Displaying similar documents to “On the Topological Complexity of Infinitary Rational Relations ”

Equivalence of analytic and rational functions

J. Bochnak, M. Buchner, W. Kucharz (1997)

Annales Polonici Mathematici

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We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.

Undecidability of topological and arithmetical properties of infinitary rational relations

Olivier Finkel (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We prove that for every countable ordinal α one cannot decide whether a given infinitary rational relation is in the Borel class Σ α 0 (respectively Π α 0 ). Furthermore one cannot decide whether a given infinitary rational relation is a Borel set or a Σ 1 1 -complete set. We prove some recursive analogues to these properties. In particular one cannot decide whether an infinitary rational relation is an arithmetical set. We then deduce from the proof of these results some other ones, like: one cannot...

On the continuity set of an Omega rational function

Olivier Carton, Olivier Finkel, Pierre Simonnet (2008)

RAIRO - Theoretical Informatics and Applications

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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  has at least one point of continuity and that its continuity set 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....

Characterization of linear rational preference structures.

Jacinto González Pachón, Sixto Ríos-Insua (1992)

Extracta Mathematicae

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We consider the multiobjective decision making problem. The decision maker's (DM) impossibility to take consciously a preference or indifference attitude with regard to a pair of alternatives leads us to what we have called doubt attitude. So, the doubt may be revealed in a conscient way by the DM. However, it may appear in an inconscient way, revealing judgements about her/his attitudes which do not follow a certain logical reasoning. In this paper, doubt will be considered...