Transformations of structures: An algebraic approach
 Hartmut Ehrig,
 HansJörg Kreowski,
 Andrea MaggioloSchettini,
 Barry K. Rosen,
 Jozef Winkowski
 … show all 5 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This paper introduces a new mathematical approach to transformations of structures, where the concept of “structure” is extremely general. Many structures and transformations that arise in biology as well as computer science are special cases of our concepts. A structure may be changed by finding an occurrence of a pattern and replacing it by another pattern as specified by a rule. To prove theorems about long sequences of applications of complicated rules, we need precise and tractable mathematical definitions of rules and how to apply them. This paper presents such definitions and three fundamental theorems, together with brief remarks on applications to control flow analysis, record handling, and evaluation of recursively defined functions. Unlike some previous efforts toward a rigorous theory of transformations of structures, this paper uses ideas and results from abstract algebra to minimize the need for elaborate constructions.
 Arbib, M. A., Manes, E. G. (1975) Arrows, Structures, and Functors. Academic Press, New York
 Berry, G., Levy, J.J. (1979) Minimal and optimal computations of recursive programs. J. ACM 26: pp. 148175
 Birkhoff, G., Lipson, J. D. (1970) Heterogeneous algebras. J. Combinatorial Theory 8: pp. 115133
 V. Claus, H. Ehrig, and G. Rozenberg (Editors),Graph Grammars and their Application to Computer Science and Biology, Lecture Notes in Computer Sci., 73 (1979).
 Codd, E. F. (1970) A relational model of data for large shared data banks. Comm. ACM 13: pp. 377387
 J. A. Darringer and W. H. Joyner,A new look at logic synthesis, IBM Research Report RC 8268, Yorktown Heights NY, May 1980.
 H. Ehrig and H.J. Kreowski, Contributions to the algebraic theory of graph grammars,Math. Nachr., to appear.
 H. Ehrig and H.J. Kreowski, Applications of graph grammar theory to consistency, synchronization, and scheduling in data base systems,Information Sciences, to appear.
 Ehrig, H., Kreowski, H.J., MaggioloSchettini, A., Rosen, B. K., Winkowski, J. (1978) Deriving structures from structures. Lecture Notes in Computer Science 64: pp. 177190
 H. Ehrig, M. Pfender, and H. J. Schneider, Graph grammars: an algebraic approach,Proc. 14th Ann. IEEE Symp. on Switching and Automata Theory, Iowa City, October 1973, pp. 167–180.
 H. Ehrig and B. K. Rosen,Commutativity of independent transformations on complex objects, IBM Research Report RC 6251, Yorktown Heights NY, October 1976.
 Ehrig, H., Rosen, B. K. (1980) The mathematics of record handling. SIAM J. Computing 9: pp. 441469
 H. Ehrig and B. K. Rosen,Commutativity, parallelism, and concurrency for transformations of structures, Bericht 79–21, Fachbereich Informatik, Tech. U. Berlin, October 1979.
 Ehrig, H., Tischer, K. W. (1975) Graph grammars and applications to specialization and evolution in biology. J. Computer and System Sci. 11: pp. 212236
 Eilenberg, S., Wright, J. (1967) Automata in general algebras. Information and Control 11: pp. 452470
 R. Farrow, K. Kennedy, and L. Zucconi, Graph grammars and global program data flow analysis,Proc. 17th Ann. IEEE Symp. on Foundations of Computer Sci., Houston, October 1976, pp. 42–56.
 Herrlich, H., Strecker, G. (1973) Category Theory. Allyn and Bacon, Rockleigh, New Jersey
 H.J. Kreowski,Ein Pumpinglemma für KantenKontextfreie GraphSprachen, Bericht 77–15, Fachbereich Informatik, Tech. U. Berlin, September 1977. (See also [4].)
 M. J. O'Donnell, Computing in systems described by equations,Lecture Notes in Computer Science, 58 (1977).
 Pacini, G., Montangero, C., Turini, F. (1974) Graph representation and computation rule for typeless recursive languages. Lecture Notes in Computer Science 14: pp. 157169
 Padawitz, P.,Graph grammars and operational semantics, Bericht 78–33, Fachbereich Informatik, Tech. U. Berlin, October 1978. (See also [4].)
 Rajlich, V. (1975) Dynamics of discrete systems ⋯. J. Computer and System Sci. 11: pp. 186202
 Rosen, B. K. (1975) Deriving graphs from graphs by applying a production. Acta Informatica 4: pp. 337357
 Schneider, H. J., Ehrig, H. (1976) Grammars on partial graphs. Acta Informatica 6: pp. 297316
 Staples, J. (1977) A class of replacement systems with simple optimality theory. Bull. Austral. Math. Soc. 17: pp. 335350
 Staples, J. (1980) Computation on graphlike expressions. Theoretical Computer Sci. 10: pp. 171185
 Staples, J. (1980) Optimal evaluations of graphlike expressions. Theoretical Computer Sci. 10: pp. 297316
 Staples, J. (1980) Speeding up subtree replacement systems. Theoretical Computer Sci. 11: pp. 3947
 Vere, S. A. (1977) Relational production systems. Artificial Intelligence 8: pp. 4768
 Vuillemin, J. (1974) Correct and optimal implementations of recursion in a simple programming language. J. Computer and System Sci. 9: pp. 332354
 Title
 Transformations of structures: An algebraic approach
 Journal

Mathematical systems theory
Volume 14, Issue 1 , pp 305334
 Cover Date
 19811201
 DOI
 10.1007/BF01752403
 Print ISSN
 00255661
 Online ISSN
 14330490
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Hartmut Ehrig
 HansJörg Kreowski ^{(1)}
 Andrea MaggioloSchettini ^{(2)}
 Barry K. Rosen ^{(3)}
 Jozef Winkowski ^{(4)}
 Author Affiliations

 1. Fachbereich Informatik, Technische Universität Berlin, 1000, Berlin 10, Federal Republic of Germany
 2. Istituto di Scienze dell'Informazione, Universita di Pisa, 56100, Pisa, Italy
 3. Computer Sciences Department, IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, NY, USA
 4. Instytut Podstaw Informatyki PAN, Box 22, 00901, Warszawa, PKiN, Poland