The weakest compositional semantic equivalence preserving nexttime-less linear temporal logic

Temporal logic model checking is a useful method for verifying properties of finite-state concurrent systems. However, due to the state explosion problem modular methods like compositional minimisation based on semantic congruences are essential in making the verification task manageable. In this paper we show that the so-called CFFD-equivalence defined by initial stability, infinite traces, divergence traces and stable failures is exactly the weakest compositional equivalence preserving nexttimeless linear temporal logic with an extra operator distinguishing deadlocks from divergences. Furthermore, a slight modification of CFFD, called the NDFD-equivalence, is exactly the weakest compositional equivalence preserving standard nexttimeless linear temporal logic.