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Algebra i logika, 2024, Volume 63, Number 1, Pages 89–99
DOI: https://doi.org/10.33048/alglog.2024.63.107 (Mi al2796) 		 
The length of an unsatisfiable subformula

A. V. Seliverstov

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
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DOI: https://doi.org/10.33048/alglog.2024.63.107
Abstract: We find a bound for the length of a conjunction of some propositional formulas, for which every unsatisfiable formula contains an unsatisfiable subformula. In particular, this technique applies to formulas in conjunctive normal form with restrictions on the number of true literals within every elementary disjunction, as well as for 2-CNFs, for symmetric 3-CNFs, and for conjunctions of voting functions in three literals. A lower bound on the rank of some matrices is used in proofs.
Keywords: propositional logic, satisfiability, rank of matrix, binary solution.
Received: 15.12.2023
Revised: 04.12.2024
English version:
Algebra and Logic, 2024, Volume 63, Issue 1, Pages 65–72
DOI: https://doi.org/10.1007/s10469-024-09771-0
Document Type: Article
UDC: 510.633
Language: Russian
Citation: A. V. Seliverstov, “The length of an unsatisfiable subformula”, Algebra Logika, 63:1 (2024), 89–99; Algebra and Logic, 63:1 (2024), 65–72
Citation in format AMSBIB
\Bibitem{Sel24}
\by A.~V.~Seliverstov
\paper The length of an unsatisfiable subformula
\jour Algebra Logika
\yr 2024
\vol 63
\issue 1
\pages 89--99
\mathnet{http://mi.mathnet.ru/al2796}
\transl
\jour Algebra and Logic
\yr 2024
\vol 63
\issue 1
\pages 65--72
\crossref{https://doi.org/10.1007/s10469-024-09771-0}
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