Liveness in broadcast networks

Abstract We study liveness and model checking problems for broadcast networks, a system of identical clients communicating via message passing. The first problem that we consider is Liveness Verification . It asks whether there computation such one visits final state infinitely often. complexity the has been open. was shown to be $$\texttt {P}$$ P -hard but in {EXPSPACE}$$ EXPSPACE close gap by polynomial-time algorithm. latter relies on characterization live computations terms paths suitable graph, combined with fixed-point iteration efficiently check existence paths. second Fair where all participating visit adjust algorithm also solve fair polynomial time. Both can instrumented answer questions networks against linear time temporal logic specifications. this context Model Checking demands network, satisfy specification. Vardi–Wolper construction reduction Sparse each client satisfies reduce