Some algebraic connections between behavior decompositions and two-sided diophantine equations

Concerns behavior-based system modelling. In this paper, the relationship between complete behaviors decomposition and the solvability of certain two-sided diophantine equations is explored. More precisely, the possibility of expressing a complete behavior as a direct sum of two subbehaviors, one of which has been chosen a priori, proves to be equivalent to the solvability of a particular two-sided Bezout equation, while, more generally, decompositions with specific intersections of the two subbehaviors are related to the solvability of diophantine equations with suitable constant terms.