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- Olivier Finkel, Pierre Simonnet
- Fundam. Inform.
- 2009

We investigate the topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets. We show that, for each integer n ≥ 1, there is a Dωn(Σ 1 1)-complete tree language Ln accepted by a (non deterministic) Muller tree automaton. On the other hand, we prove that a tree language accepted by an unambiguous… (More)

- Olivier Finkel, Pierre Simonnet
- ArXiv
- 2008

We study the links between the topological complexity of an ω-context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel ω-context free languages which are recognized by Büchi pushdown automata have a maximum degree of ambiguity. This result implies that degrees of… (More)

- Alain Courrier, G Stenbach, +5 authors Joshua Chopin
- Lancet
- 1986

- Benoit Cagnard, Pierre Simonnet
- Discrete Mathematics & Theoretical Computer…
- 2007

In his thesis Baire defined functions of Baire class 1. A function f is of Baire class 1 if it is the pointwise limit of a sequence of continuous functions. Baire proves the following theorem. A function f is not of class 1 if and only if there exists a closed nonempty set F such that the restriction of f to F has no point of continuity. We prove the… (More)

- Christian Choffrut, Hratchia Pélibossian, Pierre Simonnet
- Journal of Automata, Languages and Combinatorics
- 1999

- Olivier Carton, Olivier Finkel, Pierre Simonnet
- ITA
- 2008

In this paper, we study the continuity of rational functions realized by Büchi 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… (More)

- Benoit Cagnard, Pierre Simonnet
- ITA
- 2007

This note is about functions f : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A×B. These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such fonction are continuous or not. In 1920 W. Sierpinski showed that a function f : R → R is Baire class 1 if and only if both… (More)

- Olivier Finkel, Jean-Pierre Ressayre, Pierre Simonnet
- ArXiv
- 2008

We consider the set Rω(Γ, D) of infinite real traces, over a dependence alphabet (Γ, D) with no isolated letter, equipped with the topology induced by the prefix metric. We then prove that all rational languages of infinite real traces are analytic sets. We reprove also that there exist some rational languages of infinite real traces which are analytic but… (More)

In this paper, we study the continuity of rational functions realized by Büchi 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… (More)

- Jacqueline J Fremont, Christopher Gaudiot, +7 authors C Louco
- Lancet
- 1984