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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

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  ... 

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 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.  ... 
doi:10.4204/eptcs.277.19 fatcat:vw4areu5brau3nurhwnfzv4idi

Cardinality and counting quantifiers on omega-automatic structures [article]

Lukasz Kaiser, Sasha Rubin, Vince Bárány
2008 arXiv   pre-print
This implies Blumensath's conjecture that a countable structure with an ω-automatic presentation can be represented using 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.  ... 
arXiv:0802.2866v1 fatcat:e6u444zcmzhepp56valkfilvqm

Cardinality and counting quantifiers on omega-automatic structures

Lukasz Kaiser, Sasha Rubin, Vince Bárány, Marc Herbstritt
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 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.  ... 
doi:10.4230/lipics.stacs.2008.1360 dblp:conf/stacs/KaiserRB08 fatcat:agsicc6vevdtphqnds67suinj4

A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time [article]

Ben Moszkowski
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.  ... 
arXiv:1207.3816v1 fatcat:z4he73ipszesjnwec2ncmebpje

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

Axel Legay, Pierre Wolper
2006 Electronical Notes in Theoretical Computer Science  
Among the acceleration techniques that have been proposed, 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.  ... 
doi:10.1016/j.entcs.2005.12.020 fatcat:aypszw6vlvcxfjurvuqe23bzie

The Hanoi Omega-Automata Format [chapter]

Tomáš Babiak, František Blahoudek, Alexandre Duret-Lutz, Joachim Klein, Jan Křetínský, David Müller, David Parker, Jan Strejček
2015 Lecture Notes in Computer Science  
The format allows acceptance conditions that are either state-based or transition-based, and also supports 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.  ... 
doi:10.1007/978-3-319-21690-4_31 fatcat:ojzyxonqung2tpxerm3qusra6i

Borel Hierarchy and Omega Context Free Languages [article]

Olivier Finkel
2011 arXiv   pre-print
And 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] .  ... 
arXiv:1101.3443v1 fatcat:mchn5kjacvautj2yks4psn5aqa

Preface to the Special Issue on Computer Science in Russia 2016

Alexander S. Kulikov, Gerhard J. Woeginger
2018 Theory of Computing Systems  
infinite 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.  ... 
doi:10.1007/s00224-018-9854-5 fatcat:sbiokecipfaqldekzhdviifzx4

Omega Algebras and Regular Equations [chapter]

Michael R. Laurence, Georg Struth
2011 Lecture Notes in Computer Science  
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.  ...  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.  ... 
doi:10.1007/978-3-642-21070-9_19 fatcat:bswqjzgcyraspbt5623tkiszmi

Alternating Good-for-MDP Automata [article]

Ernst Moritz Hahn and Mateo Perez and Sven Schewe and Fabio Somenzi and Ashutosh Trivedi and Dominik Wojtczak
2022 arXiv   pre-print
When 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.  ... 
arXiv:2205.03243v1 fatcat:wkbw2u6wffczvey2uld67thyri

Logic and Rational Languages of Words Indexed by Linear Orderings

Nicolas Bedon, Alexis Bès, Olivier Carton, Chloé Rispal
2009 Theory of Computing Systems  
We prove that every rational language of 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.  ... 
doi:10.1007/s00224-009-9222-6 fatcat:ql4zjihwwfb4hc4fbppyqflqmu

Efficient Model Checking of Safety Properties [chapter]

Timo Latvala
2003 Lecture Notes in Computer Science  
Our other contribution is an efficient algorithm for translating LTL safety properties to 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.  ... 
doi:10.1007/3-540-44829-2_5 fatcat:zlkczcjjdfeijoekb66ohrtpe4

Model Checking Markov Chains Against Unambiguous Buchi Automata [article]

Michael Benedikt, Rastislav Lenhardt, James Worrell
2016 arXiv   pre-print
We give a polynomial-time algorithm for model checking 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.  ... 
arXiv:1405.4560v2 fatcat:2itq23fdsnalrcb3xfgs2rvvky
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