<i>#P</i>-hardness of Computing High Order Derivative and Its Logarithm

• ANDO Ei

  Sojo University

抄録

In this paper, we show a connection between #P and computing the (real) value of the high order derivative at the origin. Consider, as a problem instance, an integer b and a sufficiently often differentiable function F(x) that is given as a string. Then we consider computing the value F^(b)(0) of the b-th derivative of F(x) at the origin. By showing a polynomial as an example, we show that we have FP = #P if we can compute log ₂F^(b)(0) up to certain precision. The previous statement holds even if F(x) is limited to a function that is analytic at any x ∈ R. It implies the hardness of computing the b-th value of a number sequence from the closed form of its generating function.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A (6), 1382-1384, 2014

  一般社団法人 電子情報通信学会

キーワード

• computable analysis
• computational complexity
• <i>#P</i>-hardness
• SUBSET SUM

詳細情報

• CRID: 1390282681286981632
• NII論文ID: 130004770868
• DOI: 10.1587/transfun.e97.a.1382
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E97.A/6/E97.A_1382/_pdf
• 本文言語コード: en
• データソース種別:
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  • Crossref
  • CiNii Articles
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