We show an exponential gap between communication complexity and information complexity for boolean functions, by giving an explicit example of a partial function with information complexity $\leq O(k)$, and distributional communication complexity $\geq 2^k$. This shows that a communication protocol for a partial boolean function cannot always be compressed to ... more >>>

A classical bound in Information Theory asserts that small $L_1$-distance between probability distributions implies small difference in Shannon entropy, but the converse need not be true. We show that if a probability distribution on $\{0,1\}^n$ has small-bias, then the converse holds for its weight distribution in the proximity of the ... more >>>

We give a $O^*(k^{O(k)})$ time isomorphism testing algorithm for graphs of eigenvalue multiplicity bounded by $k$ which improves on the previous
best running time bound of $O^*(2^{O(k^2/\log
k)})$.

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