The first-order theory of ordering constraints over feature trees

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, 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 determine the complexity of the entailment problem of FT_⩽ with existential quantification to be PSPACE-complete, by proving its equivalence to the inclusion problem of non-deterministic finite automata. Our reduction from the entailment problem to the inclusion problem is based on a new algorithm that, given an existential formula of FT_⩽, computes a finite automaton which accepts all its logic consequences