Babai, L., Pudl ak, P., R odl, V., and Szemer edi, E. Lower bounds to the complexity of symmetric Boolean functions. Theoret. Comput. Sci. 74, 3 (1990), 313-323.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for threshold functions. For bounded width branching programs, computing any member of a large class of symmetric Boolean functions## n log n log log n) lower bound was obtained in [2] but for this they could not use the help of Ramsey type methods. It was further improved to ## n log n) in [24] and [12] independently, the later again using Ramsey methods. Alon and Maass [12, 13] have several results about lower bounds for the length of branching programs of various symmetric functions, or lower bounds for the time space complexity trado# in a general input oblivious sequential model of ....

L. Babai, P. Pudlak, V. Rodl and E. Szemeredi, Lower bounds to the complexity of symmetric Boolean functions, Theoretical Computer Science 74 (1990), 313--324.

....complexity of explicitly defined Boolean functions. The most powerful technique due to Neciporuk [7] always gives even larger bounds on the formula size and is useless for our purposes. Otherwise there are only bounds of quasilinear size like the bounds of Babai, Pudlak, Rodl, and Szemeredi [1]. They consider symmetric Boolean functions and for these functions the best known upper bounds on the formula size are much larger than their lower bounds on the branching program size. We finish the paper with the observation that the largest trade off between branching program and formula size ....

L. Babai, P. Pudlak, V. Rodl, and E. Szemeredi. Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science, 74:313--323, 1990.

....complexity of explicitly defined Boolean functions. The most powerful technique due to Neciporuk [7] always gives even larger bounds on the formula size and is useless for our purposes. Otherwise there are only bounds of quasilinear size like the bounds of Babai, Pudl ak, Rodl, and Szemer edi [1]. They consider symmetric Boolean functions and for these functions the best known upper bounds on the formula size are much larger than their lower bounds on the branching program size. We finish the paper with the observation that the largest trade off between branching program and formula size ....

L. Babai, P. Pudl'ak, V. Rodl, and E. Szemer'edi. Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science, 74:313 -- 323, 1990.

....O(G) 12 Note this construction for formulas is better than that given in Lipton (1996b) 13 See especially Wegener (1987) pp. 76, 85, 143, 243, 247, 261, 440; Razborov (1991) pp. 50, 51; Boppana and Sipser (1990) pp. 793 797. Note Razborov incorrectly quotes the BP lower bound on MAJORITY (Babai et al. 1990). The upper bound comes from Sinha and Thathachar (1994) The upper bound on formulas for symmetric functions follows directly from the upper bound Wegener gives for MAJORITY. The upper bound on circuits for DISTINCT comes from a simple application of SORT, followed by adjacent comparisons; a ....

L. Babai, P. Pudlak, V. Rodl, and E. Szemeredi. Lower bounds to the complexity of symmetric boolean functions. Theoretical Computer Science, 74:313--323, 1990.

....upper bound for nonsolvable groups. Theorem 1. 3(a) improves on a Omega Gamma n log log n= log log log n) lower bound due to Pudl ak [13] Alon and Maass [1] establish Omega Gamma n log n) lower bounds on program length for L T (g) where g(n) is of the form n ffi ; and Babai, et al. [2] find Omega Gamma n log n) lower bounds for asymptotically almost all threshold functions. Our result in 1.3(b) while smaller than the bounds established in [1] and [2] is the best one known to apply to all nonconstant threshold functions (that is, threshold g(n) where neither g(n) nor n ....

....n log n) lower bounds on program length for L T (g) where g(n) is of the form n ffi ; and Babai, et al. 2] find Omega Gamma n log n) lower bounds for asymptotically almost all threshold functions. Our result in 1. 3(b) while smaller than the bounds established in [1] and [2], is the best one known to apply to all nonconstant threshold functions (that is, threshold g(n) where neither g(n) nor n Gamma g(n) is bounded above by a constant) 4 Theorem 1.4 is an important step in our program to prove that ACC 0 is strictly contained in NC 1 : Of course, what we ....

[Article contains additional citation context not shown here]

L. Babai, P.Pudl`ak, V. Rodl and E. Szemeredi, Lower bounds to the complexity of symmetric boolean functions, Theretical Computer Science 74, 313-324 (1990).

....defined function is still that of order Omega Gamma n 2 = log 2 n) which follows by the method of Neciporuk from 1966 [79] the respective function is contained in P) There are only few other results for general branching programs. Pudlak [89] and Babai, Pudlak, Rodl, and Szemeredi [14] have proven weaker bounds by a different method for certain symmetric functions. Babai, Nisan and Szegedy [13] have applied results on multiparty communication protocols to prove a lower bound for an encoding of the so called generalized inner product function, but also this bound is smaller than ....

L. Babai, P. Pudlak, V. Rodl, and E. Szemeredi. Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science, 74:313 -- 323, 1990.

