Part of the Algorithms and Combinatorics book series (AC, volume 27)


The lower-bounds arguments we presented in this book work well for different restricted circuit classes but, so far, have not led to a non-linear lower bound for unrestricted circuits. In this concluding chapter we sketch several general results explaining this failure (the phenomenon of “natural proofs”) as well as showing a possible line of further attacks (the “fusion method”, indirect arguments).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of FrankfurtFrankfurt am MainGermany
  2. 2.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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