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Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
Abstract

Cited by 4 (3 self)
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language  the largest set commuting with a language , of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago  asking whether or not the centralizer of any rational language is rational  in the case of periodic, binary, and ternary sets of words, as well as for rational ccodes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an ccode X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.
On Semilinearity in Formal Power Series
 Proceedings of DLT 1999, Developments in Language Theory: foundations, applications, and perspectives, World Scientific
, 1999
"... A notion of semilinearity is introduced for formal power series as a natural generalization of the semilinear sets over a commutative monoid. We prove that the results known for semilinear sets are, in general, preserved in the generalization. ..."
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Cited by 2 (1 self)
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A notion of semilinearity is introduced for formal power series as a natural generalization of the semilinear sets over a commutative monoid. We prove that the results known for semilinear sets are, in general, preserved in the generalization.
Annual progress report ALAPEDES
"... s of the presentations are available upon request. 3.3.2 Other conferences and workshops Appendix C contains an overview of visits by Alapedes members to other conferences, workshops and courses, that are related to Alapedes. Probably the overview is incomplete. 3.3.3 External collaboration by Al ..."
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s of the presentations are available upon request. 3.3.2 Other conferences and workshops Appendix C contains an overview of visits by Alapedes members to other conferences, workshops and courses, that are related to Alapedes. Probably the overview is incomplete. 3.3.3 External collaboration by Alapedesmembers During the Waterford convention (the first plenary meeting of Alapedes; see x 1.3.3) several researchers from the DIAS (Dublin Institute of Applied Statistics) were welcomed. They are interested in stochastic aspects of discrete event systems. Fruitfull discussions have taken place and one presentation has been given (see Appendix D). In the framework of the establishment of DIOC's (Delft Interfaculty Research Centres), an official collaboration with the Faculty of Civil Engineering has been started. The name of the joined project is: "Seamless Multimodal Mobility". The subject areas are on mathematical applications towards transportation planning. See further in x 1.1.11. L....