Analysing nets by the invariant method.(English)Zbl 0658.68068

Petri nets: central models and their properties, Proc. Adv. Course, Bad Honnef/FRG 1986, Lect. Notes Comput. Sci. 254, 300-336 (1987).
[For the entire collection see Zbl 0619.00023.]
The authors emphasize the advantages of such a method: it works on out- of-context subnets and even on P/T-systems enriched with parameters (e.g., a predicate/transition system). The weighting vectors f (solutions of the linear system $$f^ T\cdot C=0)$$ which generate the linear invariants are called semi-flows. The main results are: (i) the computation of the smallest set of the positive semi-flows (the Farkas algorithm), (ii) the computation of semi-flows for unary predicate transition systems, and (iii) the possibility to characterize all minimal supports of the set of positive semi-flows while the net contains some parameters. The results are illustrated by a well known concept: the general channel.
Reviewer: V.Calmatuianu

MSC:

 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) 68Q65 Abstract data types; algebraic specification 68N01 General topics in the theory of software

Zbl 0619.00023