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Omega Automata and its Classes

2018
*
Current Science
*

ω-

doi:10.18520/cs/v115/i11/2042-2051
fatcat:byu5hbxpnbaclbp2rkx3qa6uhm
*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*. ...##
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Page 8168 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

The paper is a continuation of the author’s works

*on*topologi- cal properties of*omega*context free languages (@-CFL). ... We first show that some known results of*automata*theory immediately lead to an*alternative*construction which yields a simpler*word*that guarantees minimal image: it has exponential length, more precisely ...##
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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 right congruence of a regular*omega*-language is not informative enough; many regular*omega*-languages have a trivial right congruence, and in general it is not always possible to define an*omega*-automaton ... The theory of ω-*automata*enjoys many properties that the theory of*automata**on**finite**words*enjoys. ...##
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Cardinality and counting quantifiers on omega-automatic structures
[article]

2008
*
arXiv
*
pre-print

This implies Blumensath's conjecture that a countable structure with an ω-automatic presentation can be represented using

arXiv:0802.2866v1
fatcat:e6u444zcmzhepp56valkfilvqm
*automata**on**finite**words*. ... quantifiers 'there exist at most _0 many', 'there exist*finitely*many' and 'there exist k modulo m many' are*omega*-regular. ... We consider relations*on**finite*and ω-*words*recognised by multi-tape*finite**automata*operating in a synchronised letter-to-letter fashion. ...##
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Cardinality and counting quantifiers on omega-automatic structures

2008
*
Symposium on Theoretical Aspects of Computer Science
*

This implies Blumensath's conjecture that a countable structure with an ω-automatic presentation can be represented using

doi:10.4230/lipics.stacs.2008.1360
dblp:conf/stacs/KaiserRB08
fatcat:agsicc6vevdtphqnds67suinj4
*automata**on**finite**words*. ... quantifiers 'there exist at most ℵ0 many', 'there exist*finitely*many' and 'there exist k modulo m many' are*omega*-regular. ... We consider relations*on**finite*and ω-*words*recognised by multi-tape*finite**automata*operating in a synchronised letter-to-letter fashion. ...##
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A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
[article]

2012
*
arXiv
*
pre-print

*automata*and nontrivial techniques for complementing them. ... Our completeness proof uses a reduction to completeness for PITL with

*finite*time and conventional propositional linear-time temporal logic. ...

*automata*for

*finite*

*words*in order to recognise

*omega*-regular languages. ...

##
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On the Use of Automata-based Techniques in Symbolic Model Checking

2006
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Electronical Notes in Theoretical Computer Science
*

Among the acceleration techniques that have been proposed,

doi:10.1016/j.entcs.2005.12.020
fatcat:aypszw6vlvcxfjurvuqe23bzie
*one*finds both specific and generic techniques. ... Computing such a regular representation of, say, the reachable set of states of a system requires acceleration techniques that can*finitely*compute the effect of an unbounded number of transitions. ... To avoid the hard to implement algorithms needed for some operations*on*infinite-*word**automata*, only*omega*-regular sets that can be defined by weak deterministic Büchi*automata*[7] are considered. ...##
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The Hanoi Omega-Automata Format
[chapter]

2015
*
Lecture Notes in Computer Science
*

The format allows acceptance conditions that are either state-based or transition-based, and also supports

doi:10.1007/978-3-319-21690-4_31
fatcat:ojzyxonqung2tpxerm3qusra6i
*alternating**automata*. ... We propose a flexible exchange format for ω-*automata*, as typically used in formal verification, and implement support for it in a range of established tools. ... Introduction*Finite**automata*over infinite*words*, ω-*automata*, play a crucial role in formal verification. ...##
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Borel Hierarchy and Omega Context Free Languages
[article]

