Brzozowski’s and Up-To Algorithms for Must Testing

Abstract

Checking language equivalence (or inclusion) of finite automata is a classical problem in Computer Science, which has recently received a renewed interest and found novel and more effective solutions, such as approaches based on antichains or bisimulations up-to. Several notions of equivalence (or preorder) have been proposed for the analysis of concurrent systems. Usually, the problem of checking these equivalences is reduced to checking bisimilarity. In this paper, we take a different approach and propose to adapt algorithms for language equivalence to check one prime equivalence in concurrency theory, must testing semantics. To achieve this transfer of technology from language to must semantics, we take a coalgebraic outlook at the problem.

A coalgebraic view on decorated traces

“…Moreover, they only consider must testing and leave as future work capturing other decorated traces. In another paper (Bonchi, Caltais, Pous & Silva 2013), we have shown that must testing can also be captured using the generalized powerset construction. An important point is that our approach puts in evidence the underlying semilattice structure which is needed for defining bisimulations up-to whereas this is not at all considered in their paper.…”

Model-based mutant equivalence detection using automata language equivalence and simulations

“…To run the language equivalence algorithms (for WM and SM), we use the HKC library [35], an OCaml implementation of the ALE algorithm [17] compiled using OCamlbuild. This tool handles non-deterministic TSs using different strategies: the automata may be processed either forward of backwards, and the exploration strategy may be breadth-first or depth-first.…”

“…To the best of our knowledge, the HKC library [35] was the only publicly available tool able to perform ALE checking on non-deterministic TSs. We cannot guarantee that there are no other other tools providing the same features with lower execution time.…”

“…The input models are encoded using an XML format and are processed by our Java tools (part of VIBeS [36]) for the RS/BS algorithms. The ALE execution is done using HKC [35]. Both VIBeS and HKC are released under open source licences (MIT license for VIBeS, GNU LGPL for HKC), allowing one to inspect, reuse, or adapt the code.…”