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The greatest fixed-points and rational omega-tree languages

Masako Takahashi
1986 Theoretical Computer Science  
Rational omega-tree languages are defined by extending the notion of rational (or regular) expressions for languages, and their properties are investigated.  ...  A simple normal form for rational omega-tree languages is also presented.  ...  In addition, a topological consideration of omega-tree languages will yield a similar characterization of its subclass consisting of closed sets of omega-trees.  ... 
doi:10.1016/0304-3975(86)90123-4 fatcat:nhs7puq6xjdanbcagpwhrmendu

$\beta \omega -\omega $ is not first order homogeneous

Eric K. van Douwen, Jan van Mill
1981 Proceedings of the American Mathematical Society  
We find a first order property shared by some but not all point of ßu -a. 409-419, 633.  ...  (b) Let X denote e.g. the rationals or the irrationals.  ...  Our property is simpler than previously known properties shared by some, but not by all, points, the simplest of which is a: there is a countable A C co* with x E A -A, see [K] ; see also [F] and [  ... 
doi:10.1090/s0002-9939-1981-0597672-6 fatcat:vm73em6ry5hablpirueg6otbli

On the Continuity Set of an omega Rational Function [article]

Olivier Carton
2008 arXiv   pre-print
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.  ...  In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed.  ...  We recall that ω-regular languages form the class of ω-languages accepted by finite automata with a Büchi acceptance condition and this class, denoted by RAT , is the omega Kleene closure of the class  ... 
arXiv:0801.3912v1 fatcat:yzuki2pbbzahfnublpcdbmm2ry

Page 1 of Mathematical Reviews Vol. , Issue 88a [page]

1988 Mathematical Reviews  
First, the author introduces regular languages for mathematicians. Then, he shows some properties of regular languages from the theory of semigroups.  ...  Akira Nakamura (Hiroshima) 88a:03091 03D05 68Q45 Takahashi, Masako (F-PARIS7-LI) The greatest fixed-points and rational omega-tree languages. Theoret. Comput. Sci. 44 (1986), no. 3, 259-274.  ... 

Page 6958 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
the generating function of a rational language).  ...  language the zeta function is N-rational.  ... 

The Automatic Baire Property and an Effective Property of $$\omega $$-Rational Functions [chapter]

Olivier Finkel
2020 Lecture Notes in Computer Science  
We prove that ω-regular languages accepted by Büchi or Muller automata satisfy an effective automata-theoretic version of the Baire property.  ...  Then we use this result to obtain a new effective property of rational functions over infinite words which are realized by finite state Büchi transducers: for each such function F : Σ ω → Γ ω , one can  ...  Landweber studied the topological properties of regular ω-languages in [13] .  ... 
doi:10.1007/978-3-030-40608-0_21 fatcat:njgjfwt6zjfolbm6djvcbrl3su

Topological properties of omega context-free languages

Olivier Finkel
2001 Theoretical Computer Science  
This paper is a study of topological properties of omega context-free languages (!-CFL). We ÿrst extend some decidability results for the deterministic ones (!  ...  From the proof of topological properties we derive some arithmetical properties of !  ...  Thanks also to the anonymous referees for useful comments on a previous version of this paper.  ... 
doi:10.1016/s0304-3975(00)00405-9 fatcat:3dxegiguxvcadifqzisxns5pay

Topology and Ambiguity in Omega Context Free Languages [article]

Olivier Finkel
2008 arXiv   pre-print
We study the links between the topological complexity of an omega context free language and its degree of ambiguity.  ...  This result implies that degrees of ambiguity are really not preserved by the operation of taking the omega power of a finitary context free language.  ...  We thank Dominique Lecomte and Jean-Pierre Ressayre for useful discussions and the anonymous referees for useful comments on a preliminary version of this paper.  ... 
arXiv:0801.0533v1 fatcat:upiqvt2lavebtfbhsu24vrxney

