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Concurrency theory. (English) Zbl 0669.68045

Petri nets: central models and their properties, Proc. Adv. Course, Bad Honnef/FRG 1986, Lect. Notes Comput. Sci. 254, 4-24 (1987).
[For the entire collection see Zbl 0619.00023.]
The paper is one of the most fundamental contributions for the development of the theory of concurrency. A system of 22 axioms is proposed and evidence is carefully given why just these axioms are formulated.
Concurrency is one of the basic properties in partially odered systems like in event structures: two events can be either causally dependent from another, or they are concurrent to each other. The concurrency relation is a similarity relation, i.e. it is not transitive. Therefore the notion of concurrency has its importance in the theory of measuring as well (quasi-equality, indifference; indistinguishability).
Furthermore, foundations are given for basic notions like K- and N- density, for gaps and jumps in a partial order, to an extension of Dedekind’s continuity to SPOs, how all combinatorial topologies can be constructed as quotient topologies of nets, and for some more.
The reader is inclined to read this paper a second time.
Reviewer: H.Fuss

MSC:

68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
06A06 Partial orders, general
08A05 Structure theory of algebraic structures
68Q65 Abstract data types; algebraic specification
93A05 Axiomatic systems theory
03H99 Nonstandard models

Citations:

Zbl 0619.00023