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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 4, Pages 838–847 (Mi smj2129)  
This article is cited in 5 scientific papers (total in 5 papers)

On decidability of the decomposability problem for finite theories

A. S. Morozova, D. K. Ponomaryovb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Institute of Informatics Systems, Novosibirsk, Russia
Full-text PDF (316 kB) Citations (5)
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Abstract: We consider the decomposability problem for elementary theories, i.e. the problem of deciding whether a theory has a nontrivial representation as a union of two (or several) theories in disjoint signatures. For finite universal Horn theories, we prove that the decomposability problem is $\Sigma _1^0$-complete and, thus, undecidable. We also demonstrate that the decomposability problem is decidable for finite theories in signatures consisting only of monadic predicates and constants.
Keywords: decomposable theory, decomposition of a theory, Horn theory, logic programming, monadic logic.
Received: 09.10.2008
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 4, Pages 667–674
DOI: https://doi.org/10.1007/s11202-010-0068-6
Bibliographic databases:
Document Type: Article
UDC: 510.5+510.67
Language: Russian
Citation: A. S. Morozov, D. K. Ponomaryov, “On decidability of the decomposability problem for finite theories”, Sibirsk. Mat. Zh., 51:4 (2010), 838–847; Siberian Math. J., 51:4 (2010), 667–674
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/smj2129
  • https://www.mathnet.ru/eng/smj/v51/i4/p838
    • This publication is cited in the following 5 articles:
    1. Ponomaryov D., “On the Relationship Between the Complexity of Decidability and Decomposability of First-Order Theories”, Lobachevskii J. Math., 42:12 (2021), 2905–2912  crossref  mathscinet  zmath  isi  scopus
    2. Emelyanov P., Ponomaryov D., “the Complexity of and-Decomposition of Boolean Functions”, Discret Appl. Math., 280 (2020), 113–132  crossref  mathscinet  zmath  isi  scopus
    3. Ponomaryov D., Soutchanski M., “Progression of Decomposed Local-Effect Action Theories”, ACM Trans. Comput. Log., 18:2 (2017), 16  crossref  mathscinet  zmath  isi  scopus
    4. Emelyanov P.G., Ponomaryov D.K., “Algorithmic Issues of and-Decomposition of Boolean Formulas”, Program. Comput. Softw., 41:3 (2015), 162–169  crossref  mathscinet  zmath  isi  elib  scopus
    5. Emelyanov P., Ponomaryov D., “on Tractability of Disjoint and-Decomposition of Boolean Formulas”, Perspectives of System Informatics, Psi 2014, Lecture Notes in Computer Science, 8974, eds. Voronkov A., Virbitskaite I., Springer-Verlag Berlin, 2015, 92–101  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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