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The greatest fixed-points and rational omega-tree languages

Masako Takahashi
1986 Theoretical Computer Science  
A simple normal form for rational 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.  ... 
doi:10.1016/0304-3975(86)90123-4 fatcat:nhs7puq6xjdanbcagpwhrmendu

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.  ...  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.  ... 
doi:10.18520/cs/v115/i11/2042-2051 fatcat:byu5hbxpnbaclbp2rkx3qa6uhm

On Omega Context Free Languages which are Borel Sets of Infinite Rank [article]

Olivier Finkel
2010 arXiv   pre-print
This paper is a continuation of the study of topological properties of 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  ... 
arXiv:1005.5633v1 fatcat:2vfujzo3bjb2bkfb7ajtngssry

Algebraic notions of nontermination: Omega and divergence in idempotent semirings

Peter Höfner, Georg Struth
2010 The Journal of Logic and Algebraic Programming  
Two notions of nontermination are studied and compared in the setting of idempotent semirings: Cohen's 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  ... 
doi:10.1016/j.jlap.2010.07.016 fatcat:khxf6uhajraztonb4fl3m4eex4

Borel Hierarchy and Omega Context Free Languages [article]

Olivier Finkel
2011 arXiv   pre-print
context free 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 ωlanguages [Fin01c] .  ... 
arXiv:1101.3443v1 fatcat:mchn5kjacvautj2yks4psn5aqa

Omega Algebras and Regular Equations [chapter]

Michael R. Laurence, Georg Struth
2011 Lecture Notes in Computer Science  
We instantiate these results in concrete models-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 * .  ... 
doi:10.1007/978-3-642-21070-9_19 fatcat:bswqjzgcyraspbt5623tkiszmi

An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank [article]

Olivier Finkel
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.  ... 
arXiv:0801.0535v1 fatcat:q6b5x77uxnaujjxkichc2rwxyu

Left omega algebras and regular equations

Georg Struth
2012 The Journal of Logic and Algebraic Programming  
It turns out, for instance, that the 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.  ... 
doi:10.1016/j.jlap.2012.05.004 fatcat:syfjyqp7hzgilg44q43zmhqttm

Literal shuffle on ω-languages

Tetsuo Moriya, Hideki Yamasaki
1996 Information Processing Letters  
We call a subset of $\Sigma^{*}$ ( $\Sigma\omega$ , 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  ... 
doi:10.1016/0020-0190(96)00091-9 fatcat:pvlnpaulhjhl7p76svihtwg3wu

Learning Finite-State Models for Machine Translation [chapter]

Enrique Vidal, Francisco Casacuberta
2004 Lecture Notes in Computer Science  
In formal 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) .  ... 
doi:10.1007/978-3-540-30195-0_2 fatcat:n2soiu6f5ze2vb66jg5qq3y6qe

Learning finite-state models for machine translation

Francisco Casacuberta, Enrique Vidal
2006 Machine Learning  
In formal 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) .  ... 
doi:10.1007/s10994-006-9612-9 fatcat:2brzvkrv4jg7dhivheufceltya

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

Dana Angluin, Dana Fisman
2018 Electronic Proceedings in Theoretical Computer Science  
Weak regular 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  ... 
doi:10.4204/eptcs.277.19 fatcat:vw4areu5brau3nurhwnfzv4idi

There Exist some Omega-Powers of Any Borel Rank [article]

Dominique Lecomte
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.  ... 
arXiv:0706.3523v1 fatcat:e3it3lamszd6fdegdiiduwgorm

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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