....whether branching programs are more powerful than the oblivious version. Some known results about branching programs are listed next: Neciporuk proved a strong lower bound for the size of an unrestricted branching program computing a function that lies in NP in [Nec66] Also Babai et al. in [BPRS90] proved a super linear lower bound for the majority function (Pudlak also proves a non trivial bound for majority function in [Pud84] Haken in [Hak85] has shown that the pigeonhole principle requires exponential size resolution proofs (see also [BT88, BP96] Many lower bounds and general ....

L. Babai, P. Pudlak, V. Rodl, and E. Szemeredi. Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science, 74(3):313--323, 1990.

....model which is one of the natural nondeterministic extensions of the branching program model. For the class of non constant threshold functions, Barrington and Straubing [BS91] using algebraic techniques, improved this bound to Omega0 n log log n) Alon and Maass [AM88] and Babai et al. BPRS90] independently proved that any oblivious branching program of width w p n for majority has length Omega0 n log n log w ) Their bounds apply to all but a vanishingly small fraction of symmetric functions and are currently the best known length lower bounds for oblivious branching programs ....

....of symmetric functions, any constant width branching program requires length Omega0 n log n) We will give some 23 intuition on this result in the next subsection. 3.1. 2 Communication Complexity Technique Some of the best known lower bound results on branching programs (including [AM88] and [BPRS90] are based on communication complexity. Informally, communication complexity measures the amount of communication needed to compute the given function when two parties are each given half of the input. We assume that two processors (conveniently named Alice and Bob) with unlimited computational ....

[Article contains additional citation context not shown here]

L'aszl'o Babai, Pavel Pudl'ak, V. Rodl, and Endre Szemer'edi. Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science, 74:313--324, 1990.

....this is of course much weaker than what we would like to prove, the graph leveling structure used by that proof may be relevant to proving the conjecture. Also note that in the nonmonotone case, the best lower bounds for the length of BWBP programs for explicit functions are Omega Gamma n lg n) [6, 8]. 4.1 There is no Monotone Barrington Gadget Our result here states that there is no monotone gadget (of any length or width) like Barrington s gadget composed of four 5 cycles [9] Note this is not an asymptotic result, but rather a statement of impossibility. We need a few definitions to state ....

L. Babai, P. Pudl'ak, V. Rodl, and E. Szemer'edi. Lower bounds to the complexity of symmetric Boolean functions. Theor. Comput. Sci., 74:313--323, 1990.

....for pointing me to previous literature on branching programs. Thanks to my advisor John Hopfield for his support and encouragement. 14 See especially [We] pp. 76, 85, 143, 243, 247, 261, 440; Ra] pp. 50, 51; Bop] pp. 793 797. Note Razborov incorrectly quotes the BP lower bound on MAJORITY [Bab]. The upper bound comes from [Si] The upper bound on formulas for symmetric functions follows directly from the upper bound Wegener gives for MAJORITY. The upper bound on circuits for DISTINCT comes from a simple application of SORT, followed by adjacent comparisions; a better bound may be ....

Babai, L., P. Pudl'ak, V. Rodl, E. Szemeredi. Lower Bounds to the Complexity of Symmetric Boolean Functions. Theoretical Computer Science 74 (1990) 313-323.

....algebraic techniques, improved this bound to Omega Gamma n log log n) It can be easily seen that any constant width branching program can be transformed into an equivalent oblivious branching program with a constant blow up in the length and the width. Alon and Maass [AM88] and Babai et al. BPRS90] independently proved that any oblivious branching program of width w p n for majority has length Omega Gamma n log n log w ) Their bounds are based on a communication complexity argument and imply that for computing all but a vanishingly small fraction of symmetric functions, any ....

.... 2 n) has width exp(n Omega Gamma41 ) For the case of arbitrary branching programs, Pudl ak [Pud84] used a Ramsey theoretic argument to prove an unconditional size lower bound of Omega i n log log n log log log n j for computing most threshold functions (including majority) Babai et al. BPRS90] improved this to an unconditional size lower bound of Omega i n log n log log n j for computing majority. This bound also uses a communication complexity argument and applies to almost all symmetric functions. Razborov [Raz90] and Karchmer and Wigderson [KW93] proved unconditional size ....

[Article contains additional citation context not shown here]

L'aszl'o Babai, Pavel Pudl'ak, V. Rodl, and Endre Szemer'edi. Lower bounds to the complexity of symmetric Boolean functions. Theoretical Computer Science, 74:313-- 324, 1990.

No context found.

Babai, L., Pudl ak, P., R odl, V., and Szemer edi, E. Lower bounds to the complexity of symmetric Boolean functions. Theoret. Comput. Sci. 74, 3 (1990), 313-323.

No context found.

L. Babai, P. Pudlak, V. Rodl, and E. Szemeredi. Lower bounds to the complexity of symmetric boolean functions. Theoretical Computer Science, 74:313-324, 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC