Algebraic high level nets

Abstract

Petri nets, well established as a fundamental model of concurrency and as a specification technique for distributed systems, are revisited from an algebraic point of view. In a first step Petri nets can be considered as monoids with well-defined algebraic semantics. Secondly they can be combined with algebraic specifications leading to the concept of algebraic high-level nets with suitable compositionality results. The main idea of this paper is to present a revised version of algebraic high-level nets (AHL-nets) and to introduce AHL-net-transformation systems. This is a concept of high-level replacement systems for AHL-nets allowing to build up AHL-nets from basic components and to transform them using rules or productions in the sense of graph grammars. This is illustrated by extending the well-known example of “dining philosophers” to a “restaurant of dining philosophers”. Moreover we are able to extend main results from the theory of graph grammars, including local Church-Rosser, parallelism and canonical derivation theorems, to AHL-net-transformation systems. This allows to analyze concurrency in nets not only on the token level but also on the level of transformations of the net structure.KeywordsCategorical PropertyGraph GrammarAlgebraic PointAlgebraic SpecificationDine PhilosopherThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.