Prerona Chatterjee, Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse

For every constant c > 0, we show that there is a family {P_{N,c}} of polynomials whose degree and algebraic circuit complexity are polynomially bounded in the number of variables, and that satisfies the following properties:

* For every family {f_n} of polynomials in VP, where f_n is an n ...
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Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse

Assuming that the Permanent polynomial requires algebraic circuits of exponential size, we show that the class VNP *does not* have efficiently computable equations. In other words, any nonzero polynomial that vanishes on the coefficient vectors of all polynomials in the class VNP requires algebraic circuits of super-polynomial size.

In a ... more >>>