Generalized fair reachability analysis for cyclic protocols

In this paper, the notion of fair reachability is generalized to cyclic protocols with n⩾2 machines. It is shown that each fair reachable state is of equal channel length and each deadlock state is fair reachable. As a result, deadlock detection is decidable for P, the class of cyclic protocols whose fair reachable state spaces are finite. The concept of simultaneous unboundedness is defined and the lack of it is shown to be a necessary and sufficient condition for a protocol to be in P. Through finite extension of the fair reachable state space, it is also shown that detection of unspecified receptions, unboundedness, and nonexecutable transitions are all decidable for P. Furthermore, it is shown that any protocol in P is logically correct if and only if there is no logical error in its fair reachable state space. This study demonstrates that for the class P, our generalized fair reachability analysis technique not only can achieve substantial state reduction but also maintains very competitive logical error coverage. Therefore, it is a very useful technique to prove logical correctness for a wide variety of cyclic protocols