Parikh's theorem for infinite alphabets
Formal Languages and Automata Theory
2021-04-27 v1 Logic in Computer Science
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.
Cite
@article{arxiv.2104.12018,
title = {Parikh's theorem for infinite alphabets},
author = {Piotr Hofman and Marta Juzepczuk and Sławomir Lasota and Mohnish Pattathurajan},
journal= {arXiv preprint arXiv:2104.12018},
year = {2021}
}