Future-looking Logics on Data Words and Trees
Résumé
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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