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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.  ...  Finally, we derive Salomaa's axioms for the algebra of regular events. This yields a sound and complete axiomatisation in which the "regular" axioms are weaker than Kleene algebra.  ...  It is well known that regular languages can be represented by regular expressions, and we usually do not distinguish between the two. Regular expressions and Kleene algebras have the same signature.  ... 
doi:10.1007/978-3-642-21070-9_19 fatcat:bswqjzgcyraspbt5623tkiszmi

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 approach also leads to simple new relative completeness results for left omega algebras, and for Salomaa's axioms for regular expressions.  ...  I would also like to apologise to my family for having worked between Christmas and New Year 2011 to meet the special issue deadline on December 31.  ... 
doi:10.1016/j.jlap.2012.05.004 fatcat:syfjyqp7hzgilg44q43zmhqttm

Some Remarks on Regular Words

Stephen L. Bloom, Zoltán Ésik
2002 BRICS Report Series  
In particular we show that a countable word is regular iff it can be defined on an ordinary regular language (which can be chosen to be a prefix code) ordered by the lexicographical order such that the  ...  The current paper contains some new descriptions of this class of words related to properties of regular sets of binary strings, and uses finite automata to decide various natural questions concerning  ...  2. if it does, whether (P, ≤ ) is well ordered.  ... 
doi:10.7146/brics.v9i39.21754 fatcat:h63hts755re4vlpg5nuiyiehsi

On Completeness of Omega-Regular Algebras [chapter]

Michael R. Laurence, Georg Struth
2012 Lecture Notes in Computer Science  
Omega-regular algebras axiomatise the equational theory of omega-regular expressions as induced by omega-regular language identity.  ...  We introduce a first-order Horn axiomatisation for which such conditions can be avoided because additive and multiplicative units are absent.  ...  Omega Regular Algebras Wagner [16] gave a soundness and completeness result for ω-regular languages.  ... 
doi:10.1007/978-3-642-33314-9_12 fatcat:wnhk74ykdja2xhczjhiylzqsva

On the ω-language Expressive Power of Extended Petri Nets

A. Finkel, G. Geeraerts, J.-F. Raskin, L. Van Begin
2005 Electronical Notes in Theoretical Computer Science  
To prove these results, we propose original techniques that rely on well-quasi orderings and monotonicity properties.  ...  We compare the expressive power of Petri nets, Petri nets extended with nonblocking arcs and Petri nets extended with transfer arcs, in terms of ω-languages.  ...  Acknowledgements We would like to address many thanks to Raymond Devillers for proof-reading the paper and giving us many judicious advices.  ... 
doi:10.1016/j.entcs.2004.11.030 fatcat:bh47yymxf5g6bpahfw3qafexjy

Abstract abstract reduction

Georg Struth
2006 The Journal of Logic and Algebraic Programming  
This generalization covers rewriting with transitive relations, quasi-orderings and equations.  ...  Sections 6 and 7 present algebraic proofs of Church-Rosser theorems for quasi-orderings and transitive relations, which are specialized to the usual statements of equational rewriting in Section 8.  ...  Acknowledgments I would like to thank the anonymous referees, Roland Backhouse, Bernhard Möller and Gunther Schmidt for valuable comments and pointers to the literature.  ... 
doi:10.1016/j.jlap.2005.04.001 fatcat:sb642bhnqnanrohtc3cgcmwmb4

Algebraic Notions of Termination

Desharnais Jules, Bernhard Moeller, Struth Georg, Dexter Kozen
2011 Logical Methods in Computer Science  
To model infinite behaviours, idempotent semirings are extended to divergence semirings, divergence Kleene algebras and omega algebras.  ...  These applications show that modal semirings are powerful tools for reasoning algebraically about the finite and infinite dynamics of programs and transition systems.  ...  2004 conference and of LMCS for helpful comments on earlier versions.  ... 
doi:10.2168/lmcs-7(1:1)2011 fatcat:stigsogyszap7ng6b5mxfyl2r4

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.  ...  on omega and divergence.  ... 
doi:10.1016/j.jlap.2010.07.016 fatcat:khxf6uhajraztonb4fl3m4eex4

Embedding Finite and Infinite Words into Overlapping Tiles [chapter]

Anne Dicky, David Janin
2014 Lecture Notes in Computer Science  
This leads to an algebraic characterization of regular languages of finite and infinite birooted words that generalizes and unifies the known algebraic characterizations of regular languages of finite  ...  ordered ω-monoids.  ...  be E-ordered as well.  ... 
doi:10.1007/978-3-319-09698-8_30 fatcat:c35rvgtrsbdhnnbnorl5vglnwa

