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Logical Language of Description of Polynomial Computing

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Abstract

The concept of a term and, accordingly, the concept of a formula are extended using new operators. These extensions of the language preserve the expressiveness of \(\Sigma \)-formulas and, at the level of \({{\Delta }_{0}}\)-formulas and terms, they ensure the polynomiality of algorithms for calculating the value of a term and deciding the truth of a \({{\Sigma }_{0}}\)-formula.

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REFERENCES

  1. S. S. Goncharov and D. I. Sviridenko, Vychisl. Sist. 107, 3–29 (1985).

    Google Scholar 

  2. S. S. Goncharov and D. I. Sviridenko, Lect. Notes Comput. Sci. 215, 169–179 (1986).

    Article  Google Scholar 

  3. Yu. L. Ershov, S. S. Goncharov, and D. I. Sviridenko, Information Processing 86: Proceedings of IFIP 10th World Computer Congress (Elsevier, Amsterdam, 1986), Vol. 10, pp. 1113–1120.

  4. S. S. Goncharov and D. I. Sviridenko, Dokl. Akad. Nauk SSSR 289 (6), 1324–1328 (1986).

    MathSciNet  Google Scholar 

  5. Yu. L. Ershov, S. S. Goncharov, and D. I. Sviridenko, Lect. Notes Comput. Sci. 278, 116–122 (1987).

    Article  Google Scholar 

  6. Yu. L. Ershov, Dokl. Akad. Nauk SSSR 270 (4), 786–788 (1983).

    MathSciNet  Google Scholar 

  7. Yu. L. Ershov, Dokl. Akad. Nauk SSSR 273 (5), 1045–1048 (1983).

    MathSciNet  Google Scholar 

  8. Yu. L. Ershov, Definability and Computability: Siberian School of Algebra and Logic (Consultants Bureau, New York, 1996).

    Google Scholar 

  9. J. Barwise, Admissible Sets and Structures (Springer, Berlin, 1975).

    Book  MATH  Google Scholar 

  10. S. Arora and B. Barak, Computational Complexity: A  Modern Approach (Cambridge Univ. Press, Cambridge, 2009).

    Book  MATH  Google Scholar 

  11. Ch. Papadimitriou, Computational Complexity (Addison-Wesley, Reading, Mass., 1994).

    MATH  Google Scholar 

  12. S. S. Ospichev and D. Ponomarev, Sib. Electron. Math. Rep. 15, 987–995 (2018).

    Google Scholar 

  13. S. S. Goncharov, Sib. Math. J. 58 (5), 794–800 (2017).

    Article  MathSciNet  Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was supported by the Russian Science Foundation, project no. 17-11-01176.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    S. S. Goncharov & D. I. Sviridenko

Authors
  1. S. S. Goncharov
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  2. D. I. Sviridenko
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Correspondence to S. S. Goncharov or D. I. Sviridenko.

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Translated by I. Ruzanova

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Goncharov, S.S., Sviridenko, D.I. Logical Language of Description of Polynomial Computing. Dokl. Math. 99, 121–124 (2019). https://doi.org/10.1134/S1064562419020030

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  • DOI: https://doi.org/10.1134/S1064562419020030

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