Simplifying Loop Invariant Generation Using Splitter Predicates

Rahul Sharma, Isil Dillig, Thomas Dillig, Alex Aiken

Abstract: We present a novel static analysis technique that substantially improves the quality of invariants inferred by standard loop invariant generation techniques. Our technique decomposes multi-phase loops, which require disjunctive invariants, into a semantically equivalent sequence of single-phase loops, each of which requires simple, conjunctive invariants. We define splitter predicates which are used to identify phase transitions in loops, and we present an algorithm to find useful splitter predicates that enable the phase-reducing transformation. We show experimentally on a set of representative benchmarks from the literature and real code examples that our technique substantially increases the quality of invariants inferred by standard invariant generation techniques. Our technique is conceptually simple, easy to implement, and can be integrated into any automatic loop invariant generator.