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arXiv · 2104.12018

Parikh's theorem for infinite alphabets

Piotr Hofman·Marta Juzepczuk·Sławomir Lasota·Mohnish Pattathurajan
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Abstract

We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove that commutative images of languages of one-register automata are not always semi-linear, but they are always rational. We also lift the latter result to grammars: commutative images of one-register context-free languages are rational, and in consequence commutatively equivalent to register automata. We conjecture analogous results for automata and grammars with arbitrarily many registers.

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Piotr Hofman, Marta Juzepczuk, Sławomir Lasota, Mohnish Pattathurajan. 2021-04-24. Parikh's theorem for infinite alphabets. https://arxiv.org/abs/2104.12018

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