On an Effective Hierarchy of Communicating Processes: Separation Principle and Testing

This paper is concerned with an effective hierarchy of guaranteed processes. A process satisfies a guarantee requirement when that requirement holds at some forthcoming point of every computation. Cy being the class of w-languages accepted by the base of this process hierarchy, this class of processes, namely Or, is a class of universal machines. Translated in these terms, our results throw light on, first, the increased computational power of the machine resulting from communication between any finite number of such machines and, second, that the hierarchy whose next degree represents w-languages accepted by machines resulting from communication between any finite number of machines in the current degree, is infinite. Interaction product acts as jump operator. We naturally start with some effective classes of guarantee properties proven to form a hierarchy and first prove that they have not the separation property. A class k? of o-languages has the separation property if, for any pair (U, Y) in V, there exists an w-language W E V such that U II W = 0 H V n W # 0. We then induce non-separability under testing from the above language theoretic non-separability result. Two processes are said to be separable if they can be separated from each other by means of another test process from the same class. It finally turns out that some processes, having different visible behaviours, are test equivalent. We close the paper on logical complexity issues of the testing problem when test criteria and guarantee constraints range over the arithmetical hierarchy.