Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > KEYWORD > DUAL POLYNOMIALS:
Reports tagged with dual polynomials:
TR17-062 | 9th April 2017
Arkadev Chattopadhyay, Nikhil Mande

Dual polynomials and communication complexity of XOR functions

We show a new duality between the polynomial margin complexity of $f$ and the discrepancy of the function $f \circ$ XOR, called an XOR function. Using this duality,
we develop polynomial based techniques for understanding the bounded error (BPP) and the weakly-unbounded error (PP) communication complexities of XOR functions. ... more >>>


TR17-169 | 24th October 2017
Mark Bun, Robin Kothari, Justin Thaler

The Polynomial Method Strikes Back: Tight Quantum Query Bounds via Dual Polynomials

The approximate degree of a Boolean function $f$ is the least degree of a real polynomial that approximates $f$ pointwise to error at most $1/3$. The approximate degree of $f$ is known to be a lower bound on the quantum query complexity of $f$ (Beals et al., FOCS 1998 and ... more >>>




ISSN 1433-8092 | Imprint