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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| Vydáno v: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13 |
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29.06.2021
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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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| AbstractList | 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. |
| Author | Lasota, Slawomir Juzepczuk, Marta Pattathurajan, Mohnish Hofman, Piotr |
| Author_xml | – sequence: 1 givenname: Piotr surname: Hofman fullname: Hofman, Piotr organization: University of Warsaw – sequence: 2 givenname: Marta surname: Juzepczuk fullname: Juzepczuk, Marta organization: University of Warsaw – sequence: 3 givenname: Slawomir surname: Lasota fullname: Lasota, Slawomir organization: University of Warsaw – sequence: 4 givenname: Mohnish surname: Pattathurajan fullname: Pattathurajan, Mohnish organization: University of Warsaw |
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| Snippet | We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this... |
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| SubjectTerms | Automata Computer science Grammar Image recognition Orbits Registers |
| Title | Parikh's theorem for infinite alphabets |
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