Faster Algorithms for the Nonemptiness of Streett Automata and for Communication Protocol Pruning

This paper shows how a general technique, called lock-step search, used in dynamic graph algorithms, can be used to improve the running time of two problems arising in program veriication and communication protocol design. (1) We consider the nonemptiness problem for Streett automata: We are given a directed graph G = (V; E) with n = jV j and m = jEj, and a collection of pairs of subsets of vertices, called Streett pairs, hLi; Uii; i = 1::k. The question is whether G has a cycle (not necessarily simple) which, for each 1 i k, if it contains a vertex from Li then it also contains a vertex of Ui. Let b = P i=1::k jLij + jUij. The previously best algorithm takes time O((m+b) minfn; kg). We present an algorithm that takes time O(m minf p m log n; k; ng + b minflog n; kg). (2) In communication protocol pruning we are given a directed graph G = (V; E) with l special vertices. The problem is to eeciently maintain the strongly-connected components of the special vertices on a restricted set of edge deletions. Let mi be the number of edges in the strongly connected component of the ith special vertex. The previously best algorithm repeatedly recomputes the strongly-connected components which leads to a running time of O(