Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T12:35:14.170Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallelism and concurrency in high-level replacement systems

Published online by Cambridge University Press:  04 March 2009

Hartmut Ehrig ,
Annegret Habel ,
Hans-Jörg Kreowski  and
Francesco Parisi-Presicce
Hartmut Ehrig
Affiliation:
Technical University of Berlin, Berlin, Germany
Annegret Habel
Affiliation:
University of Bremen, Bremen, Germany
Hans-Jörg Kreowski
Affiliation:
University of Bremen, Bremen, Germany
Francesco Parisi-Presicce
Affiliation:
University of L'Aquila, L'Aquila, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

High-level replacement systems are formulated in an axiomatic algebraic framework based on categories pushouts. This approach generalizes the well-known algebraic approach to graph grammars and several other types of replacement systems, especially the replacement of algebraic specifications which was recently introduced for a rule-based approach to modular system design.

in this paper basic notions like productions, derivations, parellel and sequential independence are introduced for high-level replacement syetms leading to Church-Rosser, Parallelism and concurrency Theorems previously shown in the literature for special cases only. In the general case of high-level replacement systems specific conditions, called HLR1- and HLR2-conditions, are formulated in order to obtain these results.

Several examples of high-level replacement systems are discussed and classified w.r.t. HLR1- and HLR2-conditions showing which of the results are valid in each case.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 1 , Issue 3 , November 1991 , pp. 361 - 404
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arbib, M. A. and Manes, E. G. (1975) Arrows, Structures and Functors. Academic Press, New York–San Francisco–London.Google Scholar
Claus, V., Ehrig, H. and Rozenberg, G., eds, (1979) Graph grammars and their application to computer science and biology. Springer Lecture Notes in Computer Science 73.CrossRefGoogle Scholar
Corradini, A., Montanari, U., Rossi, F., Ehrig, H. and Löwe, M. (1991a) Graph grammars and logic programming. Proc. 4th Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science, to appearGoogle Scholar
Corradini, A., Rossi, F. and Parisi-Presicce, F. (1991b) Logic programming as hypergraph rewriting, In Proc. CAAP'91. Springer Lecture Notes in Computer Science 493 275–295.CrossRefGoogle Scholar
Ehrig, H. (1979) Introduction to the algebraic theory of graph grammars. Proc. 1st Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science 73 pp 1–69.CrossRefGoogle Scholar
Ehrig, H., Habel, A., Kreowski, H.-J. and Parisi-Presicce, F. (1991a) From graph grammars to high level replacement systems. Proc. 4th Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science, to appear.Google Scholar
Ehrig, H., Habel, A. and Rosen, B. K. (1986) Concurrent transformations of relational structures. Fundamenta Informaticae IX 13–50.CrossRefGoogle Scholar
Ehrig, H. and Kreowski, H.-J. (1975) Categorical theory of graph grammars. Techn. Report TU Berlin, FB 20, Bericht Nr. 75-50.Google Scholar
Ehrig, H. and Kreowski, H.-J. 1979) Pushout properties: an analysis of gluing constructions for graphs. Math. Nachr. 91 135–149.CrossRefGoogle Scholar
Ehrig, H., Kreowski, H.-J. and Rozenberg, G. (1991b) Graph grammars and their applications to computer science. Proc. 4th Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science, to appear.CrossRefGoogle Scholar
Ehrig, H., Kreowski, H.-J., Maggiolo-Schettini, A., Rosen, B. and Winkowski, J. (1981) Transformation of structures: an algebraic approach. Math. Syst. Theory 14 305–334.CrossRefGoogle Scholar
Ehrig, H. and Mahr, B. (1985) Fundamentals of algebraic specification 1. Equations and intial semantics. Springer EATCS Monographs on Theoretical Computer Science 6.Google Scholar
Ehrig, H., Nagl, M. and Rozenberg, G., eds, (1983) Graph grammars and their application to computer science. Proc. 2nd Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science 153.CrossRefGoogle Scholar
Ehrig, H., Nagl, M., Rozenberg, G. and Rosenfeld, A., eds, (1987) Graph grammars and their application to computer science. Proc. 2nd Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science 291.Google Scholar
Ehrig, H. and Rosen, B. K. (1980) Parallelism and concurrency of graph manipulations. Theor. Comp. Sci. 11 247–275.CrossRefGoogle Scholar
Ehrig, H., Pfender, M. and Schneider, H. J. (1973) Graph grammars: an algebraic approach. Proc. IEEE Conf. SWAT73, Iowa City pp 167–180.CrossRefGoogle Scholar
Habel, A. (1989) Hyperedge replacement: grammars and languages. PhD Thesis, University of Bremen. To appear in Springer Lecture Notes in Computer Science.Google Scholar
Hummert, U. (1989) Algebraische Theorie von High-Level-Netzen. PhD Thesis, TU Berlin.Google Scholar
Herrlich, H. and Strecker, G. E. (1973) Category Theory. Allyn and Bacon, Boston.Google Scholar
Kennaway, R. (1991) Graph rewriting in some categories of partial morphisms. Proc. 4th Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science, to appear.Google Scholar
Kreowski, H.-J. (1977a) Manipulation von Graphmanipulationen, PhD Thesis, TU Berlin.Google Scholar
Kreowski, H.-J. (1977b) Transformations of derivation sequences in graph grammars. Springer Lecture Notes in Computer Science 56 275–286.CrossRefGoogle Scholar
MacLane, S (1972) Categories for the Working Mathematician. springer, New York–Heidelberg–Berlin.Google Scholar
Meseguer, P. and Montanari, U. (1988) Petri nets are monoids: a new algebraic foundation for net theory. Proc. Logics in Comp. Sci. also in Information and Computation 88 (2) (1990).CrossRefGoogle Scholar
Parisi-Presicce, F. (1989) Modular system design applying graph grammar techniques. In: Proc. 16th ICALP. Springer Lecture Notes in Computer Science 372 621–636.CrossRefGoogle Scholar
Parisi-Presicce, F. (1990) A rule based approach to modular system design. Proc. 12th Int. Conf. Software Engineering.Google Scholar
Parisi-Presicce, F. and Ehrig, H. (1991) Algebraic specification grammars. Proc. 4th Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science, on appear.Google Scholar
Parisi-Presicce, F., Ehrig, H. and Montanari, U. (1987) Graph rewriting with unification and composition. In: Proc. 3rd Int. Workshop on Graph Grammars. Springer Lecture Notes in Computer Science 291 496–511.CrossRefGoogle Scholar
Schneider, H. J. and Ehrig, H. (1976) Grammars on partial graphs. Acta Informatica 6 297–316.CrossRefGoogle Scholar