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This is pure intuition, but from reading this I get the sense that this conjecture is some generalization of a fixed point theorem?
by ssalka 7y ago
This is pure intuition, but from reading this I get the sense that this conjecture is some generalization of a fixed point theorem?
- vecter 7y agoCan you explain your intuition for how this relates to fixed points?
- zeckalpha 7y agoA Boolean array is isomorphic to a fixed point number. The article discusses non-fixed equivalents, though, both a contextual variable length and a quantum super position length bit array.
- vecter 7y agoI don't understand what you said, but I and (I assume) GP were talking about https://en.wikipedia.org/wiki/Fixed_point_(mathematics) https://en.wikipedia.org/wiki/Fixed_point_(mathematics)
- zeckalpha 7y agoFrom the article: > Other measures involve looking for the simplest way to write the Boolean function as a mathematical expression, or calculating how many answers the banker would have to show a boss to prove they had made the right loan decision. There’s even a quantum physics version of query complexity in which the banker can ask a “superposition” of several questions at the same time. Figuring out how this measure relates to other complexity measures has helped researchers understand the limitations of quantum algorithms. I assumed you were discussing https://en.wikipedia.org/wiki/Fixed-point_arithmetic https://en.wikipedia.org/wiki/Fixed-point_arithmetic which is a potential application domain for this research.
- vecter 7y agoI'm not seeing the connection between this research and fixed-point arithmetic.
- eob123 7y agoI don’t exactly follow the above either, but I believe fixed point is meant in a different sense here, as in a function f(x) such there a point x0 exists where x0=f(x0). https://en.m.wikipedia.org/wiki/Fixed-point_theorem https://en.m.wikipedia.org/wiki/Fixed-point_theorem
- mschoene 7y agoWell - the eigenvalues (of the adjacency matrix), which are used in the proof, correspond to eigenvectors. Which are fixpoints (or at least fixed linear subspaces) of the corresponding linear function. So there is some "lexical" connection. But apart from that I'm not sure that I share your sense that this is "some generalization of a fixed point theorem". Can you give us more insight?