Omega Automata and its Classes

Natasha Singh, Ajay Kumar
2018 Current Science  
ω-automata is a variant of finite automata which accepts infinite strings.  ...  In addition, this paper also summarizes the applicability of omega automata in various interdisciplinary fields.  ...  The proposed finite state ω-languages are closely related to finite state automata. Study of ω-languages is a subset of topological space.  ... 
doi:10.18520/cs/v115/i11/2042-2051 fatcat:byu5hbxpnbaclbp2rkx3qa6uhm

On the continuity set of an Omega rational function

Olivier Carton, Olivier Finkel, Pierre Simonnet
2008 RAIRO - Theoretical Informatics and Applications  
In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed.  ...  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 recall that ω-regular languages form the class of ω-languages accepted by finite automata with a Büchi acceptance condition and this class, denoted by RAT , is the omega Kleene closure of the class  ... 
doi:10.1051/ita:2007050 fatcat:od2qeev6a5a6zj3762jwkckoqu

On Infinite Real Trace Rational Languages of Maximum Topological Complexity [article]

Olivier Finkel, Pierre Simonnet
2008 arXiv   pre-print
We then prove that all rational languages of infinite real traces are analytic sets and that there exist some rational languages of infinite real traces which are analytic but non Borel sets, and even  ...  We consider the set of infinite real traces, over a dependence alphabet (Gamma, D) with no isolated letter, equipped with the topology induced by the prefix metric.  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
arXiv:0801.0537v1 fatcat:6l4zbomfwrdvdi6mwkzysm2cnu

On infinite real trace rational languages of maximum topological complexity

O. Finkel, J.-P. Ressayre, P. Simonnet
2006 Journal of Mathematical Sciences  
We reprove also that there exist some rational languages of infinite real traces which are analytic but non Borel sets, and even Σ 1 1 -complete, hence of maximum possible topological complexity.  ...  We then prove that all rational languages of infinite real traces are analytic sets.  ...  Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
doi:10.1007/s10958-006-0120-z fatcat:fk3gdruhrzfwxel2s34bemcms4

Undecidability of Topological and Arithmetical Properties of Infinitary Rational Relations

Olivier Finkel
2003 RAIRO - Theoretical Informatics and Applications  
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.  ...  We prove that there exist some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [Sim92].  ...  Landweber studied first the topological properties of ω-regular languages and characterized the ω-regular languages in each of the Borel classes Σ 0 1 , Π 0 1 , Σ 0 2 , Π 0 2 , [Lan69] .  ... 
doi:10.1051/ita:2003013 fatcat:m6x2mb6nwrdrje3ipn4v5lkxou

Some problems in automata theory which depend on the models of set theory

Olivier Finkel
2011 RAIRO - Theoretical Informatics and Applications  
It is known that there are only three possibilities for the cardinality of the complement of an omega-language L(A) accepted by a Büchi 1-counter automaton A.  ...  As a corollary, this proves that the Continuum Hypothesis may be not satisfied for complements of 1-counter omega-languages and for complements of infinitary rational relations accepted by 2-tape Büchi  ...  In [Fin09a] we have recently proved a surprising result: the topological complexity of an ωlanguage accepted by a 1-counter Büchi automaton, or of an infinitary rational relation accepted by a 2-tape  ... 
doi:10.1051/ita/2011113 fatcat:dv7hrrq5w5forkchqzlcrh3kx4

On the Topological Complexity of Infinitary Rational Relations

Olivier Finkel
2003 RAIRO - Theoretical Informatics and Applications  
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [20] .  ...  Infinitary rational relations, topological properties, Borel and analytic sets. The question of the complexity of such relations on infinite words naturally arises.  ...  We recall that ω-regular languages form the class of ω-languages accepted by finite automata with a Büchi acceptance condition and this class is the omega Kleene closure of the class of regular finitary  ... 
doi:10.1051/ita:2003016 fatcat:uxy4uhxa3zcylkmrptaubthvpq
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