Geodesic
The First-Order Theory of Ordering Constraints over Feature Trees
Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2.

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The system FT< 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< and its fragments in detail, both over finite trees and over possibly infinite trees. We prove that the first-order theory of FT< 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< 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< with existential quantification is equivalent to the inclusion problem of non-deterministic finite automata. Available at http://www.ps.uni-saarland.de/Publications/documents/FTSubTheory_98.pdf 
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     title = {The {First-Order} {Theory} of {Ordering} {Constraints} over {Feature} {Trees}},
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Müller, Martin; Niehren, Joachim; Treinen, Ralf. The First-Order Theory of Ordering Constraints over Feature Trees. Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2. doi : 10.46298/dmtcs.267. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.267/

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