Lifting CDCL to Template-Based Abstract Domains for Program Verification

Abstract

The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP). ACDLP alternates between model search, which performs over-approximate deduction with constraint propagation, and conflict analysis, which performs under-approximate abduction with heuristic choice. We instantiate the model search and conflict analysis algorithms to an abstract domain of template polyhedra, strictly generalizing CDCL from the Boolean lattice to a richer lattice structure. Our template polyhedra can express intervals, octagons and restricted polyhedral constraints over program variables. We have implemented ACDLP for automatic bounded safety verification of C programs. We evaluate the performance of our analyser by comparing with CBMC, which uses CDCL, and Astrée, a commercial abstract interpretation tool. We observe two orders of magnitude reduction in the number of decisions, propagations, and conflicts as well as a 1.5x speedup in runtime compared to CBMC. Compared to Astrée, ACDLP solves twice as many benchmarks and has much higher precision. This is the first instantiation of CDCL with a template polyhedra abstract domain.

2LS for Program Analysis

“…The work [35] experimented with an incremental slicing algorithm in combination with incremental unwinding in C ; however, this is not implemented 2 . The work [30] developed an SMT solving algorithm in 2LS (which is available in a prototype branch of 2LS) that uses template polyhedra instead of Boolean literals in order to perform theory-level propagation based on the concept of Abstract Conflict Driven Learning [11].…”