Publication details

Saarland University Computer Science

Ordering Constraints over Feature Trees Expressed in Second-order Monadic Logic

Martin Müller, Joachim Niehren

Information and Computation 159(1/2):22-58, 2000

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. While the first-order theory of FT is well understood, only few complexity and decidability results are known for fragments of the first-order theory of FT$_leq$. We introduce a new handle for such decidability questions by showing how to express ordering constraints over feature trees in second-order monadic logic (S2S or WS2S). Our relationship implies a new decidability result for feature logics, namely that the entailment problem of FT$_leq$ with existential quantifiers $phi_1models exists x_1ldotsexists x_n phi_2$ is decidable. We also show that this problem is PSPACE-hard even though the quantifier-free case can be solved in cubic time. To our knowledge, this is the first time that a non-trivial decidability result of feature logic is reduced to Rabins famous tree theorem.

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