evaluated its applicability with representative case studies from the JAVA CARD domain.