On the Relationship between π-Calculus and Finite Place/Transition Petri Nets
We clarify the relationship between π-calculus and finite p/t Petri nets. The first insight is that the concurrency view to processes taken in [Eng96, AM02, BG09] and the structural view in [Mey09] are orthogonal. This allows us to define a new concurrency p/t net semantics that can be combined with the structural semantics in [Mey09]. The result is a more expressive mixed semantics, which translates precisely the so-called mixed-bounded processes into finite p/t nets. Technically, the translation relies on typing of restricted names. As second main result we show that mixed-bounded processes form the borderline to finite p/t nets. For processes just beyond this class reachability becomes undecidable and so no faithful translation into finite p/t nets exists.
KeywordsParallel Composition Structural Semantic Restricted Form Counter Machine Process Place
Unable to display preview. Download preview PDF.
- [Fok07]Fokkink, W.: Modelling Distributed Systems. Springer, Heidelberg (2007)Google Scholar
- [KKN06]Khomenko, V., Koutny, M., Niaouris, A.: Applying Petri net unfoldings for verification of mobile systems. In: Proc. of MOCA, Bericht FBI-HH-B-267/06, pp. 161–178. University of Hamburg (2006)Google Scholar
- [Mey08a]Meyer, R.: On boundedness in depth in the π-calculus. In: Proc. of IFIP TCS. IFIP, vol. 273, pp. 477–489. Springer, Heidelberg (2008)Google Scholar
- [Mey08b]Meyer, R.: Structural Stationarity in the π-calculus. PhD thesis, Department of Computing Science, University of Oldenburg (2008)Google Scholar
- [MKS09]Meyer, R., Khomenko, V., Strazny, T.: A practical approach to verification of mobile systems using net unfoldings. Fund. Inf. (to appear 2009)Google Scholar
- [Pet08]Petruchio (2008), http://petruchio.informatik.uni-oldenburg.de
- [Pis99]Pistore, M.: History Dependent Automata. PhD thesis, Dipartimento di Informatica, Università di Pisa (1999)Google Scholar