Brzozowski’s and up-to algorithms for must testing

Abstract. Checking language equivalence (or inclusion) of finite au-tomata is a classical problem in Computer Science, which has recently received a renewed interest and found novel and more effective solu-tions, 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 equiva-lence 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.