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International Conference on Rewriting Techniques and Applications

RTA 2003: Rewriting Techniques and Applications pp 467–482Cite as

Stable Computational Semantics of Conflict-Free Rewrite Systems (Partial Orders with Duplication)

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2706))

Abstract

We study orderings ⊴S on reductions in the style of Lévy reflecting the growth of information w.r.t. (super)stable sets S of ‘values’ (such as head-normal forms or Böhm-trees). We show that sets of co-initial reductions ordered by ⊴S form finitary ω-algebraic complete lattices, and hence form computation and Scott domains. As a consequence, we obtain a relativized version of the computational semantics proposed by Boudol for term rewriting systems. Furthermore, we give a pure domain-theoretic characterization of the orderings ⊴S in the spirit of Kahn and Plotkin’s concrete domains. These constructions are carried out in the framework of Stable Deterministic Residual Structures, which are abstract reduction systems with an axiomatized residual relations on redexes, that model all orthogonal (or conflict-free) reduction systems as well as many other interesting computation structures.

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Author information

Authors and Affiliations

  1. Logic and Validation Technology Intel, IDC, Haifa, Israel

    Zurab Khasidashvili

  2. School of Computing Sciences, UEA, Norwich, NR4 7TJ, UK

    John Glauert

Authors
  1. Zurab Khasidashvili
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  2. John Glauert
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Editors and Affiliations

  1. Dpt. Lenguajes y Sistemas Informáticos (LSI), Technical University of Catalonia (UPC), Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

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Khasidashvili, Z., Glauert, J. (2003). Stable Computational Semantics of Conflict-Free Rewrite Systems (Partial Orders with Duplication). In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_33

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  • DOI: https://doi.org/10.1007/3-540-44881-0_33

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  • Print ISBN: 978-3-540-40254-1

  • Online ISBN: 978-3-540-44881-5

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