Detection of Regular Predicates in a Whole Space in Distributed Computation

Given a distributed computation and a predicate, detection of the predicate in \textit{Definitely} modality means checking whether in every path from the least state to the greatest state in the state space generated from the computation, which is a distributive lattice, there exists a state satisfying the predicate. The regular predicate is a class of predicates. All the states satisfying the predicate form a sub lattice of state space. Detection of a regular predicate in \textit{Definitely} modality is proved to be coNP-complete. In this paper, we study a special kind of state spaces, the whole space, in which all states of the computation are consistent. We propose two polynomial algorithms for detection of regular predicates in \textit{Definitely} modality in a whole space.