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  Symmetric approximation arguments for monotone lower bounds without sunflowers (1999) [10 citations — 0 self]

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by Christer Berg, Staoean Ulfberg
Comput. Complexity
ftp://ftp.nada.kth.se/pub/documents/Theory/Christer-Berg/approx.ps
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Abstract:

We propose a symmetric version of Razborov's method of approximation to prove lower bounds for monotone circuit complexity. Traditionally, only DNF formulas have been used as approximators, whereas we use both CNF and DNF formulas. As a consequence we no longer need the SunAEower lemma that has been essential for the method of approximation. The new approximation argument corresponds to Haken's recent method for proving lower bounds for monotone circuit complexity (counting bottlenecks) in a natural way. We provide lower bounds for the BMS problem introduced by Haken, Andreev's polynomial problem, and for Clique. The exponential bounds obtained are the same as the previously best known for the respective problems. 1

Citations

120 Lower bounds on the monotone complexity of some boolean functions – Razborov - 1985
115 The monotone circuit complexity of boolean functions – Alon, Boppana - 1987
74 Intersection theorems for system of sets – Erdos, Rado - 1960
41 On a method for obtaining lower bounds for the complexity of individual monotone functions – Andreev - 1985
38 An exponential lower bound for the size of monotone real circuits – Haken, Cook - 1999
30 On the method of approximation – Razborov - 1989
10 The complexity of nite functions – Boppana, Sipser - 1990
9 A note on the bottleneck counting argument – Simon, Tsai - 1997
8 Potential of the approximation method – Amano, Maruoka - 1996
7 A 4n lower bound on the monotone network complexity of a one-output boolean function – Tiekenheinrich - 1984
6 Counting bottlenecks to show monotone P 6= NP – Haken - 1995
5 Finite limits and monotone computations over the reals – Jukna - 1997
3 Lower bounds for resolution and cutting planes proofs and monotone computations – Pudlk - 1997
2 Staoean Ulfberg, and Avi Wigderson. Symmetric approximation for monotone real circuits – Berg - 1996
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