The limit of splitn-language equivalence
Splitting is a simple form of action refinement that may be used to express the duration of actions. In particular, splitn subdivides each action into n phases. Petri nets N1 and N2 are splitn-language equivalent, if split n (N1) and split n (N2) are language equivalent. It is known that these equivalences get finer and finer with increasing n.
This paper characterizes the limit of this sequence by a newly defined partial order semantics. This semantics is obtained from the interval-semiword semantics, which is fully abstract for action refinement and language equivalence, by closing it under a special swap operation. The new swap equivalence lies strictly between interval-semiword and step-sequence equivalence.
Keywordsconcurrency partial order semantics action refinement
Unable to display preview. Download preview PDF.
- [BDKP91]E. Best, R. Devillers, A. Kiehn, and L. Pomello. Concurrent bisimulations in Petri nets. Acta Informatica, 28:231–264, 1991.Google Scholar
- [Dev92]R. Devillers. Maximality preservation and the ST-idea for action refinement. In G. Rozenberg, editor, Advances in Petri Nets 1992, Lect. Notes Comp. Sci. 609, 108–151. Springer, 1992.Google Scholar
- [Fis85]P.C. Fishburn. Interval Orders and Interval Graphs. J. Wiley, 1985.Google Scholar
- [GG89]R.J. v. Glabbeek and U. Goltz. Equivalence notions for concurrent systems and refinement of actions. In A. Kreczmar and G. Mirkowska, editors, MFCS 89, Lect. Notes Comp. Sci. 379, 237–248. Springer, 1989.Google Scholar
- [GL91]R. Gorrieri and C. Laneve. The limit of splitn-bisimulations for CCS agents. In A. Tarlecki, editor, MFCS 91, Lect. Notes Comp. Sci. 520, 170–180. Springer, 1991.Google Scholar
- [Gla90]R.J. v. Glabbeek. The refinement theorem for ST-bisimulation semantics. In M. Broy and C.B. Jones, editors, Programming Concepts and Methods, Proc. IFIP Working Conference, 27–52. Elsevier Science Publisher(North-Holland), 1990.Google Scholar
- [Gra81]J. Grabowski. On partial languages. Fundamenta Informaticae, IV.2:428–498, 1981.Google Scholar
- [GV91]R.J. v. Glabbeek and F. Vaandrager. The difference between splitting in n and n+1, 1991. Unpublished.Google Scholar
- [Hen88]M. Hennessy. Axiomatising finite concurrent processes. SIAM J. of Computing, 17:997–1017, 1988.Google Scholar
- [JK93]R. Janicki and M. Koutny. Representations of discrete interval orders and semi-orders. Technical Report 93-02, Dept. Comp. Sci. Sys., McMaster University, Hamilton, Ontario, 1993.Google Scholar
- [Lar88]K.S. Larsen. A fully abstract model for a process algebra with refinement. Master's thesis, Dept. Comp. Sci., Aarhus University, 1988.Google Scholar
- [Sta81]P.H. Starke. Processes in Petri nets. J. Inf. Process. Cybern. EIK, 17:389–416, 1981.Google Scholar
- [Vog92]W. Vogler. Modular Construction and Partial Order Semantics of Petri Nets. Lect. Notes Comp. Sci. 625. Springer, 1992.Google Scholar
- [Vog93a]W. Vogler. Bisimulation and action refinement. Theoret. Comput. Sci., 114:173–200, 1993.Google Scholar
- [Vog93b]W. Vogler. The limit of splitn-language equivalence. Technical Report Nr. 288, Inst. f. Mathematik, Univ. Augsburg, 1993.Google Scholar