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9
votes
Accepted
Computational complexity in quantitative finance
The question you begin with relates to predicting the stock market, but you seem to have broader concerns. I'll attempt to tackle your meta-question; apologies in advance for my sweeping generalizati …
12
votes
Uses of algebraic structures in theoretical computer science
Here are two applications from a different part of TCS.
Semirings are used for modelling annotations in databases (especially those needed for provenance), and often also for the valuation structures …
6
votes
Research problems in communication complexity
Razborov's 2011 introductory survey lists four open problems, two of which are also in the KN textbook:
(KN 2.10) Is it true that $D(f) \le O(\log \chi(f))$? … As is hinted at by Razborov's survey, there are open questions about the quantum communication setting; this area is not covered by the 1997 textbook. …
10
votes
What hierarchies and/or hierarchy theorems do you know?
Another strict hierarchy: branching programs which only test each bit a limited number of times. The more tests are allowed, the larger the class of branching programs.
Usually the branching programs …