Parikh's theorem for infinite alphabets

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...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Authors: Hofman, Piotr, Juzepczuk, Marta, Lasota, Slawomir, Pattathurajan, Mohnish
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Automata
Computer science
Grammar
Image recognition
Orbits
Registers
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Summary: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.
DOI:10.1109/LICS52264.2021.9470626