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

Abstract : 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<. 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< with existential quantifiers P |= models exists x1 ... exists xn P' 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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https://hal.inria.fr/inria-00536798
Contributor : Joachim Niehren <>
Submitted on : Tuesday, November 16, 2010 - 11:08:58 PM
Last modification on : Tuesday, October 31, 2017 - 2:22:18 PM
Long-term archiving on: : Thursday, February 17, 2011 - 3:12:59 AM

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  • HAL Id : inria-00536798, version 1

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Martin Müller, Joachim Niehren. Ordering Constraints over Feature Trees Expressed in Second-order Monadic Logic. Information and Computation, Elsevier, 2000, 159 (1/2), pp.22--58. ⟨inria-00536798⟩

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