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Star-free trace languages

Giovanna Guaiana, Antonio Restivo, Sergio Salemi
1992 Theoretical Computer Science  
., A. Restivo and S. Salemi, Star-free trace languages, Theoretical Computer Science 97 (1992) 301-311.  ...  Generalizing a classical result of Schiitzenberger to free partially commutative monoids, we prove that the family of star-free trace languages coincides with the family of aperiodic trace languages.  ...  Acknowledgment We thank the anonymous referee for his suggestions.  ... 
doi:10.1016/0304-3975(92)90080-y fatcat:zei6dzejb5hptkk34zjj54ujeq

Logical definability on infinite traces

Werner Ebinger, Anca Muscholl
1996 Theoretical Computer Science  
The main results of the present paper are the equivalence of definability by monadic secondorder logic and recognizability for real trace languages, and that first-order definable, star-free, and aperiodic  ...  real trace languages form the same class of languages.  ...  Thomas for many interesting comments.  ... 
doi:10.1016/0304-3975(95)00130-1 fatcat:4qsekf35zvftjbxixwoot2ie6y

Left omega algebras and regular equations

Georg Struth
2012 The Journal of Logic and Algebraic Programming  
The definability and solvability results are refined to concrete models, to languages, traces and relations.  ...  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

On recognizable and rational formal power series in partially commuting variables [chapter]

Manfred Droste, Paul Gastin
1997 Lecture Notes in Computer Science  
We prove that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to  ...  Moreover, if in addition the semiring is idempotent then the same result holds with a star restricted to series for which the elements in the support have connected (possibly di erent) alphabets.  ...  operations union, product and star, where the latter is applied only to connected languages.  ... 
doi:10.1007/3-540-63165-8_222 fatcat:bdp4inrslvb7foufngrepegska

On Aperiodic and Star-Free Formal Power Series in Partially Commuting Variables

Manfred Droste, Paul Gastin
2007 Theory of Computing Systems  
This generalizes a classical result of Schützenberger (1961) for aperiodic regular languages and subsumes a result of Guaiana, Restivo and Salemi (1992) on aperiodic trace languages.  ...  We also show that if K is idempotent and the matrix monoids over K have a Burnside property (satisfied, e.g. by the tropical semiring), then the aperiodic and the star-free series coincide.  ...  ., for a class of particular concurrency monoids (intersecting with trace monoids only in the class of free monoids), see [6] .  ... 
doi:10.1007/s00224-007-9064-z fatcat:v3hrgjung5bc3i5z7gtwouv2xm

On Aperiodic and Star-free Formal Power Series in Partially Commuting Variables [chapter]

Manfred Droste, Paul Gastin
2000 Formal Power Series and Algebraic Combinatorics  
This generalizes a classical result of Schützenberger (1961) for aperiodic regular languages and subsumes a result of Guaiana, Restivo and Salemi (1992) on aperiodic trace languages.  ...  We also show that if K is idempotent and the matrix monoids over K have a Burnside property (satisfied, e.g. by the tropical semiring), then the aperiodic and the star-free series coincide.  ...  ., for a class of particular concurrency monoids (intersecting with trace monoids only in the class of free monoids), see [6] .  ... 
doi:10.1007/978-3-662-04166-6_14 fatcat:umz6aa3rzzforfk4rx3lpltmhq

The Star Problem and the Finite Power Property in Trace Monoids: Reductions beyond C4

Daniel Kirsten
2002 Information and Computation  
We deal with the star problem in trace monoids which means to decide whether the iteration of a recognizable trace language is recognizable.  ...  We consider trace monoids K n = {a 1 , b 1 } * × · · · × {a n , b n } * .  ...  INTRODUCTION We deal with the star problem in free, partially commutative monoids, also known as trace monoids. The star problem was raised by Ochmański in 1984 [29] .  ... 
doi:10.1006/inco.2002.3152 fatcat:5dyguoonzbexnnsu6iukrvxnda

Page 3554 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
The decidability of the finite power problem for free monoids played a crucial role in showing decidability of the star problem for recognizable languages in trace monoids with various properties.  ...  The star problem is the problem of deciding whether the iteration of a recognizable language is recognizable. For free monoids and free commmutative monoids, the star problem is decidable.  ... 

Page 2890 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
The star problem in trace monoids is to decide whether the iter- ation of a recognizable trace language is recognizable.  ...  The main result of this paper asserts that it suffices to consider the star prob- lem on trace monoids of the form: {a),b)}* x --- x {@n,bn}*.  ... 

Algebraic recognizability of languages [article]

Pascal Weil
2006 arXiv   pre-print
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors.  ...  For instance, the question of rational expressions for trace languages remains unclear (see the star problem): the difficulty comes from the fact that the star of a recognizable trace language may not  ... 
arXiv:cs/0609110v1 fatcat:2fnhr3gu5rdbbdugq76cqfvl4y

Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids

D. Kirsten, G. Richomme
2001 Theory of Computing Systems  
In the last decade, some researches on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?)  ...  for recognizable languages which contain at most one non-connected trace.  ...  Formally, the set A of words over A with the concatenation operation is the free monoid over A. Its identity is the empty word .  ... 
doi:10.1007/s00224-001-0006-x fatcat:5grot4tre5g2hhs26mcr4cirje

Reordering Derivatives of Trace Closures of Regular Languages

Hendrik Maarand, Tarmo Uustalu, Michael Wagner
2019 International Conference on Concurrency Theory  
We provide syntactic derivative-like operations, defined by recursion on regular expressions, in the styles of both Brzozowski and Antimirov, for trace closures of regular languages.  ...  We define the uniform scattering rank of a language and show that, for a regexp whose language has finite uniform scattering rank, the truncation of the (generally infinite) refined Antimirov automaton  ...  Acknowledgements We thank Pierre-Louis Curien, Jacques Sakarovitch, Simon Doherty, Georg Struth and Ralf Hinze for inspiring discussions, and our anonymous reviewers for the exceptionally thorough and  ... 
doi:10.4230/lipics.concur.2019.40 dblp:conf/concur/MaarandU19 fatcat:zsbue57lozbxpm3es2cef2zllm

Algebraic Recognizability of Languages [chapter]

Pascal Weil
2004 Lecture Notes in Computer Science  
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  Since the beginnings of language theory, there has been an interest for other models than words -especially for the purpose of modeling distributed or timed computation (trees, traces, pomsets, graphs,  ...  For instance, the question of rational expressions for trace languages remains unclear (see the star problem): the difficulty comes from the fact that the star of a recognizable trace language may not  ... 
doi:10.1007/978-3-540-28629-5_8 fatcat:5el7wd3umvgdzhw4dxukeugoci

Page 6938 of Mathematical Reviews Vol. , Issue 93m [page]

1993 Mathematical Reviews  
Finally, it is proved that every rational language is the inverse image, under some morphism between free monoids, of a language of restricted star-height 1. For related results, see a paper by J. A.  ...  The Mazurkiewicz trace language generated by an NS is interpreted as a concurrent (noninterleaving) semantics of the NS. These synchronization operations are compositional.  ... 

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.  ...  For relation algebras we discuss primarily proof automation in a comprehensive library and present an advanced formalisation example.  ...  Last, but not least, the second author is indebted to Gunther Schmidt for his continuous support and critical encouragement.  ... 
doi:10.1016/j.jlap.2014.02.001 fatcat:jxygndlhxrheba6rninswkp65m
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