Canonical Prefixes of Petri Net Unfoldings.

摘要

In this paper, we develop a general technique for truncating Petri net unfoldings, parameterized according to the level of information about the original unfolding one wants to preserve. Moreover, we propose a new notion of completeness of a truncated unfolding, which with the standard parameters is strictly stronger than that given in (5,6), and is more appropriate for the existing model checking algorithms. A key aspect of our approach is an algorithm-independent notion of cut-off events, used to truncate a Petri net unfolding in the existing model checking systems. Such a notion is based on a cutting context and results in the unique canonical prefix of the unfolding. We show that the canonical prefix is complete in the new, stronger sense, and provide necessary and sufficient conditions for its finiteness, as well as upper bounds on its size in certain cases. We then consider the unfolding algorithm presented in (5,6), and the parallel unfolding algorithm proposed in (10). We prove that both algorithms, despite being non-deterministic, generate the canonical prefix. This gives an alternative correctness proof for the former algorithm, and a new (much simpler) proof for the latter one.