Unsafe grammars and panic automata

Teodor Knapik (1) , Damian Niwinski (2) , Pawel Urzyczyn (2) , Igor Walukiewicz (3)

1 UNC - Université de la Nouvelle-Calédonie
2 Institute of Informatics [Warsaw]
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We show that the problem of checking if an infinite tree gen- erated by a higher-order grammar of level 2 (hyperalgebraic) satisfies a given µ-calculus formula (or, equivalently, if it is accepted by an al- ternating parity automaton) is decidable, actually 2-Exptime-complete. Consequently, the monadic second-order theory of any hyperalgebraic tree is decidable, so that the safety restriction can be removed from our previous decidability result. The last result has been independently obtained by Aehlig, de Miranda and Ong. Our proof goes via a char- acterization of possibly unsafe second-order grammars by a new variant of higher-order pushdown automata, which we call panic automata. In addition to the standard pop 1 and pop 2 operations, these automata have an option of a destructive move called panic . The model-checking prob- lem is then reduced to the problem of deciding the winner in a parity game over a suitable 2nd order pushdown system.

Domaines: Logique en informatique [cs.LO]

Teodor Knapik, Damian Niwinski, Pawel Urzyczyn, Igor Walukiewicz. Unsafe grammars and panic automata. ICALP'05, 2005, Lisbonne, Portugal. pp.1450--1461. ⟨hal-00335729⟩