Algebraic semantics and complexity of term rewriting systems

  • Tohru Naoi
  • Yasuyoshi Inagaki
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)


The present paper studies the semantics of linear and non-overlapping TRSs. To treat possibly non-terminating reduction, the limit of such a reduction is formalized using Scott's order-theoretic approach. An interpretation of the function symbols of a TRS as a continuous algebra, namely, continuous functions on a cpo, is given, and universality properties of this interpretation are discussed. Also a measure for computational complexity of possibly non-terminating reduction is proposed. The space of complexity forms a cpo and function symbols can be interpreted as monotone functions on it.


Normal Form Function Symbol Continuous Homomorphism Algebraic Semantic Variable Symbol 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Tohru Naoi
    • 1
  • Yasuyoshi Inagaki
    • 1
  1. 1.Faculty of EngineeringNagoya UniversityNagoyaJapan

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