Demin, D. orcid.org/0009-0000-0780-419X and Zhukovskii, M. orcid.org/0000-0001-8763-9533 (2024) First order complexity of finite random structures. In: LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science. 39th Annual ACM/IEEE Symposium on Logic in Computer Science, 08 Jul - 11 Aug 2024, Tallinn, Estonia. ACM , pp. 1-14. ISBN 9798400706608
Abstract
For a sequence of random structures with n-element domains over a relational signature, we define its FO complexity as a certain subset in the Banach space "∞/c0. The well-known FO zero-one law and FO convergence law correspond to FO complexities equal to {0, 1} and a subset of R, respectively. We present a hierarchy of FO complexity classes, introduce a stochastic FO reduction that allows to transfer complexity results between different random structures, and deduce using this tool several new logical limit laws for binomial random structures. Finally, we introduce a conditional distribution on graphs, subject to a FO sentence φ, that generalises certain well-known random graph models, show instances of this distribution for every complexity class, and prove that the set of all φ validating 0 - 1 law is not recursively enumerable.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
Keywords: | random structures; first order logic; logical limit laws; zero-one laws; random graphs; logical complexity; recursively enumerable languages |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Nov 2024 15:10 |
Last Modified: | 07 Nov 2024 15:10 |
Status: | Published |
Publisher: | ACM |
Refereed: | Yes |
Identification Number: | 10.1145/3661814.3662127 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:219343 |