Fair Simulation for Nondeterministic and Probabilistic Buechi Automata: a Coalgebraic Perspective

Notions of simulation, among other uses, provide a computationally tractable and sound (but not necessarily complete) proof method for language inclusion. They have been comprehensively studied by Lynch and Vaandrager for nondeterministic and timed systems; for (nondeterministic) Büchi automata the notion of fair simulation has been introduced by Henzinger, Kupferman and Rajamani. We contribute generalization of fair simulation in two different directions: one for nondeterministic tree automata (this has been studied previously by Bomhard); and the other for probabilistic word automata (with a finite state space), both under the Büchi acceptance condition. The former (nondeterministic) definition is formulated in terms of systems of fixedpoint equations, hence is readily translated to parity games and then amenable to Jurdziński’s algorithm; the latter (probabilistic) definition bears a strong ranking-function flavor. These two different-looking definitions are derived from one source, namely our coalgebraic modeling of Büchi automata; the proofs of soundness (i.e. that a simulation indeed witnesses language inclusion) are based on these coalgebraic observations, too. 1998 ACM Subject Classification D.2.4 Software/Program Verification