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 P 1 ≠ NC 1. 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 P 1 ≠ NC 1. Similar results hold in Log-space.
This material is based upon work supported by National Science Foundation under grant No. 0430124.
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Yu, F. (2007). On the Representations of NC and Log-Space Real Numbers. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_32
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DOI: https://doi.org/10.1007/978-3-540-73545-8_32
Publisher Name: Springer, Berlin, Heidelberg
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