2011
*
arXiv
*
pre-print

And

arXiv:1101.3443v1
fatcat:mchn5kjacvautj2yks4psn5aqa
*one*cannot decide whether an*omega*-CFL is a Borel set. ... Then we prove some recursive analogues to preceding properties: in particular*one*cannot decide whether an*omega*-CFL is an arithmetical 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] . ...##
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Preface to the Special Issue on Computer Science in Russia 2016

2018
*
Theory of Computing Systems
*

infinite

doi:10.1007/s00224-018-9854-5
fatcat:sbiokecipfaqldekzhdviifzx4
*words*. ... The paper Level two of the quantifier*alternation*hierarchy over infinite*words*by Manfred Kufleitner and Tobias Walter addresses the membership problem for a certain fragment of first-order logic over ... He examines the predictive capabilities of*finite**automata*, pushdown*automata*, stack*automata*, and multihead*finite**automata*. ...##
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Omega Algebras and Regular Equations
[chapter]

2011
*
Lecture Notes in Computer Science
*

We study a weak variant of

doi:10.1007/978-3-642-21070-9_19
fatcat:bswqjzgcyraspbt5623tkiszmi
*omega*algebra, where*one*of the usual star induction axioms is absent, in the context of recursive regular equations. ... 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. ... A trace over a (*finite*) set P and a (*finite*) set A is a*finite*sequence over (P ∪ A) * , in which the first and last letter are in P and in which letters from P and A*alternate*. ...##
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Alternating Good-for-MDP Automata
[article]

2022
*
arXiv
*
pre-print

When

arXiv:2205.03243v1
fatcat:wkbw2u6wffczvey2uld67thyri
*omega*-regular objectives were first proposed in model-free reinforcement learning (RL) for controlling MDPs, deterministic Rabin*automata*were used in an attempt to provide a direct translation from ... Rabin*automata*, the*alternating*good-for-MDP*automata*we produce from deterministic Streett*automata*are bi-linear in the the size of the deterministic automaton and its index, and can therefore be exponentially ...*Omega*-*Automata*An alphabet is a*finite*set of letters. We write B for the binary alphabet {0, 1}. A*finite**word*over an alphabet Σ is a*finite*concatenation of symbols from Σ. ...##
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Logic and Rational Languages of Words Indexed by Linear Orderings

2009
*
Theory of Computing Systems
*

We prove that every rational language of

doi:10.1007/s00224-009-9222-6
fatcat:ql4zjihwwfb4hc4fbppyqflqmu
*words*indexed by linear orderings is definable in monadic second-order logic. ... As a corollary we prove that the inclusion problem for rational languages of*words*indexed by countable linear orderings is decidable. ... Schützenberger gave another characterization of star-free sets, based*on*the equivalence of*automata*and an algebraic formalism, the*finite*monoids, for the definition of sets of*finite**words*. ...##
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Efficient Model Checking of Safety Properties
[chapter]

2003
*
Lecture Notes in Computer Science
*

Our other contribution is an efficient algorithm for translating LTL safety properties to

doi:10.1007/3-540-44829-2_5
fatcat:zlkczcjjdfeijoekb66ohrtpe4
*finite**automata*. ... In the linear time paradigm, model checking of safety properties is simpler than the general case, because safety properties can be captured by*finite**automata*. ... ACKNOWLEDGEMENTS The author thanks Keijo Heljanko for fruitful discussions and comments*on*the paper. ...##
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Model Checking Markov Chains Against Unambiguous Buchi Automata
[article]

2016
*
arXiv
*
pre-print

We give a polynomial-time algorithm for model checking

arXiv:1405.4560v2
fatcat:2itq23fdsnalrcb3xfgs2rvvky
*finite*Markov chains against*omega*-regular specifications given as unambiguous Buchi*automata*. ... We consider*automata**alternatively*as acceptors of*finite**words*and acceptors of infinite*words*(via the Büchi acceptance condition). ... Introduction An automaton is unambiguous if each*word*has at most*one*accepting run and separated if no*word*is accepted from two distinct states. ...
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