UNDECIDABLE VERIFICATION PROBLEMS FOR PROGRAMS WITH UNRELIABLE CHANNELS

We consider the class of finite-state systems communicating through un bounded but lossy FIFO channels (called lossy channel systems). These systems have infinite state spaces due to the unboundedness of the cha nnels. In an earlier paper, we showed that the problems of checking re achability, safety properties, and eventuality properties are decidabl e for lossy channel systems. In this paper, we show that the following problems are undecidable: The model checking problem in propositional temporal logics such as propositional linear time temporal logic (PTL ) and computation tree logic (CTL). The problem of deciding eventualit y properties with fair channels: do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assu mptions? The results are obtained through reduction from a variant of the Post correspondence problem. (C) 1996 Academic Press. Inc.