Regular expressions for data words

In this paper we define and study regular expressions for data words. We first define regular expression with memory (REM), which extend standard regular ex-pressions with limited memory and show that they capture the class of data words defined by register automata. We also study the complexity of the standard deci-sion problems for REM, which turn out to be the same as for register automata. In order to lower the complexity of main reasoning tasks, we then look at two natural subclasses of REM that can define many properties of interest in the applications of data words: regular expression with binding (REWB) and regular expression with equality (REWE). We study their expressive power and analyse the com-plexity of their standard decision problems. We also establish the following strict hierarchy of expressive power: REM is strictly stronger than REWB, and in turn REWB is strictly stronger than REWE