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Two-Variable Logic on Words with Data

Mikolaj Bojanczyk 1 Anca Muscholl 2 Thomas Schwentick 3 Luc Segoufin 4 Claire David 2
4 GEMO - Integration of data and knowledge distributed over the web
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO2(~, <, +1) is decidable over finite and over infinite data words, where ~ is a binary predicate testing the data value equality and +1,< are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable.
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Mikolaj Bojanczyk, Anca Muscholl, Thomas Schwentick, Luc Segoufin, Claire David. Two-Variable Logic on Words with Data. 21st Annual IEEE Symposium on Logic in Computer Science LICS'06, 2006, Seattle, United States. pp.7-16, ⟨10.1109/LICS.2006.51⟩. ⟨hal-00151749⟩

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