Word Problem in Distributive Magmas

Article type: Research Article

Authors: Pallo, Jean Marcel

Affiliations: Universite de Dijon

Abstract: This paper shows that among the transformations which have words formed with three operators and four variables correspond to words formed with two operators and three variables, distributivity clone verifies some remarkable properties. Indeed, it is a confluent and noetherian relation which satisfies an inductive comparison theorem. One can deduce a computer – programmable algorithm which makes it possible to solve the word problem in a set of variables with two associative operators one of which is distributive on the right with respect to the other, i.e. to decide whether or not two words composed of variables and operators can be proved equal as a consequence of the identities of associativity and distributivity satisfied by these operators.

Keywords: word problem, magmas, confluent relation, noetherian relation

DOI: 10.3233/FI-1981-4410

Journal: Fundamenta Informaticae, vol. 4, no. 4, pp. 957-973, 1981