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Geschichte und Entwicklung der Concurrency-Theorie

Diploma thesis at the Department of Computer Science, University of Hamburg

Abstract:

This paper deals with several topics:

• The historical background that lead to the development of Axiomatic Concurrency Theory by Carl Adam Petri is described and examined.
• Petri's main ideas, which lead from the widely accepted Net Theory to the Theory of Concurrency, are described in an easily understandable form.
• We prove several theorems from Concurrency Theory, that might aid a theoretical foundation of computer science.

To achieve these goals some compromise between a survey paper and a detailed description of the theory had to be found.

Regarding the historical background we establish connections to the work of Reichenbach and Carnap whose work in turn was influenced by the results of Einstein, Minkowsky, and others. The ideas of Dedekind on continuity are shown to have a lasting impact on Concurrency Theory.

Petri has published many diffent paper on the subject over the years. We extract a core of invariant axioms and take it as a starting point for evaluating the various axiomatic systems of Petri. Imporant implications of the core axioms and the axioms themselves are explained in the context of the physical reality.

Supervisors:

Prof. Rüdiger Valk

Prof. C.A. Petri