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Beyond omega-Regular Languages

Mikolaj Bojanczyk, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
The paper presents some automata and logics on ω-words, which capture all ω-regular languages, and yet still have good closure and decidability properties.  ...  The class of ω-regular languages carries over to ω-words many of the good properties of regular languages of finite words.  ...  Each of the classes captures all the ω-regular languages, and more.  ... 
doi:10.4230/lipics.stacs.2010.2440 dblp:conf/stacs/Bojanczyk10 fatcat:6oaslsh6kndxzixfk6zzpwqj7m

Left omega algebras and regular equations

Georg Struth
2012 The Journal of Logic and Algebraic Programming  
Left omega algebras, where one of the usual star induction axioms is absent, are studied in the context of recursive regular equations.  ...  It turns out, for instance, that the omega operation captures precisely the empty word property in regular languages and wellfoundedness in relational models.  ...  Acknowledgements I would like to thank Michael Laurence for his collaboration and the RAMiCS referees for their comments on the conference version of this paper.  ... 
doi:10.1016/j.jlap.2012.05.004 fatcat:syfjyqp7hzgilg44q43zmhqttm

Dynamic Hypergames for Synthesis of Deceptive Strategies with Temporal Logic Objectives [article]

Lening Li, Haoxiang Ma, Abhishek N. Kulkarni, Jie Fu
2020 arXiv   pre-print
logic.  ...  We demonstrate the correctness of our deceptive planning algorithm using robot motion planning examples with temporal logic objectives and design a detection mechanism to notify the agent of potential  ...  In this subclass of omega-regular games, players' objectives are given by syntactically co-safe LTL (scLTL) formula and safe Linear Temporal Logic (LTL) formulas [26] .  ... 
arXiv:2007.15726v1 fatcat:pl6kh7nz4jf47odj4sdfxsqley

Programming and automating mathematics in the Tarski–Kleene hierarchy

Alasdair Armstrong, Georg Struth, Tjark Weber
2014 Journal of Logical and Algebraic Methods in Programming  
For Kleene algebras we show how models can be programmed, including sets of traces and paths, languages, binary relations, max-plus and min-plus algebra, matrices, formal power series.  ...  We present examples from a reference implementation of variants of Kleene algebras and Tarski's relation algebras in the theorem proving environment Isabelle/HOL.  ...  Hitoshi Furusawa and Yasuo Kawahara have helped to clarify the presentation of this paper through several discussions.  ... 
doi:10.1016/j.jlap.2014.02.001 fatcat:jxygndlhxrheba6rninswkp65m

A Weakness Measure for GR(1) Formulae [chapter]

Davide Giacomo Cavezza, Dalal Alrajeh, András György
2018 Lecture Notes in Computer Science  
In this paper we propose a more refined measure of weakness based on the Hausdorff dimension, a concept that captures the notion of size of the omega-language satisfying a linear temporal logic formula  ...  of a logical formula, the measure we propose quantifies a concept of weakness intrinsic to the LTL formula itself.  ...  Acknowledgments The support of the EPSRC HiPEDS CDT (EP/L016796/1) is gratefully acknowledged.  ... 
doi:10.1007/978-3-319-95582-7_7 fatcat:b5xo3vwklfawbd7sewvk4b4vxi

A Weakness Measure for GR(1) Formulae [article]

Davide G. Cavezza, Dalal Alrajeh, András György
2018 arXiv   pre-print
In this paper we propose a more refined measure of weakness based on the Hausdorff dimension, a concept that captures the notion of size of the omega-language satisfying a linear temporal logic formula  ...  subset of linear temporal logic formulae which is of particular interest in controller synthesis.  ...  Acknowledgments The support of the EPSRC HiPEDS CDT (EP/L016796/1) is gratefully acknowledged.  ... 
arXiv:1805.03151v1 fatcat:vquk6bguvngsjeemhbbq23ey6a

Regular omega-Languages with an Informative Right Congruence

Dana Angluin, Dana Fisman
2018 Electronic Proceedings in Theoretical Computer Science  
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  ...  Weak regular omega-languages reside in the lower levels of the expressiveness hierarchy of regular omega-languages.  ...  LTL formulas are non-counting [18, 34, 13, 28] . But, there are LTL formulas that characterize languages that are not in IT (and thus not in any of the I classes).  ... 
doi:10.4204/eptcs.277.19 fatcat:vw4areu5brau3nurhwnfzv4idi

