Question

Let $B$ be a branching program computing a Boolean function f. Prove that $\mathrm{CC}(f) \leq 3 \cdot \operatorname{size}(B)$.

   Let $B$ be a branching program computing a Boolean function f. Prove that $\mathrm{CC}(f) \leq 3 \cdot \operatorname{size}(B)$.

Communication Complexity and Parallel Computing

Communication Complexity and Parallel Computing

Juraj Hromkovi? 1st Edition

Chapter 5, Problem 4

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Step 1

$\mathrm{CC}(f)$ is the communication complexity of the Boolean function $f$. It measures the minimum number of bits that Alice and Bob need to exchange in order to compute $f$ correctly. $\operatorname{size}(B)$ is the size of the branching program $B$. It Show more…

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Let $B$ be a branching program computing a Boolean function f. Prove that $\mathrm{CC}(f) \leq 3 \cdot \operatorname{size}(B)$.

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