Fair Simulation for Nondeterministic and Probabilistic Buechi Automata: a Coalgebraic Perspective
Abstract
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 B\"{u}chi automata the notion of fair simulation has been introduced by Henzinger, Kupferman and Rajamani. We contribute to a generalization of fair simulation in two different directions: one for nondeterministic tree automata previously studied by Bomhard; and the other for probabilistic word automata with finite state spaces, both under the B\"{u}chi acceptance condition. The former nondeterministic definition is formulated in terms of systems of fixed-point equations, hence is readily translated to parity games and is then amenable to Jurdzi\'{n}ski'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 B\"{u}chi automata. Based on these coalgebraic observations, we also prove their soundness: a simulation indeed witnesses language inclusion.
Cite
@article{arxiv.1606.04680,
title = {Fair Simulation for Nondeterministic and Probabilistic Buechi Automata: a Coalgebraic Perspective},
author = {Natsuki Urabe and Ichiro Hasuo},
journal= {arXiv preprint arXiv:1606.04680},
year = {2023}
}