Abstract
The paper gives an introduction to fundamentals and recent trends in the theory of high-level nets. High-level nets are first formally derived from low-level nets by means of a quotient construction. Based on a linear-algebraic representations, we develop an invariant calculus that essentially corresponds to the algebraic core of the well-known coloured nets. We demonstrate that the modelling power of high-level nets stems from the use of expressive symbolic annotation languages, where as a typical model we consider predicate-transition nets, both concrete models and net-schemes. As examples of specific high-level analysis-tools we discuss symbolic place-invariants and reachability-trees.
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References
M. Ajmon Marsan et al. Modelling with Generalized Stochastic Petri Nets. Wiley,1995.
E. Best, H. Fleischhack, W. Fraczak, R. Hopkins, H. Klaudel, E. Pelz. A class of composable high level Petri Nets. In Application and Theory of Petri Nets 1995, vol. 935 of LNCS, pp. 103–120. Springer-Verlag, 1995.
R. Brgan, D. Poitrenaud. An efficient algorithm for the computation of stubborn sets of well formed Petri nets. In Application and Theory of Petri Nets 1995, vol. 935 of LNCS, pp. 121–140. Springer-Verlag, 1995.
G. Chiola, C. Dutheillet, G. Franceschinis, S. Haddad. On well formed colored Petri nets and their symbolic reachability graph. In [17], pp. 373–296.
S. A. Christensen, N. Hansen. Coloured Petri nets extended with place capacities, test arcs and inhibitor arcs. In Application and Theory of Petri Nets 1993, vol. 691 of LNCS, pp. 186–205. Springer-Verlag,1993.
C. Chang and H. Keisler. Model Theory. North Holland, 1973.
P Cohn. Universal Algebra. D. Reidel Publishing Company, 1985.
H. Genrich. Equivalence transformations of PTT-nets. In Advances in Petri Nets 1989, vol. 424 of LNCS, pp. 179–208. Springer-Verlag, 1990.
H. Genrich, K. Lautenbach. System modelling with high-level Petri nets. Theoretical Comput. Sci., 13:109–136, 1981.
H. J. Genrich. Predicate/transition nets. In Advances in Petri Nets 1986, part I, vol. 254 of LNCS, pp. 207–247. Springer-Verlag, 1987.
S. Haddad, J. Ilié, M. Taghelit, B. Zouari Symbolic reachability graph and partial symmetries. In Application and Theory of Petri Nets 1995, vol. 935 of LNCS, pp. 238–257. Springer-Verlag,1995.
P. Huber, A. Jensen, L. Jensen, K. Jensen. Reachability trees for high-level Petri nets. Theoretical Comput. Sci., 45:261–292, 1986.
K. Jensen. Coloured Petri nets and the invariant-method. Theoretical Comput. Sci., 14:317–336, 1981.
K. Jensen. Coloured Petri nets: A high level language for system design and analysis. In Advances in Petri Nets 1990, vol. 483 of LNCS, pp. 342–416. Springer-Verlag, 1990.
K. Jensen. Coloured Petri Nets, vol. 1. Springer-Verlag, 1992.
K. Jensen. Coloured Petri Nets, vol. 2. Springer-Verlag, 1995.
K. Jensen, G. Rozenberg (eds.) High-level Petri Nets. Springer-Verlag, 1991.
G. Lakos, S. Christensen. A general systematic approach to arc extensions for coloured Petri nets. In Application and Theory of Petri Nets 1994, vol. 815 of LNCS, pp. 338–357. Springer-Verlag, 1994.
K. Lautenbach, A. Pagnoni. Invariance and duality in predicateltransition nets and in coloured nets, Arbeitspapiere der GMD 132, 1985
M. Lindqvist. Parameterized Reachability for PredicatelTransition Nets, vol. 54 of Acta Polytechnica Scandinavica, Mathematics and Computer Science. Helsinki, 1989.
M. Lindqvist. Parameterized reachability for predicate/transition nets, In Advances in Petri Nets, vol. 674 of LNCS, pp. 321–324. Springer-Verlag, 1993.
W. Reisig. Petri-Nets. Springer-Verlag, 1985.
W. Reisig. Petri nets and algebraic specifications. Theoretical Comput. Sci., 80:1–34, 1991.
W. Reisig, J. Vautherin. An algebraic approach to high level Petri nets. In Proc. 8th Workshop on Applications and Theory of Petri Nets, pp. 51–72, Zaragoza (Spain), 1987.
G. Rozenberg, P.S. Thiagarajan. Petri nets: Basic notions, structure, behaviour. In Current Trends in Concurrency, vol. 224 of LNCS, pp. 585–668. Springer-Verlag, 1986.
K. Schmidt. Parameterized reachability trees for algebraic Petri nets. In Application and Theory of Petri Nets 1995, vol. 935 of LNCS, pp. 392–411. Springer-Verlag, 1995.
E. Smith. On net systems generated by process foldings. In Advances in Petri Nets 1991, vol. 524 of LNCS, pp. 253–276. Springer-Verlag, 1991.
E. Smith. A primer on high-level Petri-net theory. In C. Fernandez et. al., editors, Advanced Course on Petri Nets, pp. 114–140. Editorial de la Universidad de Santiago de Chile, 1996.
E. Smith, W. Reisig. The semantics of a net is a net — an exercise in general net theory. In K. Voss, H. Genrich, and G. Rozenberg, editors, Concurrency and Nets, Advances in Petri Nets, pp. 461–480. Springer-Verlag, 1987.
V. Sperschneider, G. Antoniou. Logic: A Foundation for Computer Science. Addison-Wesley, 1991.
A. Valmari. Stubborn sets for coloured Petri nets. In Proc. 12th Int. Conf on Appl. and Theory of Petri Nets 1991, pp. 102–121.
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Smith, E. (1998). Principles of high-level net theory. In: Reisig, W., Rozenberg, G. (eds) Lectures on Petri Nets I: Basic Models. ACPN 1996. Lecture Notes in Computer Science, vol 1491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-65306-6_16
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DOI: https://doi.org/10.1007/3-540-65306-6_16
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