# Publication details

##
The First-Order Theory of Ordering Constraints over Feature Trees

Martin Müller, Joachim Niehren, Ralf Treinen

Thirteenth annual IEEE Symposium on Logic in Computer Sience (LICS98), pp. 432--443, IEEE Press, 1998

The system FT$_leq$ of ordering constraints over feature trees has been introduced as an
extension of the system FT of equality constraints over feature
trees. We investigate the first-order theory of FT$_leq$
and its fragments in detail, both
over finite trees and over possibly infinite trees. We prove that the
first-order theory of FT$_leq$
is undecidable, in contrast to the first-order theory of FT
which is well-known to be decidable. We show that the entailment
problem of FT$_leq$ with
existential quantification is PSPACE-complete. So far, this problem
has been shown decidable, coNP-hard in case of finite trees,
PSPACE-hard in case of arbitrary trees, and cubic time when restricted
to quantifier-free entailment judgments. To show PSPACE-completeness,
we show that the entailment problem of FT$_leq$ with existential
quantification is equivalent to the
inclusion problem of non-deterministic finite automata.

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@INPROCEEDINGS{FTSubTheory:98,
title = {The First-Order Theory of Ordering Constraints over Feature Trees},
author = {Martin M{\"u}ller and Joachim Niehren and Ralf Treinen},
year = {1998},
month = {{21--24 June}},
publisher = {{IEEE Press}},
booktitle = {Thirteenth annual IEEE Symposium on Logic in Computer Sience (LICS98)},
pages = {{432--443}},
address = {{Indianapolis, Indiana}},
}

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