Weak Parametric Failure Equivalences and Their Congruence Formats

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing the reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric failure equivalences, which take two previously-known behavioral equivalences, i.e., the weak failure equivalence and the weak impossible future equivalence, as their special cases. More importantly, based on the idea of the structural operational semantics, a series of rule formats are further presented to congruence format for their corresponding weak parametric failure equivalences, i.e., a specific equivalence is further congruent in any languages satisfying its corresponding congruence format. This series of rule formats reflect the gradual changes in the weak parametric failure equivalences. We conclude that, when the weak parametric failure equivalences become coarser, their corresponding rule formats turn tighter.