Amalgamation of graph transformations with applications to synchronization
In the present paper we generalize the well-known PARALLELISM THEOREM for graph derivations to the AMALGAMATION THEOREM. In this theorem the assumption of ‘parallel independence’ is dropped. For each pair of productions together with a relational production (allowing productions to be associated with each other) we construct a single ‘amalgamated’ production. The AMALGAMATION THEOREM states that graph derivations which respect the given associations can be amalgamated to a single derivation via the ‘amalgamated’ production.
The amalgamation mechanism can be used to handle synchronization phenomena. The amalgamation concept is applied to synchronization of graph manipulations in a simplified railway control system as well as in GDS, a graph grammar formalism for distributed systems.
KeywordsRelational Production Direct Derivation Graph Transformation Graph Grammar Bijective Correspondence
- /AM 75/.M.A. Arbib, E.G. Manes: Arrows, Structures, and Functors, Academic Press, New YorkGoogle Scholar
- /BFH 84/.P. Boehm, H. Fonio, A. Habel: On Amalgamation of Graph Manipulations; in preparationGoogle Scholar
- /CER 79/.V. Claus, H. Ehrig, G. Rozenberg, (eds.): Graph Grammars and Their Application to Computer Science and Biology, LNCS 73 (1979)Google Scholar
- /CDM 84/.A. Corradini, P. Degano, U. Montanari: Specifying Highly Concurrent Data Structure Manipulation; Comp. Sci. Dept., Univ. of Pisa, Pisa, April 1984Google Scholar
- /CM 83/.I. Castellani, U. Montanari: Graph Grammars for Distributed Systems, LNCS 153, 20–38 (1983)Google Scholar
- /DM 83/.P. Degano, U. Montanari: A Model of Distributed Systems Based on Graph Rewriting, Note Cnet 111, Comp. Sci. Dept., Univ. of Pisa, Pisa 1983, submitted for publicationGoogle Scholar
- /Eh 79/.H. Ehrig: Introduction to the Algebraic Theory of Graph Grammars, LNCS 73 (1979), 1–69Google Scholar
- /Eh 83/.— Aspects of Concurrency in Graph Grammars, LNCS 153 (1983), 58–81Google Scholar
- /EHR 83/.H. Ehrig, A. Habel, B.K. Rosen: Concurrent Transformations of Structures: From Graphs to Relational Data Structures; TU Berlin, FB 20, Technical Report No. 83-01, January 1983Google Scholar
- /EK 80/.
- /ENR 83/.H. Ehrig, M. Nagl, G. Rozenberg (eds.): Graph Grammars and Their Application to Computer Science, LNCS 153 (1983)Google Scholar
- /EPS 73/.H. Ehrig, M. Pfender, H.J. Schneider: Graph-Grammars: An Algebraic Approach, Proc. of the IEEE Conf. on Automata and Switching Theory, Iowa City 1973, pp. 167–180Google Scholar
- /ER 79a/.
- /ER 79b/.— Decomposition of Graph Grammar Productions and Derivations, LNCS 73 (1979), pp. 192–205Google Scholar
- /Fo 84/.H.-R. Fonio: Amalgamation of Graph Transformations with Application to Synchronization in Distributed Systems, to appear as Techn. Report, TU Berlin, FB 20Google Scholar
- /Ha 80/.A. Habel: Concurrency in Graph-Grammatiken, TU Berlin, FB 20, Technical Report No. 80–11, March 1980Google Scholar
- /HBR 81/.C.A.R. Hoare, S.D. Brookes, A.W. Roscoe: A Theory of Communicating Sequential Processes, Techn. Monograph PRG-16, Progr. Research Group, Oxford Univ., 1981Google Scholar
- /JKRE 82/.D. Janssens, H.-J. Kreowski, G. Rozenberg, H. Ehrig: Concurrency of Node-label Controlled Graph Transformations, Techn. Report No. 82-38, Univ. of Antwerp, U.I.A. (1982)Google Scholar
- /Ku 80/.H.T. Kung: The Structures of Parallel Algorithms, Advances in Computers, Vol. 19, 65–108, Academic Press Inc. 1980Google Scholar
- /MW 82/.B. Mahr, A. Wilharm: Graph Grammars as a Tool for Description in Computer Processed Control: A Case Stude, Proc. 8th Conf. on Graphtheoretic Concepts in Comp. Sci. (WG'82), 165–176 (1982)Google Scholar
- /Mi 83/.R. Milner: Calculi for Synchrony and Asynchrony, Theoret. Comp. Sci. 25 (1983), pp. 267–310Google Scholar
- /Na 79/.M. Nagl: A Tutorial and Bibliographical Survey on Graph Grammars, LNCS 73 (1979), 70–126Google Scholar
- /Pe 80/.C.A. Petri: Concurrency, Proc. Net Theory and Applications, LNCS 84 (1980), 251–260Google Scholar
- /Ro 75/.