Linear Encodings of Bounded LTL Model Checking

TL;DR

This paper introduces linear-size encodings for bounded model checking of LTL and PLTL, extending to minimal counterexamples and enabling incremental SAT-based verification with improved performance.

Contribution

It presents novel linear and quadratic encodings for BMC of LTL and PLTL, including techniques for minimal counterexamples and incremental verification.

Findings

Encodings are linear in size, improving efficiency.

Incremental encoding enhances BMC performance.

Methods are effective for bug detection and property proving.

Abstract

We consider the problem of bounded model checking (BMC) for linear temporal logic (LTL). We present several efficient encodings that have size linear in the bound. Furthermore, we show how the encodings can be extended to LTL with past operators (PLTL). The generalised encoding is still of linear size, but cannot detect minimal length counterexamples. By using the virtual unrolling technique minimal length counterexamples can be captured, however, the size of the encoding is quadratic in the specification. We also extend virtual unrolling to Buchi automata, enabling them to accept minimal length counterexamples. Our BMC encodings can be made incremental in order to benefit from incremental SAT technology. With fairly small modifications the incremental encoding can be further enhanced with a termination check, allowing us to prove properties with BMC. Experiments clearly show that our new encodings improve performance of BMC considerably, particularly in the case of the incremental encoding, and that they are very competitive for finding bugs. An analysis of the liveness-to-safety transformation reveals many similarities to the BMC encodings in this paper. Using the liveness-to-safety translation with BDD-based invariant checking results in an efficient method to find shortest counterexamples that complements the BMC-based approach.