Uniformisation of Regular Relations in First-Order Logic with Two Variables
Article No.: 54, Pages 1 - 13
Abstract
A uniformisation of a binary relation is a functional relation contained in it, with the same domain. The uniformisation problem asks whether such a uniformisation can be defined in a given formalism.
We solve this problem in the context of regular relations over finite words, for the fragment FO2[<] of First-Order Logic with two variables: we provide an algorithm that decides if a given regular relation over finite words admits a uniformisation definable in FO2[<].
The paper provides a new representation of languages definable in FO2[<], which can be used for the decidability of other problems involving this formalism, e.g. the problem of separability of two regular languages by a language definable in FO2[<].
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Index Terms
- Uniformisation of Regular Relations in First-Order Logic with Two Variables
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Information & Contributors
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Published In
July 2024
988 pages
ISBN:9798400706608
DOI:10.1145/3661814
- Conference Chair:
- Pawel Sobocinski,
- Program Chairs:
- Ugo Dal Lago,
- Javier Esparza
This work is licensed under a Creative Commons Attribution International 4.0 License.
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- IEEE Computer Society
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Association for Computing Machinery
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Published: 08 July 2024
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LICS '24: 39th Annual ACM/IEEE Symposium on Logic in Computer Science
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