Abstract
In this paper, the notion of fair reachability is generalized to cyclic protocols with more than two processes, where all the processes in a protocol are connected via a unidirectional ring and each process might contain internal transitions and can be non-deterministic. We identify ‘indefiniteness’ as a new type of logical error due to reachable internal transition cycles. By properly incorporating internal transitions into the formulation, we show that, with a few modifications, all the previous results established for cyclic protocols without non-deterministic and internal transitions still hold in the augmented model. Furthermore, by combining fair progress and maximal progress during state exploration, we prove that the following three problems are all decidable for Q, the class of cyclic protocols with finite fair reachable state spaces: (1) global state reachability; (2) abstract state reachability; and (3) execution cycle reachability. In the course of the investigation, we also show that detection of k-indefiniteness and k-livelock are decidable for Q.
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