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An improved lower bound for the elementary theories of trees

  • Sergei Vorobyov
Session 4A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1104)

Abstract

The first-order theories of finite and rational, constructor and feature trees possess complete axiomatizations and are decidable by quantifier elimination [15, 13, 14, 5, 10, 3, 20, 4, 2]. By using the uniform inseparability lower bounds techniques due to Compton and Henson [6], based on representing large binary relations by means of short formulas manipulating with high trees, we prove that all the above theories, as well as all their subtheories, are non-elementary in the sense of Kalmar, i.e., cannot be decided within time bounded by a k-story exponential function exp k (n) for any fixed k. Moreover, for some constant d>0 these decision problems require nondeterministic time exceeding exp (⌊dn⌋) infinitely often.

Keywords

Logic Program Binary Relation Turing Machine Logic Programming Predicate Symbol 
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 1996

Authors and Affiliations

  • Sergei Vorobyov
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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