Bridging the gap between place- and Floyd-invariants with applications to preemptive scheduling
The notion of linear place-invariants for coloured nets is extended to sums of non-linear functions. The extension applies to such places where all tokens are removed by the occurrence of an output transition. It is shown how this covers the case of variable assignments and invariants in traditional programs. The result helps in understanding the relation of place-invariants of coloured nets in comparison with traditional Floyd-invariants of programs. In the second part the property of token clearing is introduced to the occurrence rule, showing that the results of the first part are still valid. Such types of nets are important for the modelling of fault tolerant applications.
Keywordsanalysis and synthesis structure and behavior of Petri nets higher-level net models coloured Petri nets program verification place-invariants Floyd-invariants selfmodifying coloured Petrinets
Unable to display preview. Download preview PDF.
- [Floyd 67]Floyd, R.: Assigning meaning to programs. Mathematical Aspects of Computer Science, XIX American Mathematical Society (1967), 19–32Google Scholar
- [Gries 81]Gries, D.: The Science of Programming, Springer, Berlin 1981Google Scholar
- [Hoare 69]Hoare, C.A.R.: An axiomatic approach to computer programming, Comm. ACM 12(1969), 576–580,583Google Scholar
- [Jensen 81]Jensen, K.: Coloured Petri Nets and the invariant method. Theoretical Computer Science 14(1981), 317–336Google Scholar
- [Jensen 87]Jensen, K.: Coloured Petri Nets, in Petri Nets: Central Models and Their Properties, in Brauer, W. et al. (Eds), Lecture Notes in Computer Science No 254, Springer, Berlin 1987, 248–299Google Scholar
- [Valk 78]Valk, R.: Selfmodifying Nets, a Natural Extension of Petri Nets, Lecture Notes in Computer Science No 62, Springer, Berlin 1978, 464–476Google Scholar
- [Valk 83]Valk, R.: Facts in Place/Transition Nets with Unrestricted Capacities, Annales Univ. Scie. Budapestensis R. Eötvös, Sect. Comput. Tom. IV, 1983, 97–105Google Scholar
- [Valk 93]Valk, R.: Extending S-invariants for Coloured and Selfmodifying Nets, Techn. Report,Univ. Hamburg, Dep. of Computer Science, 1993Google Scholar
- [Vautherin 85]Vautherin, J.: Non-linear invariants for safe coloured nets and appli cation to the proof of parallel programs, Proc. 6th European Workshop on Applications and Theory of Petri Nets, Espoo, Finland, 1985Google Scholar