Monadic partition logics and finite automata

Enshao Shen, Qijia Tian
1996 Theoretical Computer Science  
They are strictly weaker in expressive power than monadic second-order logic, have some good semantic features and offer better specification formalisms for studying finite automata and forlnal languages  ...  By argumenting first-order logic with monadic partition quantifiers we get a new family of extended logics.  ...  Acknowledgements The first author would like to propose naming the partition quantifiers as Ebbinghaus quantifiers, for his first proposition of them and pushing forward their study anonymously.  ... 
doi:10.1016/0304-3975(95)00113-1 fatcat:jf5c7duqb5bt3g4nvtj3dfpjnm

Efficient Model Checking of Safety Properties [chapter]

Timo Latvala
2003 Lecture Notes in Computer Science  
This work discusses the theoretical and some of the practical issues related to model checking LTL properties.  ...  Our first contribution is a theorem relating abstraction for Coloured Petri nets as defined by Lakos [36] and preservation of safety properties.  ...  The financial support of Helsinki Graduate School in Computer Science and Engineering, the Academy of Finland (project 47754), the Wihuri Foundation and Tekniikan Edistämissäätiö (Foundation for Technology  ... 
doi:10.1007/3-540-44829-2_5 fatcat:zlkczcjjdfeijoekb66ohrtpe4

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier–Stokes equations

Mikael Mortensen, Hans Petter Langtangen, Garth N. Wells
2011 Advances in Water Resources  
formulation of equations and algorithms.  ...  The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical  ...  Subclasses of CoupledBase provide the exact formula for the variational form through the form method.  ... 
doi:10.1016/j.advwatres.2011.02.013 fatcat:ct3g5rjhobh3nemojqgomtkaa4

FAST: acceleration from theory to practice

Sébastien Bardin, Alain Finkel, Jérôme Leroux, Laure Petrucci
2008 International Journal on Software Tools for Technology Transfer (STTT)  
They are the most commonly encountered properties in practice, and allow specification of important properties such as the absence of deadlock, capacity overflow and division by zero.  ...  A configuration c ′ is reachable from a configuration c if and only if (c, c ′ ) ∈− → * , where − → * denotes the reflexive and transitive closure of − →.  ...  , and to Ales Smrcka for adapting the Omega source code to recent compilers.  ... 
doi:10.1007/s10009-008-0064-3 fatcat:3msu4gglojfpbignampzd2fz44

Deterministic Automata for the (F,G)-fragment of LTL [article]

Jan Křetínský, Javier Esparza
2012 arXiv   pre-print
When dealing with linear temporal logic properties in the setting of e.g. games or probabilistic systems, one often needs to express them as deterministic omega-automata.  ...  We investigate the complexity of this translation and provide experimental results and compare them to the traditional method.  ...  Acknowledgement Thanks to Andreas Gaiser for pointing out to us that ltl2dstar constructs surprisingly large automata for fairness constraints and the anonymous reviewers for their valuable comments.  ... 
arXiv:1204.5057v1 fatcat:52na5t5asbgsfcystiyccfr73y

Fragments of first-order logic over infinite words [article]

Volker Diekert, Manfred Kufleitner
2009 arXiv   pre-print
We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for omega-languages: Sigma_2, FO^2, the intersection  ...  The paper is about the interplay of algebraic, topological, and language theoretic properties.  ...  Acknowledgements We thank the anonymous referees for many useful suggestions which helped to improve the presentation of the paper.  ... 
arXiv:0906.2995v2 fatcat:7cxh3pglwrhznmqyenolwqixxi

Generate Certified Test Cases by Combining Theorem Proving and Reachability Analysis [chapter]

Richard Castanet, Davy Rouillard
2002 IFIP Advances in Information and Communication Technology  
Test purposes are expressed by timed regular expressions and then translated into a corresponding automaton using a certified function.  ...  We present a test case generation method which conciliates theorem proving and model checking.  ...  Since the property Q in the goal 2 is a formula of HOL logic, one disposes of a large expressive language.  ... 
doi:10.1007/978-0-387-35497-2_19 fatcat:2undk7xqqzavbowkj3zml44a7y

Deterministic Automata for the (F,G)-Fragment of LTL [chapter]

Jan Křetínský, Javier Esparza
2012 Lecture Notes in Computer Science  
Finally, a third strategy is to search for more efficient or simpler algorithms for subclasses of ω-regular languages. A natural choice is to investigate classes of LTL formulas.  ...  When dealing with linear temporal logic properties in the setting of e.g. games or probabilistic systems, one often needs to express them as deterministic omega-automata.  ...  Thanks to Andreas Gaiser for pointing out to us that ltl2dstar constructs surprisingly large automata for fairness constraints and the anonymous reviewers for their valuable comments.  ... 
doi:10.1007/978-3-642-31424-7_7 fatcat:rqucuwvhezhtrpdqdpgazdwarq
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