Generalized Fair Reachability Analysis for Cyclic Protocols: Part 1

Abstract

In this paper, the notion of fair reachability is generalized to cyclic protocols with n > 2 communicating finite state machines. An equivalence is established between the set of fair reachable states and the set of reachable states with equal channel length. As a result, deadlock detection is decidable for cyclic protocols with finite fair reachability graphs. The concept of simultaneous unboundedness is defined and the lack of it is shown to be a necessary and sufficient condition for a cyclic protocol to have a finite fair reachability graph. For the first time, we are able to exactly characterize the class of protocols whose fair reachability graphs are finite. As far as decidability of deadlock detection is concerned, our result extends the class of cyclic protocols studied by Peng & Purushothaman, and complements the one investigated by Pachl. More importantly, our decision procedure is much more straightforward and efficient, as compared to Pachl’s and the one by Peng & Purushothaman. In this respect, we have improved the complexity of deadlock detection for the class of cyclic protocols with finite fair reachability graphs. To further demonstrate the strength of generalized fair reachability analysis, we also show that livelock detection is decidable for the class of cyclic protocols with finite fair reachability graphs.Keyword CodesC.2.2D.2.1D.2.4KeywordsNetwork ProtocolsRequirements/SpecificationsProgram Verification