Winning regions of higher-order pushdown games

Arnaud Carayol (1) , Matthew Hague (2) , Antoine Meyer (3) , Luke Ong (2) , Olivier Serre (3)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 OUCL - Computing Laboratory
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

In this paper we consider parity games defined by higher-order pushdown automata. These automata generalise pushdown automata by the use of higher-order stacks, which are nested ``stack of stacks'' structures. Representing higher-order stacks as well-bracketed words in the usual way, we show that the winning regions of these games are regular sets of words. Moreover a finite automaton recognising this region can be effectively computed. A novelty of our work are abstract pushdown processes which can be seen as (ordinary) pushdown automata but with an infinite stack alphabet. We use the device to give a uniform presentation of our results. From our main result on winning regions of parity games we derive a solution to the Modal Mu-Calculus Global Model-Checking Problem for higher-order pushdown graphs as well as for ranked trees generated by higher-order safe recursion schemes.

Mots clés: infinite games; higher-order pushdown automata; higher-order recursion schemes; mu-calculus model checking

Domaines: Informatique et langage [cs.CL]

Arnaud Carayol, Matthew Hague, Antoine Meyer, Luke Ong, Olivier Serre. Winning regions of higher-order pushdown games. Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008), Jun 2008, Pittsburgh, United States. pp.193-204. ⟨hal-00345939⟩