Petri Nets and Algebraic Specifications

HIGH-LEVEL REPLACEMENT SYSTEMS APPLIED TO ALGEBRAIC SPECIFICATIONS AND PETRI NETS

Handbook of Graph Grammars and Computing by Graph Transformation ◽

10.1142/9789812814951_0006 ◽

1999 ◽

pp. 341-399 ◽

Cited By ~ 13

Author(s):

H. EHRIG ◽

M. GAJEWSKY ◽

F. PARISI-PRESICCE

Keyword(s):

Petri Nets ◽

Algebraic Specifications ◽

High Level

Download Full-text

Parallel systems specifications with coloured Petri nets and algebraic specifications

Lecture Notes in Computer Science - Advances in Petri Nets 1987 ◽

10.1007/3-540-18086-9_31 ◽

1987 ◽

pp. 293-308 ◽

Cited By ~ 48

Author(s):

Jacques Vautherin

Keyword(s):

Petri Nets ◽

Parallel Systems ◽

Coloured Petri Nets ◽

Algebraic Specifications

Download Full-text

Algebraic high-level net transformation systems

Mathematical Structures in Computer Science ◽

10.1017/s0960129500000724 ◽

1995 ◽

Vol 5 (2) ◽

pp. 217-256 ◽

Cited By ~ 57

Author(s):

Julia Padberg ◽

Hartmut Ehrig ◽

Leila Ribeiro

Keyword(s):

Petri Nets ◽

The Other ◽

Graph Grammars ◽

Data Types ◽

Algebraic Specifications ◽

Categorical Framework ◽

The One ◽

High Level ◽

Transformation Systems ◽

Dining Philosophers

The concept of algebraic high-level net transformation systems combines two important lines of research recently introduced in the literature:algebraic high-level nets(AHL-nets for short) andhigh-level replacement systems(HLR-systems for short). In both cases a categorical formulation of the corresponding theory has turned out to be highly important and is also a good basis for the integration of these concepts in this paper.AHL-nets combine Petri nets with algebraic specifications and provide a powerful specification technique for distributed systems including data types and processes.HLR-systems are transformation systems for high-level structures such as graphs, hypergraphs, algebraic specifications and different kinds of Petri nets. The theory of HLRsystems - formulated already in a categorical framework - is applied in this paper to AHLnets. Thus we obtain AHL-net transformation systems as an instantiation of HLR-systems to AHL-nets. This allows us to build up AHL-nets from basic components and to transform the net structure using rules or productions in the sense of graph grammars. This concept is illustrated by extending the well-known example of ‘dining philosophers’. We are able to show that AHL-net-transformation systems satisfy several important compatibility properties. On the one hand we obtain a local Church-Rosser and Parallelism Theorem, which is well-known for graph grammars and has recently been generalized to HLR-systems. This allows us to analyse concurrency in AHL-nets not only on the token level but also on the level of transformations of the net structure. On the other hand, we consider the ‘fusion’ and ‘union’ constructions for high-level structures, motivated by corresponding concepts for high-level Petri nets in the literature, and we show compatibility of these constructions with derivations of HLR-systems in general and AHL-nettransformations in particular. This means compatibility of vertical and horizontal structuring in terms of software development.

Download Full-text