A Theory of Name Boundedness

We develop a theory of name-bounded π-calculus processes, which have a bound on the number of restricted names that holds for all reachable processes. Name boundedness reflects resource constraints in practical reconfigurable systems, like available communication channels in networks and address space limitations in software. Our focus is on the algorithmic analysis of name-bounded processes. First, we provide an extension of the Karp-Miller construction that terminates and computes the coverability set for any name-bounded process. Moreover, the Karp-Miller tree shows that name-bounded processes have a pumping bound as follows. When a restricted name is distributed to a number of sequential processes that exceeds this bound, the name may be distributed arbitrarily. Second, using the bound, we construct a Petri net bisimilar to the name-bounded process. The Petri net keeps a reference count for each restricted name, and recycles names that are no longer in use. The pumping property ensures that bounded zero tests are sufficient for recycling. With this construction, name-bounded processes inherit decidability properties of Petri nets. In particular, reachability is decidable for them. We complement our decidability results by a non-primitive recursive lower bound.