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Algebra Logika, 2016, Volume 55, Number 6, Pages 647–669 (Mi al769)  

This article is cited in 14 scientific papers (total in 14 papers)

Structures computable in polynomial time. I

P. E. Alaevab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

Abstract: It is proved that every computable locally finite structure with finitely many functions has a presentation computable in polynomial time. Furthermore, a structure computable in polynomial time is polynomially categorical iff it is finite. If a structure is computable in polynomial time and locally finite then it is weakly polynomially categorical (i.e., categorical with respect to primitive recursive isomorphisms) iff it is finite.

Keywords: locally finite structure, computable structure, structure computable in polynomial time, polynomially categorical structure, weakly polynomially categorical structure.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00376
Supported by RFBR, project No. 14-01-00376.


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English version:
Algebra and Logic, 2017, 55:6, 421–435

Bibliographic databases:

UDC: 510.5+512+510.6
Received: 09.11.2015
Revised: 07.12.2015

Citation: P. E. Alaev, “Structures computable in polynomial time. I”, Algebra Logika, 55:6 (2016), 647–669; Algebra and Logic, 55:6 (2017), 421–435

Citation in format AMSBIB
\by P.~E.~Alaev
\paper Structures computable in polynomial time.~I
\jour Algebra Logika
\yr 2016
\vol 55
\issue 6
\pages 647--669
\jour Algebra and Logic
\yr 2017
\vol 55
\issue 6
\pages 421--435

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    This publication is cited in the following articles:
    1. P. E. Alaev, V. L. Selivanov, “Polynomial computability of fields of algebraic numbers”, Dokl. Math., 98:1 (2018), 341–343  mathnet  crossref  zmath  isi  scopus
    2. P. E. Alaev, “Structures computable in polynomial time. II”, Algebra and Logic, 56:6 (2018), 429–442  mathnet  crossref  crossref  isi
    3. P. E. Alaev, “Categoricity for primitive recursive and polynomial Boolean algebras”, Algebra and Logic, 57:4 (2018), 251–274  mathnet  crossref  crossref  isi
    4. K. V. Blinov, “Primitively recursively categorical linear orderings”, Siberian Math. J., 60:1 (2019), 20–26  mathnet  crossref  crossref  isi  elib
    5. I. Sh. Kalimullin, R. Miller, “Primitive recursive fields and categoricity”, Algebra and Logic, 58:1 (2019), 95–99  mathnet  crossref  crossref  isi
    6. M. V. Zubkov, I. Sh. Kalimullin, A. G. Mel'nikov, A. N. Frolov, “Punctual copies of algebraic structures”, Siberian Math. J., 60:6 (2019), 993–1002  mathnet  crossref  crossref  isi  elib
    7. P. E. Alaev, V. L. Selivanov, “Fields of algebraic numbers computable in polynomial time. I”, Algebra and Logic, 58:6 (2020), 447–469  mathnet  crossref  crossref  isi
    8. N. Bazhenov, R. Downey, I. Kalimullin, A. Melnikov, “Foundations of online structure theory”, Bull. Symb. Log., 25:2 (2019), 141–181  crossref  mathscinet  zmath  isi  scopus
    9. P. E. Alaev, “Polynomially computable structures with finitely many generators”, Algebra and Logic, 59:3 (2020), 266–272  mathnet  crossref  crossref  isi
    10. I. Sh. Kalimullin, “Constructing punctually categorical semigroups”, Algebra and Logic, 59:5 (2020), 408–411  mathnet  crossref  crossref  isi
    11. N. Bazhenov, I. Kalimullin, A. Melnikov, K. M. Ng, “Online presentations of finitely generated structures”, Theor. Comput. Sci., 844 (2020), 195–216  crossref  mathscinet  zmath  isi  scopus
    12. R. Downey, M. Harrison-Trainor, I. Kalimullin, A. Melnikov, D. Turetsky, “Graphs are not universal for online computability”, J. Comput. Syst. Sci., 112 (2020), 1–12  crossref  mathscinet  zmath  isi  scopus
    13. J. Carson, D. Cenzer, J. B. Remmel, “Effective categoricity of automatic equivalence and nested equivalence structures”, Theor. Comput. Syst., 64:6 (2020), 1110–1139  crossref  mathscinet  zmath  isi  scopus
    14. A. Melnikov, K. M. Ng, “A structure of punctual dimension two”, Proc. Amer. Math. Soc., 148:7 (2020), 3113–3128  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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