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The greatest fixed-points and rational omega-tree languages

1986
*
Theoretical Computer Science
*

A simple normal form for rational

doi:10.1016/0304-3975(86)90123-4
fatcat:nhs7puq6xjdanbcagpwhrmendu
*omega*-tree*languages*is also presented. ... Rational*omega*-tree*languages*are defined by extending the notion of rational (or regular) expressions for*languages*, and their properties are investigated. ... a i*states*such that st ---* s~+~ in M (i~ 0)}, Greatest fixed.points and rational*omega*-tree*languages*265 where So is the initial*state*of M. ...##
###
Omega Automata and its Classes

2018
*
Current Science
*

ω-automata is a variant of

doi:10.18520/cs/v115/i11/2042-2051
fatcat:byu5hbxpnbaclbp2rkx3qa6uhm
*finite*automata which accepts infinite strings. ... In addition, this paper also summarizes the applicability of*omega*automata in various interdisciplinary fields. ... Staiger 40 proposed the concept of*finite**state*ω-*languages*based on structural properties. The proposed*finite**state*ω-*languages*are closely related to*finite**state*automata. ...##
###
On Omega Context Free Languages which are Borel Sets of Infinite Rank
[article]

2010
*
arXiv
*
pre-print

This paper is a continuation of the study of topological properties of

arXiv:1005.5633v1
fatcat:2vfujzo3bjb2bkfb7ajtngssry
*omega*context free*languages*(*omega*-CFL). ... We prove here that there exist some*omega*context free*languages*which are Borel sets of infinite (but not*finite*) rank, giving additional answer to questions of Lescow and Thomas [Logical Specifications ... Definition 2.1 : A*finite**state*machine (FSM) is a quadruple M = (K, Σ, δ, q 0 ), where K is a*finite*set of*states*, Σ is a*finite*input alphabet, q 0 ∈ K is the initial*state*and δ is a mapping from K ...##
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Algebraic notions of nontermination: Omega and divergence in idempotent semirings

2010
*
The Journal of Logic and Algebraic Programming
*

Two notions of nontermination are studied and compared in the setting of idempotent semirings: Cohen's

doi:10.1016/j.jlap.2010.07.016
fatcat:khxf6uhajraztonb4fl3m4eex4
*omega*operator and a divergence operator. ... It turns out that divergence yields a simple and natural way of modelling infinite behaviours of programs and discrete systems, whereas the*omega*operator shows some anomalies. ... Acknowledgements The authors are grateful to Roland Glück and Bernhard Möller for proofreading the paper, to the reviewers for their suggestions, and to Ernie Cohen and Jules Desharnais for discussions on*omega*...##
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Borel Hierarchy and Omega Context Free Languages
[article]

2011
*
arXiv
*
pre-print

context free

arXiv:1101.3443v1
fatcat:mchn5kjacvautj2yks4psn5aqa
*languages*: there exist some*omega*-CFL which are non Borel sets. ... We give also an answer to questions of Niwinski and Simonnet about*omega*powers of finitary*languages*, giving an example of a finitary context free*language*L such that L^*omega*is not a Borel set. ... We have previously proved the existence of analytic but non Borel sets in another class of ω-*languages*, the class of locally*finite*ω*languages*[Fin01c] . ...##
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Omega Algebras and Regular Equations
[chapter]

2011
*
Lecture Notes in Computer Science
*

We instantiate these results in concrete models-

doi:10.1007/978-3-642-21070-9_19
fatcat:bswqjzgcyraspbt5623tkiszmi
*languages*, traces and relations-showing, for instance, that the*omega*captures precisely the empty word property in regular*languages*. ... We study a weak variant of*omega*algebra, where one of the usual star induction axioms is absent, in the context of recursive regular equations. ... Example 1 . 1 Regular*languages*form Kleene algebras. Let Σ be a*finite*set or alphabet and let Σ * be the free monoid (set of all*finite*words) over Σ. A*language*is a subset X of Σ * . ...##
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An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank
[article]

2008
*
arXiv
*
pre-print

*Omega*-powers of finitary

*languages*are

*omega*

*languages*in the form V^

*omega*, where V is a finitary

*language*over a

*finite*alphabet X. ... We answer this question in this paper, giving an example of a finitary

*language*whose

*omega*-power is Borel of infinite rank. ... Remark that in terms of code theory Lemma 3.4

*states*that the

*language*h(V) is an ω-code. Lemma 3.5 The set (h(V)) ω is a Borel set. Proof. ...

