Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-20T07:37:27.656Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of replacement systems with simple optimality theory

Published online by Cambridge University Press:  17 April 2009

John Staples
John Staples
Affiliation:
Department of Mathematics and Computer Science, Queensland Institute of Technology, Brisbane, Queensland.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A class of replacement systems is studied which satisfies a “subcommutativity” condition. Examples of systems satisfying this condition are many of the systems of graph-like expressions which have recently been studied in connection with the efficient evaluation of recursive definitions. An optimality theory of subcommutative systems is developed and is used to give conditions which are sufficient to ensure that an evaluation (reduction) procedure is optimal. The optimality theory is also applied to develop conditions under which a given subcommutative system speeds up, in a natural sense, another replacement system.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 3 , December 1977 , pp. 335 - 350
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Ehrig, Hartmut and Rosen, Barry K., “Commutativity of independent transformations on complex objects” (IBM Research Report RC 6251 (#26882), New York, 1976).Google Scholar
[2]Pacini, G., “An optimal fix-point computation rule for a simple recursive language” (Nota Interna B73–10, Pisa, 1973).Google Scholar
[3]Pacini, G., Montangero, C., Turini, F., “Graph representation and computation rules for typeless recursive languages”, Automata, languages and programming, 157–169 (2nd Colloquium, University of Saarbrücken, 1974. Lecture Notes in Computer Science, 14. Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[4]Rosen, Barry K., “Tree-manipulating systems and Church-Rosser theorems”, J. Assoc. Comput. Mach. 20 (1973), 160–187.CrossRefGoogle Scholar
[5]Staples, John, “Optimal reduction in replacement systems”, Bull. Austral. Math. Soc. 16 (1977), 341–349.CrossRefGoogle Scholar
[6]Staples, John, “Speeding up subtree replacement systems”, submitted.Google Scholar
[7]Staples, John, “Optimal evaluations of nonlinear expressions”, submitted.Google Scholar
[8]Vuillemin, Jean, “Correct and optimal implementations of recursion in a simple programming language”, Proc. Fifth Annual ACM Sympos. Theory of Computing, 224–259 (Austin, Texas, 1973).Google Scholar
[9]Wadsworth, Christopher Peter, “Semantics and pragmatics of the lamda-calculus” (PhD thesis, University of Oxford, Oxford, 1971).Google Scholar