914 research outputs found
An Example of Pi^0_3-complete Infinitary Rational Relation
We give in this paper an example of infinitary rational relation, accepted by
a 2-tape B\"{u}chi automaton, which is Pi^0_3-complete in the Borel hierarchy.
Moreover the example of infinitary rational relation given in this paper has a
very simple structure and can be easily described by its sections
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]
On the Continuity Set of an omega Rational Function
In this paper, we study the continuity of rational functions realized by
B\"uchi finite state transducers. It has been shown by Prieur that it can be
decided whether such a function is continuous. We prove here that surprisingly,
it cannot be decided whether such a function F has at least one point of
continuity and that its continuity set C(F) cannot be computed. In the case of
a synchronous rational function, we show that its continuity set is rational
and that it can be computed. Furthermore we prove that any rational
Pi^0_2-subset of X^omega for some alphabet X is the continuity set C(F) of an
omega-rational synchronous function F defined on X^omega.Comment: Dedicated to Serge Grigorieff on the occasion of his 60th Birthda
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