Algebraic Techniques in Software Verification : Challenges and Opportunities

One of the main application areas and driving forces behind the development of Satisfiability Modulo Theory (SMT) solvers is software verification. The requirements of software verification are somewhat different to other applications of automated reasoning, posing a number of challenges but also providing some interesting opportunities. This paper brings together and summarises the algebras and structures of interest, along with some of the problems that are characteristic of software verification. It is hoped that this will allow computer algebra researchers to assess the applicability of their techniques to this challenging, but rewarding domain. Software verification is the prototypical application domain for Satisfiability Modulo Theory (SMT) solvers. There are many aspects of the two research fields that show a significant degree of co-evolution. For example, the central role of theories (and the theories that are available – for example bit-vectors and arrays) can be seen as a formalisation of the domain specific decision procedures that were used in early verification systems [1]. Universal quantification is challenging for most SMT solver algorithms, leading to poor performance and thus many software verification systems avoid generating quantifiers. Likewise the importance of model generation1 is in part driven but the utility of these models for providing execution or error traces in verification systems. The coevolution can also be seen in the SMT-LIB benchmarks which feature many benchmark collections generated by verification tools. This paper aims to highlight some of the requirements and ‘evolutionary pressures’ that software verification places on SMT solver development. It is hoped that this context will help computer algebra researchers to identify, develop and refine algorithms so that they can demonstrate impact on commercial-scale software verification problems. The topics raised are a mix between challenges that have to be overcome and opportunities in under-explored / critical areas.