## Paper: Two-Variable Logic on Words with Data (at LICS 2006)

**Mikołaj Bojańczyk Anca Muscholl Thomas Schwentick Luc Segoufin Claire David**

### 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 FO^2(~,\le,+1) is decidable over finite and over infinite data words, where ¡« is a binary predicate testing the data value equality and +1,\le 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.

### BibTeX

@InProceedings{BojaczykMuschollSch-TwoVariableLogiconW, author = {Mikołaj Bojańczyk and Anca Muscholl and Thomas Schwentick and Luc Segoufin and Claire David}, title = {Two-Variable Logic on Words with Data}, booktitle = {Proceedings of the Twenty-First Annual IEEE Symposium on Logic in Computer Science (LICS 2006)}, year = {2006}, month = {August}, pages = {7--16}, location = {Seattle, Washington, USA}, publisher = {IEEE Computer Society Press} }