Revised Singleton Failures Equivalence for Labelled Transition Systems

Based on previous researches, the set of all traces and Singleton failures (SF) pairs is used to characterize SF equivalence. Since the trace information can not be obtained from the SF information, the set of all SF pairs alone can not characterize SF equivalence. We propose a Revised version of singleton failures (RSF) pair, show that the set of all RSF pairs alone can characterize SF equivalence, RSF equivalence and SF equivalence are equivalent, and discuss the difference between RSF and SF. The main conclusion of this paper is that RSF equivalence algorithm is the most efficient one among all SF equivalence algorithms. We present several examples showing RSF equivalence algorithm is computationally quite efficient.