Fixed point equations with parameters in the projective model (Q580971)

Existence and uniqueness theorems are given for solving infinite and finite systems of fixed point equations with parameters in the projective model (a natural model in the calculus of communicating processes). The results obtained are derived by exploiting the special topological and combinatorial properties of the projective model and the polynomial operators defined on it. The topological methods employed in the proofs of the existence and uniqueness theorems use a combination of the following three ideas: compactness argument, density argument, and Banach's contraction principle. As a converse to the uniqueness theorem it is also shown, using combinatorial methods, that in certain signatures guarded equations are the only ones that have unique fixed points.