My Favorite Ten Complexity Theorems of the Past Decade

  title={My Favorite Ten Complexity Theorems of the Past Decade},
  author={Lance Fortnow},
  journal={Electron. Colloquium Comput. Complex.},
  • L. Fortnow
  • Published 15 December 1994
  • Mathematics
  • Electron. Colloquium Comput. Complex.
We review the past ten years in computational complexity theory by focusing on ten theorems that the author enjoyed the most. We use each of the theorems as a springboard to discuss work done in various areas of complexity theory. 
2 Citations
Relaxation in constraint satisfaction problems
This thesis deals with some aspects of the physics of disordered systems. The thesis consists of two papers and an introductory part. The introduction briefly describes the theory of coarsening for
A Random Walk in Statistical Physics
This thesis deals with some aspects of the physics of disordered systems. It consists of four papers and an introductory part. An introduction, suitable for physicists, to theoretical computer


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For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.
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Some criteria for obtaining lower bounds for the formula size of Boolean functions are presented and the boundnΩ(logn) for the function “MINIMUM COVER” is obtained using methods considerably simpler than all previously known.
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  • Computer Science
    30th Annual Symposium on Foundations of Computer Science
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The author presents a very simple proof of the fact that any language accepted by polynomial-size depth-k unbounded-fan-in circuits of AND and OR gates is accepted by depth-three threshold circuits
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  • Computer Science, Mathematics
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We present exponential lower bounds on the size of depth-k Boolean circuits for computing certain functions. These results imply that there exists an oracle set A such that, relative to A, all the
In this paper, it is proven that when both randomization and interaction are allowed, the proofs that can be verified in polynomial time are exactly those proofs that can be generated with polynomial
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The gap between monotone and non-monotone circuit complexity is exponential
The proof is immediate by combining the Alon—Boppana version of another argument of Razborov with results of Grötschel—Lovász—Schrijver on the Lovász — capacity of a graph.
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Every formal complexity measure which can prove super-polynomial lower bounds for a single function, can do so for almost all functions, which is one of the key requirements to a natural proof in the authors' sense.