A Casual Tour Around a Circuit Complexity Bound · HackerPapers discussions

A Casual Tour Around a Circuit Complexity Bound — mentioned by ccppurcell

Thu, 20 Jun 2024 06:09:49 GMT

The next step book wise is Arora and Barak, Computational Complexity: a modern approach. Of course that book is already out of date. The breakthrough that comes to mind is Ryan Williams' circuit lower bounds. He wrote a nice explanation of the proof here: https://arxiv.org/abs/1111.1261 He defines all the key terms pretty well but probably requires a bit of "maturity" to understand. There are also various breakthroughs to do with interactive proofs.

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A Casual Tour Around a Circuit Complexity Bound — mentioned by j2kun

Wed, 04 Jan 2017 06:42:20 GMT

There is a large, emerging body of research in which one proves the impossibility of solving problem A by finding an algorithm for solving a different problem B. For Mulmuley et al. (it's been a while since I was in the thick of this) it's finding an algorithm for computing a particular decomposition of a representation[1] having to do with determinants and permanents. This essentially shows the matrix permanent formula can't be written as a determinant of a small matrix (of smaller formulas of the variables), which is the "algebraic" analogue of P vs NP, and which Mulmuley et al. believe…

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A Casual Tour Around a Circuit Complexity Bound — mentioned by j2kun

Thu, 01 May 2014 13:16:10 GMT

I recently read a paper of Ryan Williams explaining how one discovers the biggest breakthrough in circuit complexity in the last decade. http://arxiv.org/abs/1111.1261

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