@MISC{ASYMPT_2.MIZ,
  AUTHOR = {Okazaki, Hiroyuki and Futa, Yuichi},
  TITLE = {Polynomially Bounded Sequences and Polynomial Sequences},
  SECTION1 = {Preliminaries},
  SECTION2 = {Polynomially Bounded Sequences},
  SECTION3 = {Polynomial Sequences},
  DAY = {30},
  MONTH = {June},
  YEAR = {2015},
  ADDRESS1 = {Shinshu University, Nagano, Japan},
  ADDRESS2 = {Japan Advanced Institute of Science and Technology, Ishikawa, Japan},
  SUMMARY = {In this article, we formalize polynomially bounded sequences
            that plays an important role in computational complexity theory.
            The class P is a fundamental  computational complexity class that
            contains all polynomial-time decision problems \cite{ALDESIGN}.
            It takes polynomially bounded amount of computation
            time to solve polynomial-time decision problems
            by a deterministic Turing machine.
            Moreover we formalize polynomial sequences.},
  ACKNOWLEDGEMENT = {The authors would also like to express our gratitude to
    Prof. Yasunari Shidama for his support and encouragement.}}

@BOOK{ALDESIGN,
      AUTHOR = {Jon Kleinberg and Eva Tardos},
      TITLE = {Algorithm Design},
      PUBLISHER = {Addison-Wesley},
      YEAR = {2005}}

