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New uses for Grothendieck topologies

December 12th, 2005 by PeterMcB

I’ve been saying for a while that the big problems in computer science (eg, P vs NP; a theory of distributed systems; effective GO-playing machines; etc) need radical new methods, and I have suggested algebraic topology as a likely source of ideas. Joel Friedman has just applied some alg-top to boolean complexity, motivated by the P vs. NP problem, in Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity.

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One Response to “New uses for Grothendieck topologies”

  1. Ars Mathematica » Blog Archive » Says:
    December 15th, 2005 at 7:04 am

    [...] In a post below, I mentioned algebraic topology in computer science. A nice application of alg-top is for study of concurrency in distributed systems. For instance, one approach is to consider execution traces of a computational system being represented by time-directed paths through a space, and then to use alg-top methods to ask and answer questions about the structure of this space. [...]

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