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In distributed systems it is often important to be able to determine the temporal relationships between events generated by different processes. An algorithm to determiue such relationships is presented in [3] and [5]. This algorithm has many favorable attributes such as it allows for any kind of interprocess communication, and it requires no extra synchronization messages, additional communication links or cent ral t imestamping authority.The algorithm, however, requires O(n) space for each process (where n is the number of processes).i.e., it requires an overall space of 0(n2 ). This can be a large overhead especially when there are a very large number of processes.By cutting down on this generality, we can significantly decrease the amount of space required to determine temporal relationships.In this paper, we show how one may reduce the space requirements by assuming that the communication links between processes is static and known ahead oj time; and also that one is interested only in determining the temporal ordering between messages arriving at the same process. We argue that these assumptions are reasonable to make for a large class of problems.

We describe a general module language integrating abstract data types, specifications and object-oriented

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The current algebraic models for nondeterminism focus on the notion of possibility rather than necessity and consequently equate (nondeterministic) terms that one would intuitively not consider equal. Furthermore, existing models for nondeterminism depart radically from the standard models for (equational) specifications of deterministic operators. One would prefer that a specification language for nondeterministic operators be based on an extension of the standard model concepts, preferably in such a way that the reasoning system for (possibly nondeterministic) operators becomes the standard equational one whenever restricted to the deterministic operators—the objective should be to minimize the departure from the standard frameworks. In this article we define a specification language for nondeterministic operators and multialgebraic semantics. The first complete reasoning system for such specifications is introduced. We also define a transformation of specifications of nondeterministic operators into derived specifications of deterministic ones, obtaining a “computational” semantics of nondeterministic specification by adopting the standard semantics of the derived specification as the semantics of the original one. This semantics turns out to be a refinement of multialgebra semantics. The calculus is shown to be sound and complete also with respect to the new semantics.