Authors: Natsuki Urabe ; Ichiro Hasuo

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 Büchi 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 Büchi 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 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. Based on these coalgebraic observations, we also prove their soundness: a simulation indeed witnesses language inclusion.

• 68Q45 - Formal languages and automata
• 68Q70 - Algebraic theory of languages and automata