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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 507, Pages 61–65
DOI: https://doi.org/10.31857/S2686954322600501 (Mi danma320) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Computational complexity of theories of a binary predicate with a small number of variables

M. Rybakov

Institute for Information Transmission Problems (Kharkevich Institute) of Russian Academy of Sciences, Moscow, Russia
Citations (2)
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DOI: https://doi.org/10.31857/S2686954322600501
Abstract: We prove $\Sigma^0_1$-hardness of a number of theories of a binary predicate with three individual variables (in languages without constants or equality). We also show that, in languages with equality and the operators of composition and of transitive closure, theories of a binary predicate are $\Pi_1^1$-hard with only two individual variables.
Keywords: first-order logic, dyadic logic, undecidability, Church's theorem, Trakhtenbrot's theorem.
Funding agency Grant number
Russian Science Foundation 21-18-00195
The research was carried out at the IITP RAS with the financial support of the Russian Science Foundation, project no. 21-18-00195.
Presented: A. L. Semenov
Received: 07.08.2022
Revised: 19.09.2022
Accepted: 23.09.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 3
DOI: https://doi.org/10.1134/S1064562422700053
Bibliographic databases:
Document Type: Article
UDC: 510.635, 510.665
Language: Russian
Citation: M. Rybakov, “Computational complexity of theories of a binary predicate with a small number of variables”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 61–65
Citation in format AMSBIB
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\by M.~Rybakov
\paper Computational complexity of theories of a binary predicate with a small number of variables
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 507
\pages 61--65
\mathnet{http://mi.mathnet.ru/danma320}
\crossref{https://doi.org/10.31857/S2686954322600501}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563848}
\elib{https://elibrary.ru/item.asp?id=49991286}
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