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arXiv · 1810.02953

On shuffle products, acyclic automata and piecewise-testable languages

Simon Halfon·Philippe Schnoebelen
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Abstract

We show that the shuffle $L \unicode{x29E2} F$ 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 $L \unicode{x29E2} F$.

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Simon Halfon, Philippe Schnoebelen. 2019-02-01. On shuffle products, acyclic automata and piecewise-testable languages. https://doi.org/10.1016/j.ipl.2019.01.012

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