My Favorite Ten Complexity Theorems of the Past Decade

@article{Fortnow1994MyFT,
  title={My Favorite Ten Complexity Theorems of the Past Decade},
  author={Lance Fortnow},
  journal={Electron. Colloquium Comput. Complex.},
  year={1994},
  volume={1}
}
  • 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

References

SHOWING 1-10 OF 114 REFERENCES
The Complexity of Computing the Permanent
  • L. Valiant
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1979
The Complexity of Enumeration and Reliability Problems
  • L. Valiant
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1979
TLDR
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.
Applications of matrix methods to the theory of lower bounds in computational complexity
TLDR
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.
A note on the power of threshold circuits
  • E. Allender
  • Computer Science
    30th Annual Symposium on Foundations of Computer Science
  • 1989
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
Separating the polynomial-time hierarchy by oracles
  • A. Yao
  • Computer Science, Mathematics
  • 1985
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
IP = PSPACE
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
Parity, circuits, and the polynomial-time hierarchy
TLDR
A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
The gap between monotone and non-monotone circuit complexity is exponential
TLDR
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.
Natural proofs
TLDR
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.
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