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Open Problems About Regular Languages, 35 Years Later [chapter]

Jean-Éric Pin
2017 The Role of Theory in Computer Science  
The languages of star-height n form a length-preserving variety of languages and hence can be defined by length-preserving profinite equations.  ...  Theorem (Plyushchenko and Shur 2011) For n = 2 and m = 1, the conjecture holds for all the elements containing an overlap-free or an almost overlap-free word.  ...  A striking selection of problems! (1) Limitedness problem (2) Star height ?? (3) Restricted star height (4) Group complexity ?  ... 
doi:10.1142/9789813148208_0007 dblp:conf/birthday/Pin17 fatcat:6priedkxnngivbnqss5a6l7bji

The influence of Imre Simon's work in the theory of automata, languages and semigroups

Jean-Éric Pin
2019 Semigroup Forum  
The purpose of this tribute is to review three major results due to Simon that had a considerable influence on the development of automata and semigroup theory.  ...  Acknowledgements I would like to thank László Márki and Norman Reilly for their help during the preparation of this article.  ...  49, 51, 56] and the star-height problem.  ... 
doi:10.1007/s00233-019-09999-8 fatcat:ebozes2olbddliniyrteshre4m

Weak MSO+U with Path Quantifiers over Infinite Trees [chapter]

Mikołaj Bojańczyk
2014 Lecture Notes in Computer Science  
Cost functions can be seen as a special case of mso+u in the sense that decision problems regarding cost functions, such as limitedness or domination, can be easily encoded into satisfiability of mso+u  ...  A significantly more powerful fragment of the logic, albeit for infinite words, was shown decidable in [3] using automata with counters.  ...  ωS-regular languages of infinite words, as defined in [3] .  ... 
doi:10.1007/978-3-662-43951-7_4 fatcat:fg7cwa6t2vgttdan4wtvs4wvs4

Regular Cost Functions, Part I: Logic and Algebra over Words

Thomas Colcombet, Wolfgang Thomas
2013 Logical Methods in Computer Science  
boundedness problem for monadic-second order logic over words.  ...  These models of automata have been successfully used for solving the star-height problem, the finite power property, the finite substitution problem, the relative inclusion star-height problem and the  ...  I am also very grateful to the two anonymous reviewers for their constructive remarks and their very thorough reading of the document.  ... 
doi:10.2168/lmcs-9(3:3)2013 fatcat:qn4wgvvrsjesricz6lddvgjwlm

Weak MSO+U with Path Quantifiers over Infinite Trees [article]

Mikołaj Bojańczyk
2014 arXiv   pre-print
The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.  ...  This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths.  ...  ωS-regular languages of infinite words, as defined in [3] .  ... 
arXiv:1404.7278v1 fatcat:hwgiicw2ojhvtn2jeb5s5j2xry

The Ackermann Award 2012

Thierry Coquand, Anuj Dawar, Damian Niwiński
Szymon Toruńczyk receives the 2012 Ackermann Award of the European Association of Computer Science Logic (EACSL) for his thesis Languages of profinite words and the limitedeness problem.  ...  It is a basic fact of the theory of profinite words that the completions of the ordinary regular languages form the family of clopen (closed and open) sets of profinite words.  ...  Detailed reports on their work appeared in the CSL proceedings, and are also available via the EACSL homepage.  ... 

Editors: Nicolas Ollinger and Heribert Vollmer; Article No. 29

Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, Szymon Toruńczyk
2007 13 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
of first-order definable languages, the class of languages accepted by counter-free automata, and the class of languages definable by aperiodic monoids (i.e. those that satisfy the equation x n+1 = x  ...  This gives an algebraic and effective characterisation of the class of star-free languages. The theory of regular languages has been extended in many directions-to infinite etc.  ...  of Schützenberger's seminal work on star-free languages [16] .  ...