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.
CITATION STYLE
Vorobyov, S. (1996). An improved lower bound for the elementary theories of trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1104, pp. 275–287). Springer Verlag. https://doi.org/10.1007/3-540-61511-3_91
Mendeley helps you to discover research relevant for your work.