On the Accepting Power of 2-Tape Büchi Automata

Olivier Finkel (1)

1 ELM - Équipe de Logique Mathématique

We show that, from a topological point of view, 2-tape Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition. In particular, we show that for every non null recursive ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete infinitary rational relations accepted by 2-tape Büchi automata. This very surprising result gives answers to questions of W. Thomas [Automata and Quantifier Hierarchies, in: Formal Properties of Finite automata and Applications, Ramatuelle, 1988, LNCS 386, Springer, 1989, p.104-119] , of P. Simonnet [Automates et Théorie Descriptive, Ph. D. Thesis, Université Paris 7, March 1992], and of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In: "A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621].

Domaines: Complexité [cs.CC]; Logique en informatique [cs.LO]; Logique [math.LO]

Olivier Finkel. On the Accepting Power of 2-Tape Büchi Automata. 23rd International Symposium on Theoretical Aspects of Computer Science, STACS 2006, 2006, France. pp.301-312. ⟨hal-00139152v2⟩