Introduction aux langages reconnaissables
We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most is not finitely based for all . More specifically, for each pair of positive integers , we construct a monoid of complexity , all of whose -generated submonoids have complexity at most .
We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most n is not finitely based for all n>0. More specifically, for each pair of positive integers n,k, we construct a monoid of complexity n+1, all of whose k-generated submonoids have complexity at most n.
Partially-additive monoids (pams) were introduced by Arbib and Manes ([1]) in order to provide an algebraic approach to the semantic of recursion in theoretical computer science. Here we extend the range of application of pams for capturing information theory concepts as componibility and sequential continuity, which arise naturally in this framework.