Hierarchy of piecewise-testable languages and complexity of the two-variable logic of subsequences

Hierarchy of piecewise-testable languages and complexity of the two-variable logic of subsequences Abstract. We prove that FO 2 pÅ , Ďq, the two-variable fragment of the first-order logic of sequences with the subsequence ordering, can only express piecewise-testable properties and is decidable with elementary complexity. To prove this we develop new techniques for bounding the piecewise-testability level of regular languages.

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