Detection of Conjunctive Stable Predicates in Dynamic Systems

We present a distributed on-line algorithm for detecting conjunctive stable predicates in dynamic systems. The algorithm consists of a virtual network topology to maintain the causality relationships between distributed events and protocols to check the verification of the predicates over consistent global states. A lazy detection protocol has been developed to minimize the number of messages for the detection. Let M_c be the number of detection messages, then the message complexity of the algorithm is M_c ¿ M + n₀, where M is the number of computation messages and n₀ is the number of initial processes the computation starts with. Computation trees are maintained in the virtual network to reduce the detection delay. Suppose that h_max is the maximum height of the computation trees. The detection delay is O(h_max + n₀). It has been proved that a solution is declared if and only if the global predicate is verified during the progress of the underlying distributed computation.