Jean-Pierre Ressayre

Learn More
(I) Wadge de ned a natural re nement of the Borel hierarchy, now called the Wadge hierarchy WH. The fundamental properties of WH follow from the results of Kuratowski, Martin, Wadge and Louveau. We give a transparent restatement and proof of Wadge’s main theorem. Our method is new for it yields a wide and unexpected extension: from Borel sets of reals to a(More)
(1) Shepherdson proved that a discrete unitary commutative semi-ring A satisfies IE0 (induction scheme restricted to quantifier free formulas) iff A is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let T range over axiom systems for ordered fields with(More)
We describe the Wadge hierarchy of the ω-languages recognized by deterministic Petri nets. This is an extension of the celebrated Wagner hierarchy which turned out to be the Wadge hierarchy of the ω-regular languages. Petri nets are more powerful devices than finite automata. They may be defined as partially blind multi-counter automata. We show that the(More)
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)
This paper presents the contents of a talk given in December 1990, during the second “Journées sur les Arithmétiques Faibles” held at the LITP, Paris; the talk was repeated during the 1991 Ecole de Printemps of Méjannes le Clap. The paper proves a polynomial time computability result for a class of NP inter co-NP problems, for which only the obvious(More)