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Semigroups and Automata on Infinite Words [chapter]

Dominique Perrin, Jean-Eric Pin
1995 Semigroups, Formal Languages and Groups  
Acknowledgements The authors would like to thank Olivier Carton and Pascal Weil for their comments on a preliminary version of this article.  ...  words the notions of finite automata, of a semigroup recognizing a set of words and finally of syntactic semigroup.  ...  This definition suffices to extend Kleene's theorem to infinite words: the sets of infinite words recognized by finite Büchi automata are exactly the ω-rational sets.  ... 
doi:10.1007/978-94-011-0149-3_3 fatcat:baawnkgzrbdenmohs5wv3mgr6y

A purely algebraic proof of McNaughton's theorem on infinite words [chapter]

Bertrand Saec, Jean-Eric Pin, Pascal Weil
1991 Lecture Notes in Computer Science  
We give a new, purely algebraic proof of McNanghton's theorem on infinite words, which states that each recognizable set X of infinite words can be recognized by a deterministic Muller automaton.  ...  Our proof uses the semigroup approach to recognizability and relies on certain algebraic properties of finite semigroups.  ...  The D = ND result implies for instance that the set of words recognized by non-deterministic automata is closed under complementation.  ... 
doi:10.1007/3-540-54967-6_66 fatcat:ekeyenzmh5fkbkbs36gukhzyyi

Operations on Weakly Recognizing Morphisms [chapter]

Lukas Fleischer, Manfred Kufleitner
2016 Lecture Notes in Computer Science  
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such  ...  This includes the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, and complementation.  ...  There are some similarities between recognizing morphisms over finite and over infinite words.  ... 
doi:10.1007/978-3-319-41114-9_10 fatcat:ykhj7ovl4ffvra43xbwzyigjya

Operations on Weakly Recognizing Morphisms [article]

Lukas Fleischer, Manfred Kufleitner
2016 arXiv   pre-print
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such  ...  This includes the conversion from and to B\"uchi automata, the conversion into strongly recognizing morphisms, and complementation.  ...  There are some similarities between recognizing morphisms over finite and over infinite words. Strong recognition is the natural counterpart to recognition for finite words.  ... 
arXiv:1603.05376v2 fatcat:gfdsgl4mc5asvmwtummdqqjwiu

FACTORIZATIONS AND UNIVERSAL AUTOMATON OF OMEGA LANGUAGES

VINCENT CARNINO, SYLVAIN LOMBARDY
2014 International Journal of Foundations of Computer Science  
We define a normal form for Büchi automata and introduce a universal automaton for Büchi automata in normal form.  ...  In this paper, we extend the concept of factorization on finite words to ω-rational languages and show how to compute them.  ...  In this paper, we focus on Büchi automata, which are the most intuitive kind of automata accepting infinite words.  ... 
doi:10.1142/s0129054114400279 fatcat:g37glxigbrcrffzzfa5nnz5ffe

Factorizations and Universal Automaton of Omega Languages [chapter]

Vincent Carnino, Sylvain Lombardy
2013 Lecture Notes in Computer Science  
We define a normal form for Büchi automata and introduce a universal automaton for Büchi automata in normal form.  ...  In this paper, we extend the concept of factorization on finite words to ω-rational languages and show how to compute them.  ...  In this paper, we focus on Büchi automata, which are the most intuitive kind of automata accepting infinite words.  ... 
doi:10.1007/978-3-642-38771-5_30 fatcat:udko2aucwfcjbhooli77wxpbsi

Page 8172 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
It turns out that the corresponding va- riety of «,-semigroups is defined by an equation which has a topological interpretation in the case of infinite words.  ...  Eilenberg’s result concerning &-trivial semigroups and extensive automata [see S. Eilenberg, Automata, languages, and ma- chines. Vol. B, Academic Press, New York, 1976; MR 58 #26604b].  ... 

A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : Part I

Jérémie Cabessa, Jacques Duparc
2009 RAIRO - Theoretical Informatics and Applications  
We then define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game.  ...  The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height  ...  In the case of finite structures, these objects represent a convincing algebraic counterpart to automata reading infinite words: given any finite Büchi automaton, one can build a finite ω-semigroup recognizing  ... 
doi:10.1051/ita/2009004 fatcat:vnyqwj35wnbgpon7oz2a6sw5ti

Page 4402 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
varieties of languages of arbitrary words on semigroups and automata.  ...  words of four kinds: finite, right infinite, left infinite and bi-infinite.  ... 

Page 2884 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
Finally, we separate classes of infinite words generated by double and triple DOL TAG systems.”  ...  (English summary) Words, semigroups, & transductions, 141-154, World Sci. Publishing, River Edge, NJ, 2001.  ... 

Page 3931 of Mathematical Reviews Vol. 58, Issue 5 [page]

1979 Mathematical Reviews  
Chapter 13 is concerned with infinite words and their interpreta- tion as real numbers.  ...  Sequential functions between sets of infinite words are introduced and certain remarkable examples of such functions related to Peano and Hilbert square-filling curves are presented.  ... 

Page 3837 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Arnold, André (F-POIT) 87g:68032 Deterministic and nonambiguous rational w-languages. Automata on infinite words (Le Mont-Dore, 1984), 18-27, Lecture Notes in Comput.  ...  For i = 1,---,k, let A; be an alphabet and A%*° the set of all words (finite or infinite) over A;; also, ¢ denotes the empty word.  ... 

COMPLEMENTATION OF RATIONAL SETS ON COUNTABLE SCATTERED LINEAR ORDERINGS

CHLOÉ RISPAL, OLIVIER CARTON
2005 International Journal of Foundations of Computer Science  
These automata are a generalization of automata for finite, infinite, bi-infinite and even transfinite words studied by Büchi. Kleene's theorem has been generalized to these words.  ...  In a preceding paper (Bruyère and Carton, automata on linear orderings, MFCS'01), automata have been introduced for words indexed by linear orderings.  ...  These linear structures include finite words, infinite, transfinite words and their mirrors. These automata are usual automata on finite words, extended with limit transitions.  ... 
doi:10.1142/s0129054105003285 fatcat:vn7hdn4q3zhgxaqm66crc77pym

Complementation of Rational Sets on Countable Scattered Linear Orderings [chapter]

Chloé Rispal, Olivier Carton
2004 Lecture Notes in Computer Science  
These automata are a generalization of automata for finite, infinite, bi-infinite and even transfinite words studied by Büchi. Kleene's theorem has been generalized to these words.  ...  In a preceding paper (Bruyère and Carton, automata on linear orderings, MFCS'01), automata have been introduced for words indexed by linear orderings.  ...  These linear structures include finite words, infinite, transfinite words and their mirrors. These automata are usual automata on finite words, extended with limit transitions.  ... 
doi:10.1007/978-3-540-30550-7_32 fatcat:qxr3qakxabhpzkulci3w5ilnli

On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata [article]

Thibault Godin and Ines Klimann and Matthieu Picantin
2014 arXiv   pre-print
This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and  ...  We focus on the somehow antipodal class of invertible reversible Mealy automata and prove that for a wide subclass the generated semigroup is torsion-free.  ...  In Section 2, we set up notation, provide well-known definitions and facts concerning Mealy automata and automaton semigroups.  ... 
arXiv:1410.4488v2 fatcat:lvgxoucjyvdg5oxmmbbwmojlem
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