Complexity of counting output patterns of logic circuits

Kei Uchizawa, Zhenghong Wang, Hiroki Morizumi, Xiao Zhou

研究成果: Conference contribution

抄録

Let C be a logic circuit consisting of s gates g1, g2, gs, then the output pattern of C for an input x ε {0, 1}n is defined to be a vector (g1(x), g2(x), gs(x)) ε {0, 1}s of the outputs of g1, g2, gs for x. For each f : {0, 1}2 → {0, 1}, we define an f-circuit as a logic circuit where every gate computes f, and investigate computational complexity of the following counting problem: Given an f-circuit C, how many output patterns arise in C? We then provide a dichotomy result on the counting problem: We prove that the problem is solvable in polynomial time if f is PARITY or any degenerate function, while the problem is #P-complete even for constant-depth f-circuits if f is one of the other functions, such as AND, OR, NAND and NOR.

本文言語English
ホスト出版物のタイトルConferences in Research and Practice in Information Technology Series
編集者Anthony Wirth
出版社Australian Computer Society
ページ37-42
ページ数6
ISBN(印刷版)9781921770265
出版ステータスPublished - 2013
イベントComputing: The Australasian Theory Symposium, CATS 2013 - Adelaide, Australia
継続期間: 2013 1 292013 2 1

出版物シリーズ

名前Conferences in Research and Practice in Information Technology Series
141
ISSN(印刷版)1445-1336

Other

OtherComputing: The Australasian Theory Symposium, CATS 2013
国/地域Australia
CityAdelaide
Period13/1/2913/2/1

ASJC Scopus subject areas

  • コンピュータ ネットワークおよび通信
  • コンピュータ サイエンスの応用
  • ハードウェアとアーキテクチャ
  • 情報システム
  • ソフトウェア

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