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2015 | 23 | 3 | 205-213
Tytuł artykułu

Polynomially Bounded Sequences and Polynomial Sequences

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, we formalize polynomially bounded sequences that plays an important role in computational complexity theory. Class P is a fundamental computational complexity class that contains all polynomial-time decision problems [11], [12]. It takes polynomially bounded amount of computation time to solve polynomial-time decision problems by the deterministic Turing machine. Moreover we formalize polynomial sequences [5].
Słowa kluczowe
Twórcy
  • Shinshu University Nagano, Japan
autor
  • Japan Advanced Institute of Science and Technology Ishikawa, Japan
Bibliografia
  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [3] Grzegorz Bancerek. Increasing and continuous ordinal sequences. Formalized Mathematics, 1(4):711-714, 1990.
  • [4] Grzegorz Bancerek and Piotr Rudnicki. Two programs for SCM. Part I - preliminaries. Formalized Mathematics, 4(1):69-72, 1993.
  • [5] E.J. Barbeau. Polynomials. Springer, 2003.
  • [6] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [7] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [8] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [11] Jon Kleinberg and Eva Tardos. Algorithm Design. Addison-Wesley, 2005.
  • [12] Donald E. Knuth. The Art of Computer Programming, Volume 1: Fundamental Algorithms, Third Edition. Addison-Wesley, 1997.
  • [13] Artur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181-187, 2005.
  • [14] Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2 (1):17-28, 1991.
  • [15] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  • [16] Richard Krueger, Piotr Rudnicki, and Paul Shelley. Asymptotic notation. Part I: Theory. Formalized Mathematics, 9(1):135-142, 2001.
  • [17] Richard Krueger, Piotr Rudnicki, and Paul Shelley. Asymptotic notation. Part II: Examples and problems. Formalized Mathematics, 9(1):143-154, 2001.
  • [18] Yatsuka Nakamura and Hisashi Ito. Basic properties and concept of selected subsequence of zero based finite sequences. Formalized Mathematics, 16(3):283-288, 2008. doi:10.2478/v10037-008-0034-y.[Crossref]
  • [19] Jan Popiołek. Some properties of functions modul and signum. Formalized Mathematics, 1(2):263-264, 1990.
  • [20] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
  • [21] Konrad Raczkowski and Andrzej Nedzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991.
  • [22] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
  • [23] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.
  • [24] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [26] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
  • [27] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [28] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_forma-2015-0017
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