@Article{Müller_et_al:2001,
AUTHOR = {Müller, Martin and Niehren, Joachim and Treinen, Ralf},
TITLE = {The First-Order Theory of Ordering Constraints over Feature Trees},
YEAR = {2001},
JOURNAL = {Discrete Mathematics and Theoretical Computer Science},
VOLUME = {4},
NUMBER = {2},
PAGES = {193-234},
URL = {ftp://ftp.ps.uni-sb.de/pub/papers/ProgrammingSysLab/FTSubTheory-98.ps.gz},
ABSTRACT = {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.},
ANNOTE = {COLIURL : Muller:2001:FOT.pdf}
}
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