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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 5, Pages 42–60
DOI: https://doi.org/10.26907/0021-3446-2022-5-42-60
(Mi ivm9774)
 

Computational complexity of the word problem in modal and pseudo-Boolean algebras with a small number of generators

M. Rybakov

Tver State University, 33 Zhelyabova str., Tver, 170100 Russia
References:
Abstract: We consider the computational complexity of the word problem for finitely generated Heyting and modal algebras. It is shown that the word problem is PSPACE-complete if only constant modal terms or only $0$-generated modal algebras are considered; similar results are obtained for two-variable terms and $2$-generated Heyting algebras. It is also shown that, if an equation of positive terms is refuted in a Heyting algebra, it is refuted in a $2$-generated algebra. We also consider the word problem for certain classes of modal and Heyting algebras and obtain results similar to those mentioned above for infinite families of such classes. The obtained results are optimal in the number of generators: reduction in generators leads to the polynomial time decidable word problem.
Keywords: word problem, modal algebra, Heyting algebra, pseudo-Boolean algebra, finitely generated algebra.
Funding agency Grant number
Russian Science Foundation 21-18-00195
Received: 25.07.2021
Revised: 21.08.2021
Accepted: 29.09.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 5, Pages 33–48
DOI: https://doi.org/10.3103/S1066369X22050061
Bibliographic databases:
Document Type: Article
UDC: 512.579: 519.766: 510.52: 510.643: 510.649
Language: Russian
Citation: M. Rybakov, “Computational complexity of the word problem in modal and pseudo-Boolean algebras with a small number of generators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 5, 42–60; Russian Math. (Iz. VUZ), 66:5 (2022), 33–48
Citation in format AMSBIB
\Bibitem{Ryb22}
\by M.~Rybakov
\paper Computational complexity of the word problem in modal and pseudo-Boolean algebras
with a small number of generators
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 5
\pages 42--60
\mathnet{http://mi.mathnet.ru/ivm9774}
\crossref{https://doi.org/10.26907/0021-3446-2022-5-42-60}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4458053}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 5
\pages 33--48
\crossref{https://doi.org/10.3103/S1066369X22050061}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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