A Decidable Two-Way Logic on Data Words

Diego Figueira (1)

1 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

We study the satisfiability problem for a logic on data words. A data word is a finite word where every position carries a label from a finite alphabet and a data value from an infinite domain. The logic we consider is two-way, contains " future " and " past " modalities, where these are considered as reflexive and transitive relations, and data equality and inequality tests. This logic corresponds to the fragment of XPath with the 'following-sibling-or-self' and 'preceding-sibling-or-self' axes over a data word. We show that this problem is decidable, EXPSPACE-complete. This is surprising considering that with the strict navigation relations (non-reflexive) the satisfiability problem is undecidable. To show this we first reduce the problem to a derivation problem for an infinite transition system, and then we show how to abstract this problem into a reachability problem of a finite transition system.

Domaines: Base de données [cs.DB]; Logique en informatique [cs.LO]

Diego Figueira. A Decidable Two-Way Logic on Data Words. Annual IEEE Symposium on Logic in Computer Science (LICS), Jun 2011, Toronto, United States. ⟨10.1109/LICS.2011.18⟩. ⟨hal-01803452⟩