On the representations of NC and log-space real numbers

Authors:
Fuxiang Yu
Affiliations:
Computer Science Department, Stony Brook University, Stony Brook, New York
Venue:
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Year:
2007

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Abstract

We study the representations of NC and Log-space real numbers in this paper. We show that the classes of the NC and Log-space real numbers under the general left cut representation are among the most expressive representations. On the other hand, although the general left cut representation and the Cauchy function representation have the same expressive power in P, the expressive power of the Cauchy function representation is weaker than that of the general left cut representation in NC if P1 ≠ NC1. In addition, although the expressive power of the standard left cut representation is weaker than that of the Cauchy function representation in P, the expressive powers of these two representations are incomparable in NC if P1 ≠ NC1. Similar results hold in Log-space.