On shuffle products, acyclic automata and piecewise-testable languages

Abstract We show that the shuffle L ⊔ ⊔ F of a piecewise-testable language L and a finite language F is piecewise-testable. The proof relies on a classic but little-used automata-theoretic characterization of piecewise-testable languages. We also discuss some mild generalizations of the main result, and provide bounds on the piecewise complexity of L ⊔ ⊔ F .

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