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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 987–995
DOI: https://doi.org/10.17377/semi.2018.15.083 (Mi semr973) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Mathematical logic, algebra and number theory

On the complexity of formulas in semantic programming

S. Ospichevab, D. Ponomarevabc

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia
c A.P. Ershov Institute of Informatics Systems, pr. Lavrentyeva, 6, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2018.15.083
Abstract: We consider the complexity of $\Delta_0$ formulas augmented with conditional terms. We show that for formulas having $n$ bounded quantifiers, for a fixed $n$, deciding the truth in a list superstructure with polynomial computable basic operations is of polynomial complexity. When the quantifier prefix has $n$ alternations of quantifiers, the truth problem is complete for the $n$-th level of the polynomial-time hierarchy. Under no restrictions on the quantifier prefix the truth problem is PSPACE-complete. Thus, the complexity results indicate the analogy between the truth problem for $\Delta_0$ formulas with conditional terms and the truth problem for quantified boolean formulas.
Keywords: semantic programming, list structures, polynomial time/space complexity, $\Delta_0$-formulas.
Funding agency Grant number
Russian Science Foundation 17-11-01176
The authors were supported by the Russian Science Foundation (Grant No. 17-11-01176).
Received June 28, 2018, published September 10, 2018
Bibliographic databases:
Document Type: Article
UDC: 510.5
MSC: 03D15, 68Q15
Language: English
Citation: S. Ospichev, D. Ponomarev, “On the complexity of formulas in semantic programming”, Sib. Èlektron. Mat. Izv., 15 (2018), 987–995
Citation in format AMSBIB
\Bibitem{OspPon18}
\by S.~Ospichev, D.~Ponomarev
\paper On the complexity of formulas in semantic programming
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 987--995
\mathnet{http://mi.mathnet.ru/semr973}
\crossref{https://doi.org/10.17377/semi.2018.15.083}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454860200025}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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