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A Criterion for P-Computability of Structures

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References

  1. D. Cenzer and J. Remmel, “Polynomial-time versus recursive models,” Ann. Pure Appl. Log., 54, No. 1, 17-58 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  2. P. E. Alaev, “Structures computable in polynomial time. I,” Algebra and Logic, 55, No. 6, 421-435 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  3. P. E. Alaev and V. L. Selivanov, “Fields of algebraic numbers computable in polynomial time. I,” Algebra and Logic, 58, No. 6, 447-469 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Cenzer and J. B. Remmel, “Complexity theoretic model theory and algebra,” in Handbook of Recursive Mathematics, Vol. 1, Recursive Model Theory, Y. L. Ershov, S. S. Goncharov, A. Nerode, and J. B. Remmel (Eds.), Stud. Log. Found. Math., 138, Elsevier, Amsterdam (1998), pp. 381-513.

  5. P. E. Alaev, “Finitely generated structures computable in polynomial time,” Sib. Math. J., 63, No. 5, 801-818 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Alaev, “Quotient structures and groups computable in polynomial time,” Lect. Notes Comput. Sci., 13296, Springer, Cham (2022), pp. 35-45.

  7. P. E. Alaev, “The complexity of inversion in groups,” to appear in Algebra and Logic.

  8. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, London (1974).

    MATH  Google Scholar 

  9. I. Kalimullin, R. Miller, and H. Schoutens, “Degree spectra for transcendence in fields,” in Lect. Notes Comput. Sci., 11558, Springer, Cham (2019), pp. 205-216.

  10. A. T. Nurtazin, “Computable classes and algebraic criteria for autostability,” Ph. D. Thesis, Institute of Mathematics and Mechanics, Alma-Ata (1974).

  11. M. Harrison-Trainor, A. Melnikov, and A. Montalbán, “Independence in computable algebra,” J. Alg., 443, 441-468 (2015).

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

I am grateful to S. S. Goncharov, N. A. Bazhenov, and A. V. Nechesov for discussing the results of the paper, which allowed me to improve some formulations.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    P. E. Alaev

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  1. P. E. Alaev
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Correspondence to P. E. Alaev.

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Translated from Algebra i Logika, Vol. 61, No. 5, pp. 640-646, September-October, 2022. Russian DOI: https://doi.org/10.33048/alglog.2022.61.507.

Supported by Russian Science Foundation, project No. 23-11-00170; https://rscf.ru/project/23-11-00170.

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Alaev, P.E. A Criterion for P-Computability of Structures. Algebra Logic 61, 437–441 (2022). https://doi.org/10.1007/s10469-023-09710-5

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