A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra(PA) processes is given. Its time complexity is O(n3+ mn), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for totally normed basic process algebra(BPA) as well as basic parallel process(BPP).
We extend the traditional nonnegative reward testing with negative rewards.In this new testing framework,may preorder and must preorder are the inverse of each other.More surprisingly,it turns out that the real reward must testing is no more powerful than the nonnegative reward testing,at least for finite processes. In order to prove that result,we exploit an important property of failure simulation about the inclusion of the testing outcomes between two related processes.