##
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Left omega algebras and regular equations

2012
*
The Journal of Logic and Algebraic Programming
*

It turns out, for instance, that the

doi:10.1016/j.jlap.2012.05.004
fatcat:syfjyqp7hzgilg44q43zmhqttm
*omega*operation captures precisely the empty word property in regular*languages*and wellfoundedness in relational models. ... The definability and solvability results are refined to concrete models, to*languages*, traces and relations. ... The*omega*operation is explicitly definable in models that are inherently*finite*, for instance regular*languages*, sets of*finite*paths or traces, or binary relations. ...##
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Literal shuffle on ω-languages

1996
*
Information Processing Letters
*

We call a subset of $\Sigma^{*}$ ( $\Sigma\

doi:10.1016/0020-0190(96)00091-9
fatcat:pvlnpaulhjhl7p76svihtwg3wu
*omega*$ , resp.) a*language*( $\*omega*$ -*language*) over $\Sigma$ . A deterministic*finite*$auto? ... {l}\mathrm{p}1_{1}\mathrm{a}\mathrm{b}\mathrm{e}\mathrm{t},$ $\delta$ : $S\cross\Sigmaarrow S$ is a next*state*function, $s_{0}\in S$ is an initial*state*, and $F\subseteq S$ is a set of accepting*states*...##
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Learning Finite-State Models for Machine Translation
[chapter]

2004
*
Lecture Notes in Computer Science
*

In formal

doi:10.1007/978-3-540-30195-0_2
fatcat:n2soiu6f5ze2vb66jg5qq3y6qe
*language*theory,*finite*-*state*transducers are well-know models for simple "input-output" mappings between two*languages*. ... Moreover, the relative simplicity of these mappings has recently led to the development of techniques for learning*finite*-*state*transducers from a training set of inputoutput sentence pairs of the*languages*... by*finite*-*state*devices (Kornai, 1985) . ...##
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Learning finite-state models for machine translation

2006
*
Machine Learning
*

In formal

doi:10.1007/s10994-006-9612-9
fatcat:2brzvkrv4jg7dhivheufceltya
*language*theory,*finite*-*state*transducers are well-know models for simple "input-output" mappings between two*languages*. ... Moreover, the relative simplicity of these mappings has recently led to the development of techniques for learning*finite*-*state*transducers from a training set of inputoutput sentence pairs of the*languages*... by*finite*-*state*devices (Kornai, 1985) . ...##
###
Page 2061 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

Paris 7, Paris, 1992; per bibl.] about

*omega*powers of finitary*languages*. ... Summary: “This paper is a study of topological properties of*omega*context-free*languages*(w-CFLs). ...##
###
Regular omega-Languages with an Informative Right Congruence

2018
*
Electronic Proceedings in Theoretical Computer Science
*

Weak regular

doi:10.4204/eptcs.277.19
fatcat:vw4areu5brau3nurhwnfzv4idi
*omega*-*languages*reside in the lower levels of the expressiveness hierarchy of regular*omega*-*languages*. ... The same does not hold for regular*omega*-*languages*. ... One of the fundamental theorems of regular*languages*on*finite*words is the Myhill-Nerode theorem*stating*a one-to-one correspondence between the*state*of the minimal deterministic*finite*automaton (DFA ...##
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There Exist some Omega-Powers of Any Borel Rank
[article]

2007
*
arXiv
*
pre-print

*Omega*-powers of finitary

*languages*are

*languages*of infinite words (

*omega*-

*languages*) in the form V^

*omega*, where V is a finitary

*language*over a

*finite*alphabet X. ... Since the set of infinite words over a

*finite*alphabet X can be equipped with the usual Cantor topology, the question of the topological complexity of

*omega*-powers of finitary

*languages*naturally arises ... In the full version of this paper we give many Wadge degrees of ω-powers and this confirms the great complexity of these ω-

*languages*. ...

##
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Page 8168 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

*state*tree automaton. (6) L is recognizable by a

*finite*

*state*tree automaton of index zero. ... L is a

*language*of

*finitely*branching

*finite*, or infinite trees. ...

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