Parallel Composition of Graph Grammars

The specification of complex systems is usually done by the ‘divide and conquer’ idea: the system is divided into smaller, less complex components that are developed separately and then merged in some way to form the specification of the whole system. The main aim of this paper is to provide an approach to the parallel composition of graph grammars, formalizing the intuitive idea of ‘divide and conquer’ described above. This parallel composition of graph grammars provides a suitable formalism for the specification of concurrent systems based on the specifications of their components. ‘Dividing’ is formalized by special graph grammar morphisms, called specialization morphisms. These morphisms also describe structural and behavioural compatibilities between graph grammars. As a main result, we characterize the parallel composition as the pullback in the category of graph grammars.

[1]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1982, Lecture Notes in Computer Science.

[2]  Martin Korff.  Generalized graph structure grammars with applications to concurrent object-oriented systems , 1996 .

[3]  Hartmut Ehrig,et al.  The Category of Typed Graph Grammars and its Adjunctions with Categories , 1994, TAGT.

[4]  Reiko Heckel,et al.  Horizontal and vertical structuring of typed graph transformation systems , 1996, Mathematical Structures in Computer Science.

[5]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 2: Module Specifications and Constraints , 1990 .

[6]  Dirk Janssens,et al.  ESM Systems and the Composition of Their Computations , 1993, Dagstuhl Seminar on Graph Transformations in Computer Science.

[7]  Ugo Montanari,et al.  On the semantics of place/transition Petri nets , 1997, Mathematical Structures in Computer Science.

[8]  Hartmut Ehrig,et al.  Graph-Grammars: An Algebraic Approach , 1973, SWAT.

[9]  Reiko Heckel,et al.  Algebraic Approaches to Graph Transformation - Part II: Single Pushout Approach and Comparison with Double Pushout Approach , 1997, Handbook of Graph Grammars.

[10]  Leila Ribeiro,et al.  Parallel composition and unfolding semantics of graph grammars , 1996 .

[11]  Francesca Rossi,et al.  Graph Processes , 1996, Fundam. Informaticae.

[12]  Dirk Janssens,et al.  The Decomposition of ESM Computations , 1994, TAGT.

[13]  Reiko Heckel,et al.  Algebraic Approaches to Graph Transformation - Part I: Basic Concepts and Double Pushout Approach , 1997, Handbook of Graph Grammars.

[14]  Annegret Habel,et al.  Amalgamation of Graph Transformations: A Synchronization Mechanism , 1987, J. Comput. Syst. Sci..

[15]  Glynn Winskel,et al.  Models for Concurrency , 1994 .

[16]  Michael Löwe,et al.  Algebraic Approach to Single-Pushout Graph Transformation , 1993, Theor. Comput. Sci..

[17]  Hartmut Ehrig,et al.  Introduction to the Algebraic Theory of Graph Grammars (A Survey) , 1978, Graph-Grammars and Their Application to Computer Science and Biology.

[18]  Reiko Heckel,et al.  A compositional approach to structuring and refinement of typed graph grammars , 1995, SEGRAGRA.

[19]  Michael Löwe,et al.  Extended algebraic graph transformation , 1991 .