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Upper and Lower Bounds on the Number of Experiments

We first show that an exponential number of experiments are required in the worst case.

Proposition   At least 2n - 1 experiments must be performed in order to identify a gene regulatory network in the worst case.


\begin{proof}Consider a boolean function of $(n-1)$\space variables $f(x_1,x_2,... ...aminations without suffice (we get one output bit per experiment). \end{proof}

Proposition   n2n - 1 experiments always suffice in order to identify a gene regulatory network.


\begin{proof}% latex2html id marker 223 For each node $2^{n - 1}$\space experime... ...\space experiments suffice in order to identify the whole network. \end{proof}

 \begin{theorem} An exponential number of experiments are necessary and sufficient for the identification of a gene regulatory network. \end{theorem}

Peer Itsik
2001-03-04