In the paper, we introduce the concept of monotone rank, and using it as a powerful tool, we obtain several important and strong separation results in computational complexity.

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\item We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to ... more >>>

We show two new direct product results in two different models of communication complexity. Our first result is in the model of one-way public-coin model. Let $f \subseteq X \times Y \times Z $ be a relation and $\epsilon >0$ be a constant. Let $R^{1,pub}_{\epsilon}(f)$ represent the communication complexity of ... more >>>

We initiate a study of input-oblivious proof systems, and present a few preliminary results regarding such systems.
Our results offer a perspective on the intersection of the non-uniform complexity class P/poly with uniform complexity classes such as NP and IP.
In particular, we provide a uniform complexity formulation of the ... more >>>