Transformations of structures: An algebraic approach
 Hartmut Ehrig,
 HansJörg Kreowski,
 Andrea MaggioloSchettini,
 Barry K. Rosen,
 Jozef Winkowski
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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.
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 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