Deciding orthogonal bisimulation
Bergstra, Ponse and van der Zwaag introduced in 2003 the notion of orthogonal bisimulation equivalence on labeled transition systems. This equivalence is a refinement of branching bisimulation, in which consecutive tau's (silent steps) can be compressed into one (but not zero) tau's. The main advantage of orthogonal bisimulation is that it combines well with priorities. Here we solve the problem of deciding orthogonal bisimulation equivalence in finite (regular) labeled transition systems. Unlike as in branching bisimulation, in orthogonal bisimulation, cycles of silent steps cannot be eliminated. Hence, the algorithm of Groote and Vaandrager (1990) cannot be adapted easily. However, we show that it is still possible to decide orthogonal bisimulation with the same complexity as that of Groote and Vaandrager's algorithm. Thus if n is the number of states, and m the number of transitions then it takes O(n(m + n)) time to decide orthogonal bisimilarity on finite labeled transition systems, using O(m + n) space.
orthogonal bisimulation equivalence labeled transition system silent step concurrency theory branching bisimulation equivalence