Hierarchies of DLOGTIME-uniform circuits

  • Authors:

  • Chuzo Iwamoto;Naoki Hatayama;Kenichi Morita;Katsunobu Imai;Daisuke Wakamatsu

  • Affiliations:

  • Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan;Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan;Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan;Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan;Murata Machinery, Kyoto, Japan

  • Venue:
  • MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
  • Year:
  • 2004

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Abstract

We present complexity hierarchies on circuits under two DLOGTIME-uniformity conditions. It is shown that there is a language which can be recognized by a family of $U_{\mbox{\tiny E}}$-uniform circuits of depth $d(1+\epsilon)(\log n)^{r_1}$ and size $n^{r_2(1+\epsilon)}$ but not by any family of $U_{\mbox{\tiny E}}$-uniform circuits of depth $d(\log n)^{r_1}$ and size $n^{r_2}$, where ε0, d0, r11, and r2≥1 are arbitrary rational constants. It is also shown that there is a language which can be recognized by a family of $U_{\mbox{\tiny D}}$-uniform circuits of depth (1+o(1))t(n)log z(n) and size (16t(n)+ψ(n)(log z(n))2)(z(n))2 but not by any family of $U_{\mbox{\tiny D}}$-uniform circuits of depth t(n) and size z(n), where ψ(n) is an arbitrary slowly growing function not bounded by O(1).