Nonassociativity à la Kleene

  • Jean-Marcel Pallo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4728)


First we recall the work of Suschkewitsch (1929) about the generalization of the associative law which is the starting point of the theory of quasigroups. Then we show that it is a particular case of the notion of relative associativity introduced by Roubaud in 1965. Thereafter we prove a coherence theorem over an infinite set of nonassociative operations. This result contains all the uppermentioned contributions. This allows to obtain a very general à-la-Kleene theorem on rational series which uses concatenations that can be associative or not.


Binary Operation Rational Series Formal Power Series Tree Language Free Monoid 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jean-Marcel Pallo
    • 1
  1. 1.Université de Bourgogne, LE2I UMR 5158, BP 47870, 21078 DIJON-CedexFrance

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