Ingo Wegener, Philipp Woelfel

It is well known that the hardest bit of integer multiplication is the middle bit, i.e. MUL_{n-1,n}.

This paper contains several new results on its complexity.

First, the size s of randomized read-k branching programs, or, equivalently, its space (log s) is investigated.

A randomized algorithm for MUL_{n-1,n} with k=O(log ...
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Vaibhav Krishan

We prove that all functions that have low degree torus polynomials approximating them with small error also have $MidBit^+$ circuits computing them. This serves as a partial converse to the result that all $ACC$ functions have low degree torus polynomials approximating them with small error, by Bhrushundi, Hosseini, Lovett and ... more >>>

Vaibhav Krishan

We give a conversion from non-classical polynomials to $\mathit{MidBit}^+$ circuits and vice-versa. This conversion, along with previously known results, shows that torus polynomials, non-classical polynomials and $\mathit{MidBit}^+$ circuits can all be converted to each other. Therefore lower bounds against any of these models lead to lower bounds against all three ... more >>>