Some algebraic connections between behavior decompositions andtwo-sided diophantine equations

摘要

Concerns behavior-based system modelling. In this paper, therelationship between complete behaviors decomposition and thesolvability of certain two-sided diophantine equations is explored. Moreprecisely, the possibility of expressing a complete behavior as a directsum of two subbehaviors, one of which has been chosen a priori, provesto be equivalent to the solvability of a particular two-sided Bezoutequation, while, more generally, decompositions with specificintersections of the two subbehaviors are related to the solvability ofdiophantine equations with suitable constant terms