SPM Bulletin 14 [article]

Boaz Tsaban
2005 arXiv   pre-print
CONTENTS: New reals: Can live with them, can live without them; Uniform almost everywhere domination; Heredity of tau-pseudocompactness; Understanding preservation theorems: omega^omega-bounding; Classification  ...  problems in continuum theory; Residuality of families of F_sigma sets; First countable, countably compact spaces and the continuum hypothesis; Game approach to universally Kuratowski-Ulam spaces; Small  ...  The proofs use some general results concerning the wider class of analytic quasi-orders. Andrzej Kucharski and Szymon Plewik 2.9. Small Valdivia compact spaces.  ... 
arXiv:math/0509432v1 fatcat:mmekipstybdxrcbzf5yylhrvrq

Numerical Approximation of Orthogonal Maps

Alexandre Caboussat, Roland Glowinski, Dimitrios Gourzoulidis, Marco Picasso
2019 SIAM Journal on Scientific Computing  
Numerical experiments validate the accuracy and the efficiency of the method for various domains and meshes.  ...  They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal maps is considered here.  ...  Dacorogna (EPFL) and Prof. Marcellini (University of Firenze) for fruitful discussions, and the two anonymous referees for constructive remarks.  ... 
doi:10.1137/19m1243683 fatcat:e4lulhbqh5fo5ex7cpn4d6umbi

Automated NLO QCD Corrections with WHIZARD [article]

C. Weiss, B. Chokoufe Nejad, W. Kilian, J. Reuter
2015 arXiv   pre-print
Greiner for many helpful discussions on NLO event generation in general as well as technical support with GoSam. Also, we thank J.  ...  We present the preliminary results for the total cross section at next-to-leading order as well as fixed-order NLO event shapes for selected observables.  ...  Moreover, the simulation and analysis can be very conveniently performed using the built-in script language SINDARIN. WHIZARD is written in Fortran2003.  ... 
arXiv:1510.02666v1 fatcat:jxibv6pyrbgelgkm4y5wvv4lnm

On the ω-language expressive power of extended Petri nets

A. Finkel, G. Geeraerts, J.-F. Raskin, L. Van Begin
2006 Theoretical Computer Science  
To prove these results, we propose original techniques that rely on well-quasi orderings and monotonicity properties.  ...  We compare the expressive power of Petri nets, Petri nets extended with non-blocking arcs and Petri nets extended with transfer arcs, in terms of -languages.  ...  Acknowledgements We would like to address many thanks to Raymond Devillers for proof-reading the paper and giving us many judicious advices.  ... 
doi:10.1016/j.tcs.2006.02.008 fatcat:vkpjkpg6ojd35krax3vxhk4c7i

Polyunsaturated fatty acids (PUFAs) for children with specific learning disorders

May Loong Tan, Jacqueline J Ho, Keng Hwang Teh
2016 The Cochrane library  
Polyunsaturated fatty acids (PUFAs), in particular, omega-3 and omega-6 fatty acids, which normally are abundant in the brain and in the retina, are important for learning.  ...  Both studies used three months of a combination of omega-3 and omega-6 supplements as the intervention compared with placebo.  ...  types; Language=All languages; #15 TS=(written expression disorder*) DocType=All document types; Language=All languages; S5 PUFA OR PUFAS S4 FATTY ACID* S3 fatty acid* S2 OMEGA 6 S1 OMEGA 3 CDSR  ... 
doi:10.1002/14651858.cd009398.pub3 pmid:27678554 pmcid:PMC6457739 fatcat:23ddyqnkrjegnfukrsly6bxc4a

Modal Tools for Separation and Refinement

Georg Struth
2008 Electronical Notes in Theoretical Computer Science  
Kleene modules and modal Kleene algebras are applied to automatically verify refinement laws for infinite loops and separation of termination.  ...  Equational axioms for divergence are introduced, and the concept is refined for different contexts. In particular it is related to Löb's formula, which describes termination in modal logics.  ...  Acknowledgement I am very grateful to Nachum Dershowitz, Jules Desharnais and Bernhard Möller for inspiring discussions and suggestions.  ... 
doi:10.1016/j.entcs.2008.06.005 fatcat:gzvmozk35nhzncfs5p5arvwos4
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