A Complete Set of Satisfaction Rules for Property Detection in Distributed Computations

This paper presents a general framework for speciication and detection of properties in distributed computations. A property of states in distributed computation in progress is deened by predicates (called behavioral patterns) and satisfaction rules (called modal operators). A behavioral pattern is obtained by combining basic predicates that are deened over either local states or consistent global states of the computation. In both cases, we model a distributed computation by a directed acyclic graph in which vertices represent (local or global) states and edges represent causal relation over the states. Speciication and veriication of behavioral patterns are formulated as instances of the language recognition problem, and basic concepts used in formal language theory are applied. A basic predicate is assimilated to a symbol, and a behavioral pattern is speciied as a language (i.e. a set of words) deened over an alphabet of symbols. Based on this model and given a behavioral pattern, we deene four modal operators (i.e. four diierent satisfaction rules). Three of them are equivalent to modal operators previously introduced in related works. Finally, we present algorithms to verify each of the four modal operators over a class of behavioral patterns, called regular patterns. A Complete Set of Satisfaction Rules ...