The geometry of orthogonal reduction spaces

  • Zurab Khasidashvili
  • John Glauert
Session 16: Rewriting
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)


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.


Optimal Computation Reduction Space Normalization Theorem Residual Relation Term Rewrite System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Zurab Khasidashvili
    • 1
  • John Glauert
    • 2
  1. 1.NTT Basic Research LaboratoriesKanagawaJapan
  2. 2.School of Information SystemsUEANorwichEngland

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