The computing power of programs over finite monoids

Authors:
Pascal Tesson;Denis Thérien
Affiliations:
School of Computer Science, McGill University, 3480 University, Montréal, Québec, H3A 2A7 Canada;School of Computer Science, McGill University, 3480 University, Montréal, Québec, H3A 2A7 Canada
Venue:
Journal of Automata, Languages and Combinatorics - Selected papers of the workshop on logic and algebra for concurrency
Year:
2001

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Abstract

The formalism of programs over monoids has been studied for its close connection to parallel complexity classes defined by small-depth boolean circuits. We investigate two basic questions about this model. When is a monoid rich enough that it can recognize arbitrary languages (provided no restriction on length is imposed)? When is a monoid weak enough that all its computations can be realized in polynomial length? Surprisingly, these two properties appear to be dual to each other.