On the Succinctness of Alternating Parity Good-for-Games Automata

Udi Boker (1) , Denis Kuperberg (2, 3, 4, 5) , Karoliina Lehtinen (6) , Michał Skrzypczak (7)

1 IDC - Interdisciplinary Center [Israël]
2 CNRS - Centre National de la Recherche Scientifique
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 DI-ENS - Département d'informatique - ENS Paris
5 PLUME - Preuves et Langages
6 University of Liverpool
7 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

We study alternating parity good-for-games (GFG) automata, i.e., alternating parity automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show that they can be exponentially more succinct than both their nondeterministic and universal counterparts. Furthermore, we present a single exponential determinisation procedure and an Exptime upper bound to the problem of recognising whether an alternating automaton is GFG. We also study the complexity of deciding "half-GFGness", a property specific to alternating automata that only requires nondeterministic choices to be resolved in an online manner. We show that this problem is PSpace-hard already for alternating automata on finite words.

Mots clés: 2012 ACM Subject Classification Theory of computation → Logic and verification phrases Good for games; history-determinism; alternation

Domaines: Théorie et langage formel [cs.FL]

Udi Boker, Denis Kuperberg, Karoliina Lehtinen, Michał Skrzypczak. On the Succinctness of Alternating Parity Good-for-Games Automata. FSTTCS 2020, Dec 2020, Goa, India. pp.41:1--41:13. ⟨hal-03046213⟩