Algebraic and fixed point equations over inverse limits of algebras (Q1177146)

Algebraic and fixed point equations over inverse limits of algebras have been studied extensively in the theory of semantics. It is possible to introduce a natural metric that takes into account the inverse limit structure of the given algebra. Systems of fixed point equations can then be viewed as ``contractions'' in the given metric, in which case, existence and uniqueness theorems from the theory of metric spaces are applicable in the context of semantics. The authors prove that a process is definable by a (finite) guarded system of equations if and only if it is definable by a single guarded equation. It is interesting to note that the related question ``if a process is the unique solution of a finite system of fixed point equations, is it the unique solution of finite guarded system of equations?'' (raised by the reviewer [Inf. Comput. 75, 264-288 (1987; Zbl 0626.68029)]) still remains open. In fact, the last reference solves this problem for systems consisting of a single equation.