arXiv subjects
Publications and source records attributed to Jeffrey C. Jackson.
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently accepted as convincing, it is inconsistent to deny similar acceptance to the evidence provided for the existence of proofs by certain randomized computations.
We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\tilde{O}(s^{3}/ε+ s^{2}/ε^{2})$, where $s$ is the size of DNF formula and $ε$ is the PAC error accuracy. If $s$ and $1/ε$ are comparable, this gives a modest improvement over a previously known classical query complexity of $\tilde{O}(ns^{2}/ε^{2})$. We also show a lower bound of $Ω(s\log n/n)$ on the query complexity of any quantum PAC algorithm for learning a DNF of size $s$ with $n$ inputs under the uniform distribution.