State-action pairs reduction for strong cyclic planning via state reachability

Strong cyclic planning under all state-action pairs has been addressed in the literature. Normally, the more the state-action pairs are, the higher of complexity is. In fact, there are many state-action pairs which are useless for strong cyclic planning. Before finding strong cyclic planning, it is significant to find a set of state-action pairs which are useless for strong cyclic planning, and to best of our knowledge, it is still an open problem. In this paper, hypergraph is defined for a nondeterministic state-transition system, adjacency matrix and reachability matrix of the hypergraph are defined. A method about how to use the adjancey matrix to count the reachability matrix is designed, and a way about how to use the reachability matrix to count the state reachability is presented in a nondeterministic state-transition system. Some important conclusions about strong cyclic planning are obtained by using the state reachability. These conclusions tell us what state-action pairs are useless when we search strong cyclic planning. So a lot of state-action pairs can be eliminated directly from all state-action pairs before searching strong cyclic planning. Our first contribution is the method which finds state reachability in nondeterministic state-transition system. A second contribution is the some important conclusions about strong cyclic planning, these works are significant to improve the efficiency of algorithm for solving strong cyclic planning.