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Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.
Drawing on an analogy with temporal fixpoint logic, we relate the
arithmetic fixpoint definable sets to the winning positions of certain
games, namely games whose winning conditions lie in the difference
hierarchy over . This both provides a simple characterization
of the fixpoint hierarchy, and refines existing results on the power of
the game quantifier in descriptive set theory. We raise the problem of
transfinite fixpoint hierarchies.
Carlitz a défini sur une fonction et une série formelle , analogues respectivement à la fonction de Riemann et au réel . Yu a montré, en utilisant les modules de Drinfeld, que est transcendant pour tout non divisible par . Nous donnons ici une preuve «automatique» de la transcendance de pour , en utilisant le théorème de Christol, Kamae, Mendès France et Rauzy.
In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word from a given set of substrings (fragments) of a word . We introduce an hypothesis involving the set of fragments and the maximal length of the minimal forbidden factors of . Such hypothesis allows us to reconstruct uniquely the word from the set in linear...
In this paper methods and results related to the notion of minimal
forbidden words are applied to the fragment assembly problem. The
fragment assembly problem can be formulated, in its simplest form,
as follows: reconstruct a word w from a given set I of
substrings (fragments) of a word w. We introduce an
hypothesis involving the set of fragments I and the maximal
length m(w) of the minimal forbidden factors of w. Such
hypothesis allows us to reconstruct uniquely the word w from the
set I in linear...
We study hybrid systems with strong resets from the perspective of
formal language theory. We define a notion of hybrid regular
expression and prove a Kleene-like theorem for hybrid systems. We
also prove the closure of these systems under determinisation and
complementation. Finally, we prove that the reachability problem is
undecidable for synchronized products of hybrid systems.
Starting from late 90’s the public administration has started to employ a quite relevant amount of its budget in developing ICT solutions to better deliver services to citizens. In spite of this effort many statistics show that the mere availability of ICT based services does not guarantee per se their usage. Citizens have continued to largely access services through “traditional” means. In our study we suggest that the highlighted situation is partly due to the fact that relevant domain dependent...
Starting from late 90’s the public administration has started to employ a quite relevant
amount of its budget in developing ICT solutions to better deliver services to citizens.
In spite of this effort many statistics show that the mere availability of ICT based
services does not guarantee per se their usage. Citizens have continued to largely access
services through “traditional” means. In our study we suggest that the highlighted
situation is partly...
Floating-point arithmetic provides a fast but inexact way of
computing geometric predicates. In order for these predicates to be
exact, it is important to rule out all the numerical situations where
floating-point computations could lead to wrong results. Taking into
account all the potential problems is a tedious work to do by hand. We
study in this paper a floating-point implementation of a filter for the
orientation-2 predicate, and how a formal and partially automatized
verification of this...
Based on the Petri net definitions and theorems already formalized in the Mizar article [13], in this article we were able to formalize the definition of cell Petri nets. It is based on [12]. Colored Petri net has already been defined in [11]. In addition, the conditions of the firing rule and the colored set to this definition, that defines the cell Petri nets are further extended to CPNT.i further. The synthesis of two Petri nets was introduced in [11] and in this work the definition is extended...
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