On the bounded theories of finite trees

  • Sergei Vorobyov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1179)


The theory of finite trees is the full first-order theory of equality in the Herbrand Universum (the set of ground terms) over a functional signature containing non-unary function symbols and constants. Albeit decidable, this theory turns out to be of non-elementary complexity [14].

To overcome the intractability of the theory of finite trees, we introduce in this paper the bounded theory of finite trees. This theory replaces the usual equality=, interpreted as identity, with the infinite family of approximate equalities “down to a fixed given depth” {= d }d∈ω, with d written in binary notation, and s= d t meaning that the ground terms s and t coincide if all their branches longer than d are cut off.

By using a refinement of Ferrante-Rackoff 's complexity-tailored Ehrenfeucht-Fraïssé games, we demonstrate that the bounded theory of finite trees can be decided within linear double exponential space\(2^{2^{cn} }\)(n is the length of input) for some constant c>0.


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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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