Boolean closure and unambiguity of rational sets

2005 ◽  
pp. 512-525
Author(s):  
Maryse Pelletier
Keyword(s):  
Rational Sets

scholarly journals COMPLETELY REDUCIBLE SETS

2013 ◽  
Vol 23 (04) ◽  
pp. 915-941 ◽  
Author(s):  
DOMINIQUE PERRIN
Keyword(s):  
Closure Properties ◽  
Linear Representations ◽  
Complete Reducibility ◽  
The Family ◽  
Syntactic Representation ◽  
Completely Reducible ◽  
Rational Sets ◽  
Cyclic Sets

We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a result on linear representations of monoids which gives a generalization of the result concerning the complete reducibility of the submonoid generated by a bifix code to sets called birecurrent. We also give a new proof of the result concerning cyclic sets.

scholarly journals Higher Dimensional Automata

2002 ◽  
Vol 9 (44) ◽  
Author(s):  
Zoltán Ésik ◽  
Zoltán L. Németh
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Dimensional Theory ◽  
Higher Dimensional ◽  
Second Order Logic ◽  
Rational Sets ◽  
Monadic Second Order Logic

We provide the basics of a 2-dimensional theory of automata on series-parallel biposets. We define recognizable, regular and rational sets of series-parallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.

Rational sets in finitely generated nilpotent groups

2000 ◽  
Vol 39 (4) ◽  
pp. 215-223 ◽  
Author(s):  
G. A. Bazhenova
Keyword(s):  
Nilpotent Groups ◽  
Finitely Generated ◽  
Rational Sets

scholarly journals Strongly rational sets for normal-form games

2016 ◽  
Vol 5 (1) ◽  
pp. 35-46
Author(s):  
Gilles Grandjean ◽  
Ana Mauleon ◽  
Vincent Vannetelbosch
Keyword(s):  
Normal Form ◽  
Normal Form Games ◽  
Rational Sets

scholarly journals COMPLEMENTATION OF RATIONAL SETS ON COUNTABLE SCATTERED LINEAR ORDERINGS

2005 ◽  
Vol 16 (04) ◽  
pp. 767-786 ◽  
Author(s):  
CHLOÉ RISPAL ◽  
OLIVIER CARTON
Keyword(s):  
Algebraic Approach ◽  
Preceding Paper ◽  
Linear Orderings ◽  
Rational Sets

In a preceding paper (Bruyère and Carton, automata on linear orderings, MFCS'01), automata have been introduced for words indexed by linear orderings. 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. We prove that rational sets of words on countable scattered linear orderings are closed under complementation using an algebraic approach.

THE WAGNER HIERARCHY

1999 ◽  
Vol 09 (05) ◽  
pp. 597-620 ◽  
Author(s):  
OLIVIER CARTON ◽  
DOMINIQUE PERRIN
Keyword(s):  
New Approach ◽  
Rational Sets

This paper is the second part of a series of two in which we present a new version of K. Wagner's hierarchy of ω-rational sets. The first paper presents a new approach to the concepts of chains and superchains. This one presents the classification itself.

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