8 research outputs found
Computing the Rabin Index of a Regular Language of Infinite Words
AbstractThe Rabin index of a regular language of infinite words is the minimum number of accepting pairs used in any deterministic Rabin automaton recognizing this language. We show that the Rabin index of a language given by a Muller automaton withnstates andmaccepting sets is computable in timeO(m2nc) wherecis the cardinality of the alphabet
An Effective Extension of the Wagner Hierarchy to Blind Counter Automata
International audienceThe extension of the Wagner hierarchy to blind counter automata accepting infinite words with a Muller acceptance condition is effective. We determine precisely this hierarchy
Borel Ranks and Wadge Degrees of Context Free Omega Languages
We show that, from a topological point of view, considering the Borel and the
Wadge hierarchies, 1-counter B\"uchi automata have the same accepting power
than Turing machines equipped with a B\"uchi acceptance condition. In
particular, for every non null recursive ordinal alpha, there exist some
Sigma^0_alpha-complete and some Pi^0_alpha-complete omega context free
languages accepted by 1-counter B\"uchi automata, and the supremum of the set
of Borel ranks of context free omega languages is the ordinal gamma^1_2 which
is strictly greater than the first non recursive ordinal. This very surprising
result gives answers to questions of H. Lescow and W. Thomas [Logical
Specifications of Infinite Computations, In:"A Decade of Concurrency", LNCS
803, Springer, 1994, p. 583-621]