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The geometry of orthogonal reduction spaces

  • Session 16: Rewriting
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Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

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Abstract

We investigate mutual dependencies of subexpressions of a computable expression, in orthogonal rewrite systems, and identify conditions for their concurrent independent computation. To this end, we introduce concepts familiar from ordinary Euclidean Geometry (such as basis, projection, distance, etc.) for reduction spaces. We show how a basis for an expression can be constructed so that any reduction starting from that expression can be decomposed as the sum of its projections on the axes of the basis. To make the concepts more relevant computationally, we relativize them w.r.t. stable sets of results, and show that an optimal concurrent computation of an expression w.r.t. S consists of optimal computations of its S-independent subexpressions. All these results are obtained for Stable Deterministic Residual Structures, Abstract Reduction Systems with an axiomatized residual relation, which model all orthogonal rewrite systems.

Part of this work was supported by the Engineering and Physical Sciences Research Council of Great Britain under grant GR/H 41300

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Author information

Authors and Affiliations

  1. NTT Basic Research Laboratories, Atsugi, 243-01, Kanagawa, Japan

    Zurab Khasidashvili

  2. School of Information Systems, UEA, NR4 7TJ, Norwich, England

    John Glauert

Authors
  1. Zurab Khasidashvili
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  2. John Glauert
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Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Khasidashvili, Z., Glauert, J. (1997). The geometry of orthogonal reduction spaces. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_219

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  • DOI: https://doi.org/10.1007/3-540-63165-8_219

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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