A logical characterization of data languages

The ideal case of formal languages. In the formal languages framework, the class of regular languages can be characterized in various ways: finite automata, rational expressions, monadic second-order logic, extended temporal logics, finite monoids... (see e.g. [RS97]). Among all these equivalences, the logical characterization is of particular interest since many subclasses of regular languages (like star-free languages or locally threshold testable languages) can be exactly described through fragments of the whole logics, like first-order logics or linear temporal logics [Pin94,PP01]. All these characterizations constitute not only one of the cornerstones of theoretical computer science but also form the fundamental basis for much more practical research on verification (see e.g. [CGP99,BBF+01]).

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