On the Weak Index Problem for Game Automata

Abstract

Abstract. Game automata are known to recognise languages arbitrarily high in both the non-deterministic and alternating Rabin-Mostowski index hierarchies. Recently it was shown that for this class both hierarchies are decidable. Here we complete the picture by showing that the weak index hierarchy is decidable as well. We also provide a procedure computing for a game automaton an equivalent weak alternating automaton with the minimal index and a quadratic number of states. As a by-product we obtain that, as for deterministic automata, the weak index and the Borel rank coincide.

Index Problems for Game Automata

“…As the characterization effectively yields an equivalent game automaton, we obtain procedures computing the alternating, weak alternating, and non-deterministic index for a given alternating automaton equivalent to some game automaton. This paper collects results from two conference papers: [Facchini et al 2013] and [Facchini et al 2015]. Additionally, it contains a discussion of the maximality of the class of game automata, which adapts a reasoning from [Duparc et al 2011] to the index problem.…”

“…This paper collects results from two conference papers: [Facchini et al 2013] and [Facchini et al 2015]. Additionally, it contains a discussion of the maximality of the class of game automata, which adapts a reasoning from [Duparc et al 2011] to the index problem.…”