## An Improved Lower Bound for the Elementary Theories of Trees (1996)

Citations: | 28 - 3 self |

### BibTeX

@INPROCEEDINGS{Vorobyov96animproved,

author = {Sergei Vorobyov},

title = {An Improved Lower Bound for the Elementary Theories of Trees},

booktitle = {},

year = {1996},

pages = {275--287},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### 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 1 exp k (n) for any fixed k. Moreover, for some constant d ? 0 these decision problems require nondeterministic time exceeding exp 1 (bdnc) infinitely often. 1 Introduction Trees are fundamental in Computer Science. Different tree structures are used as underlying domains in automated theorem proving, term rewriting, functional and logic programming, constraint solving, symbolic computation, knowledge re...