On the progress of communication between two machines

Abstract

We consider the following problem concerning any two finite state machines M and N which exchange messages via two one-directional channels. "Is there a positive integer K such that M and N with K-capacity channels never reach a nonprogress state?" The problem is shown to be undecidable in general. For a reasonable class of communicating machines, the problem is shown to be decidable; and the decidability algorithm is polynomial. We also discuss some sufficient conditions for the problem to have a a positive answer; these sufficient conditions can be checked for the given M and N in polynomial time.KeywordsBounded communicationcommunicating finite state machinecommunication deadlockcommunication protocolprogressunspecified reception