Future-looking Logics on Data Words and Trees

Diego Figueira 1, 2 Luc Segoufin 2, 1
2 DAHU - Verification in databases
CNRS - Centre National de la Recherche Scientifique : UMR8643, Inria Saclay - Ile de France, ENS Cachan - École normale supérieure - Cachan, LSV - Laboratoire Spécification et Vérification [Cachan]
Abstract : In a data word or a data tree each position carries a label from a finite alphabet and a data value from an infinite domain. Over data words we consider the logic LTL_↓^1 (F), that extends LTL(F) with one register for storing data values for later comparisons. We show that satisfiability over data words of LTL_↓^1 (F) is already non primitive recursive. We also show that the extension of LTL_↓^1 (F) with either the backward modality F^{−1} or with one extra register is undecidable. All these lower bounds were already known for LTL_↓^1(X, F) and our results essentially show that the X modality was not necessary. Moreover we show that over data trees similar lower bounds hold for certain fragments of XPath.
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Diego Figueira, Luc Segoufin. Future-looking Logics on Data Words and Trees. International Symposium on Mathematical Foundations of Computer Science (MFCS), Aug 2009, Novy Smokovec, Slovakia. pp.331-343. ⟨hal-01806188⟩

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