Abstract
In this paper we define a special kind of graph grammars, called linear ordered graph grammars, that can be used to describe distributed systems with mobility and object-based systems. Then we show how to model such grammars and their semantics in terms of tiles making explicit the aspects of interactivity and compositionality, that are of great importance in distributed systems.
This work was partially supported by the projects AGILE (FET project), COMETA (MIUR project), IQ-Mobile (CNPq and CNR) and ForMOS (CNPq and Fapergs).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Bruni and U. Montanari, Zero-Safe Nets: Comparing the Collective and Individual Token Approaches, Information and Computation, Vol. 156, 2000, pp. 46–89.
R. Bruni, U. Montanari and F. Rossi, An Interactive Semantics of Logic Programming, TLP 6(1): 647–690, Nov. 2001.
R. Bruni, J. Meseguer, U. Montanari, and V. Sassone, Functorial models for Petri nets, Information and Computation, Vol. 170, 2001, pp. 207–236.
A. Corradini and F. Gadducci, An Algebraic Presentation of Term Graphs via Gs-Monoidal Categories, Applied Categorical Structures, Vol. 7, 1999, pp. 299–331.
A. Corradini, U. Montanari and F. Rossi, Graph processes, Fundamentae Informatica, Vol. 26, no. 3–4, 1996, pp. 241–265.
F. Dotti and L. Ribeiro, Specification of mobile code systems using graph grammars, Formal Methods for Open Object-based Systems IV, Kluwer Academic Publishers, 2000, pp. 45–64.
H. Ehrig, G. Engels, H.-J. Kreowski, and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 2: Applications, Languages and Tools, World Scientific, 1999.
H. Ehrig, R. Heckel, M. Korff, M. Löwe, L. Ribeiro, A. Wagner and A. Corradini, Algebraic approaches to graph transformation II: Single pushout approach and comparison with double pushout approach, in [18], pp. 247–312.
G. Ferrari and U. Montanari, Tile Formats for Located and Mobile Systems, Information and Computation, Vol. 156, no. 1/2, 2000, pp. 173–235.
F. Gadducci and U. Montanari, Comparing Logics for Rewriting: Rewriting Logic, Action Calculi and Tile Logic, TCS, to appear. Available at http://www.di.unipi.it/~ugo/ABSTRACT.html#TCS-Asilomar.
R. Heckel, Open Graph Transformation Systems: A New Approach to the Compositional Modelling of Concurrent and Reactive Systems, Ph.D. thesis, Technical University of Berlin, 1998.
M. Korff, True concurrency semantics for single pushout graph transformations with applications to actor systems, Information Systems-Correctness and Reusability, World Scientific, 1995, pp. 33–50.
M. Korff, Generalized graph structures with application to concurrent object-oriented systems, Ph.D. thesis, Technical University of Berlin, 1995.
M. Löwe, Algebraic approach to single-pushout graph transformation, Theoretical Computer Science, Vol. 109, 1993, 181–224.
J. Meseguer and U. Montanari. Mapping Tile Logic into Rewriting Logic, Springer, LNCS 1376, 1998, pp. 62–91.
U. Montanari, M. Pistore and F. Rossi, Modeling concurrent, mobile and coordinated systems via graph transformations, The Handbook of Graph Grammars, vol. 3: Concurrency, Parallelism and Distribution, World Scientific, 1999, pp. 189–268.
U. Montanari and F. Rossi, Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems, Applied Categorical Structures 7(4): 333–370; Dec 1999.
G. Rozenberg (editor), The Handbook of Graph Grammars, vol. 1: Foundations, World Scientific, 1997.
G. Taentzer, Parallel and distributed graph transformation: Formal description and application to communication-based systems, Ph.D. thesis, Technical University of Berlin, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Montanari, U., Ribeiro, L. (2002). Linear Ordered Graph Grammars and Their Algebraic Foundations. In: Corradini, A., Ehrig, H., Kreowski, H.J., Rozenberg, G. (eds) Graph Transformation. ICGT 2002. Lecture Notes in Computer Science, vol 2505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45832-8_24
Download citation
DOI: https://doi.org/10.1007/3-540-45832-8_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44310-0
Online ISBN: 978-3-540-45832-6
eBook Packages: Springer Book Archive