On the Computation of McMillan’s Prefix for Contextual Nets and Graph Grammars
In recent years, a research thread focused on the use of the unfolding semantics for verification purposes. This started with a paper by McMillan, which devises an algorithm for constructing a finite complete prefix of the unfolding of a safe Petri net, providing a compact representation of the reachability graph. The extension to contextual nets and graph transformation systems is far from being trivial because events can have multiple causal histories. Recently, we proposed an abstract algorithm that generalizes McMillan’s construction to bounded contextual nets without resorting to an encoding into plain P/T nets. Here, we provide a more explicit construction that renders the algorithm effective. To allow for an inductive definition of concurrency, missing in the original proposal and essential for an efficient unfolding procedure, the key intuition is to associate histories not only with events, but also with places. Additionally, we outline how the proposed algorithm can be extended to graph transformation systems, for which previous algorithms based on the encoding of read arcs would not be applicable.
Unable to display preview. Download preview PDF.
- 3.Baldan, P., Corradini, A., König, B., Schwoon, S.: McMillan’s complete prefix for contextual nets. In: Jensen, K., van der Aalst, W.M.P., Billington, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency I. LNCS, vol. 5100, pp. 199–220. Springer, Heidelberg (2008)CrossRefGoogle Scholar
- 9.Langerak, R.: Transformation and Semantics for LOTOS. Ph.D. thesis, Department of Computer Science, University of Twente (1992)Google Scholar
- 10.McMillan, K.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–174. Springer, Heidelberg (1993)Google Scholar