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The greatest fixed-points and rational omega-tree languages

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. ...

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

1981
*
Proceedings of the American Mathematical Society
*

We find

doi:10.1090/s0002-9939-1981-0597672-6
fatcat:vm73em6ry5hablpirueg6otbli
*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 [ ...##
###
On the Continuity Set of an omega Rational Function
[article]

2008
*
arXiv
*
pre-print

Furthermore we prove that any

arXiv:0801.3912v1
fatcat:yzuki2pbbzahfnublpcdbmm2ry
*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 ...##
###
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]

2020
*
Lecture Notes in Computer Science
*

We prove that ω-regular

doi:10.1007/978-3-030-40608-0_21
fatcat:njgjfwt6zjfolbm6djvcbrl3su
*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] . ...##
###
Topological properties of omega context-free languages

2001
*
Theoretical Computer Science
*

This paper is

doi:10.1016/s0304-3975(00)00405-9
fatcat:3dxegiguxvcadifqzisxns5pay
*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. ...##
###
Topology and Ambiguity in Omega Context Free Languages
[article]

2008
*
arXiv
*
pre-print

We study the links between the

arXiv:0801.0533v1
fatcat:upiqvt2lavebtfbhsu24vrxney
*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. ...##
###
Omega Automata and its Classes

2018
*
Current Science
*

ω-automata is

doi:10.18520/cs/v115/i11/2042-2051
fatcat:byu5hbxpnbaclbp2rkx3qa6uhm
*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. ...##
###
On the continuity set of an Omega rational function

2008
*
RAIRO - Theoretical Informatics and Applications
*

In the case

doi:10.1051/ita:2007050
fatcat:od2qeev6a5a6zj3762jwkckoqu
*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 ...##
###
On Infinite Real Trace Rational Languages of Maximum Topological Complexity
[article]

2008
*
arXiv
*
pre-print

We then prove that all

arXiv:0801.0537v1
fatcat:6l4zbomfwrdvdi6mwkzysm2cnu
*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. ...##
###
On infinite real trace rational languages of maximum topological complexity

2006
*
Journal of Mathematical Sciences
*

We reprove also that there exist some

doi:10.1007/s10958-006-0120-z
fatcat:fk3gdruhrzfwxel2s34bemcms4
*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. ...##
###
Undecidability of Topological and Arithmetical Properties of Infinitary Rational Relations

2003
*
RAIRO - Theoretical Informatics and Applications
*

Furthermore one cannot decide whether

doi:10.1051/ita:2003013
fatcat:m6x2mb6nwrdrje3ipn4v5lkxou
*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] . ...##
###
Some problems in automata theory which depend on the models of set theory

2011
*
RAIRO - Theoretical Informatics and Applications
*

It is known that there are only three possibilities for the cardinality

doi:10.1051/ita/2011113
fatcat:dv7hrrq5w5forkchqzlcrh3kx4
*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 ω*language*accepted by*a*1-counter Büchi automaton, or*of*an infinitary*rational*relation accepted by*a*2-tape ...##
###
On the Topological Complexity of Infinitary Rational Relations

2003
*
RAIRO - Theoretical Informatics and Applications
*

We prove in this paper that there exists some infinitary

doi:10.1051/ita:2003016
fatcat:uxy4uhxa3zcylkmrptaubthvpq
*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 ...
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