Detection of a Weak Conjunction of Unstable Predicates in Dynamic Systems

A weak conjunctive predicate is a conjunction of local predicates that is evaluated under the Possibly modality. In this study, we have proposed a distributed on-line algorithm for detecting weak conjunctions of unstable predicates in dynamic systems. In the algorithm, a virtual network of a logical ring combined with computation trees is dynamically maintained using local variables to keep track of causality relationships between distributed events. The differential technique is exploited to minimize the size of detection related information. During the execution of the distributed computation, each process maintains a vector containing potential solutions. Detection will be announced when the global predicate is verified. This algorithm does not require extra messages except those for process termination. The detection of a solution may not be announced until the termination of the underlying distributed computation in the case where a process never communicates with others. At each process, storage need is proportional to the number of processes in the system. This demand will increase in some extreme cases, although they are very rare in practice.