C-SHORe

Abstract

Higher-order recursion schemes (HORS) have recently received much attention as a useful abstraction of higher-order functional programs with a number of new verification techniques employing HORS model-checking as their centrepiece. This paper contributes to the ongoing quest for a truly scalable model-checker for HORS by offering a different, automata theoretic perspective. We introduce the first practical model-checking algorithm that acts on a generalisation of pushdown automata equi-expressive with HORS called collapsible pushdown systems (CPDS). At its core is a substantial modification of a recently studied saturation algorithm for CPDS. In particular it is able to use information gathered from an approximate forward reachability analysis to guide its backward search. Moreover, we introduce an algorithm that prunes the CPDS prior to model-checking and a method for extracting counter-examples in negative instances. We compare our tool with the state-of-the-art verification tools for HORS and obtain encouraging results. In contrast to some of the main competition tackling the same problem, our algorithm is fixed-parameter tractable, and we also offer significantly improved performance over the only previously published tool of which we are aware that also enjoys this property. The tool and additional material are available from

A Type-Directed Negation Elimination

“…Whereas the decidability of HFL model-checking against finite transition systems is rather simple, it took more time to understand the decidability of HORS model-checking against the ordinary (order 0) modal µ-calculus. This situation actually benefited to HORS: the intense research on HORS produced several optimized algorithms and implementations of HORS model-checking [2,9,19], whereas HFL model-checking remains a rather theoretical and unexplored topic. HORS can be thought as recursive formulas with no boolean connectives and least fixed points everywhere.…”

Saturation algorithms for model-checking pushdown systems

“…More recently this approach was developed by Broadbent et al to obtain a saturation algorithm for the full case of collapsible pushdown systems [9], leading to the analysis tool C-SHORe [10]. This algorithm was applied directly to the analysis of recursion schemes (without the intermediate automata model) by Broadbent and Kobayashi, resulting in the HorSat tool [11].…”