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Recently data trees and data words have received considerable amount ofattention in connection with XML reasoning and system verification. These aretrees or words that, in addition to labels from a finite alphabet, carry datavalues from an infinite alphabet (data). In general it is rather hard to obtainlogics for data words and trees that are sufficiently expressive, but stillhave reasonable complexity for the satisfiability problem. In this paper weextend and study the notion of B\"uchi automata for omega-words with data. Weprove that the emptiness problem for such extension is decidable in elementarycomplexity. We then apply our result to show the decidability of two kinds oflogics for omega-words with data: the two-variable fragment of first-orderlogic and some extensions of classical linear temporal logic for omega-wordswith data.

Extending B\"uchi Automata with Constraints on Data Values