Michael Luby, Boban Velickovic, and Avi Wigderson. Deterministic approximate counting of depth-2 circuits. In Proceedings of the 2nd ISTCS, pages 18--24, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[NW94] construct a pseudorandom generator that fools constant depth circuits and that has poly logarithmic seed length. As a consequence, they achieve n (log n) O(1) time algorithms for the counting and satisfiability problems for constant depth circuits. Luby, Velickovic and Wigderson [LVW93] optimize the constructions of Nisan and Wigderson [Nis91, NW94] to the case of depth 2 circuits, thus solving the counting and satisfiability problem in time n O( log n) for general CNF and DNF. Luby and Velickovic [LV91] show how to reduce arbitrary CNF and DNF to formula in a simplified ....

Michael Luby, Boban Velickovic, and Avi Wigderson. Deterministic approximate counting of depth-2 circuits. In Proceedings of the 2nd ISTCS, pages 18--24, 1993.

....will give two examples. Our first application is to the deterministic DNF approximate counting problem. Given a DNF formula F of n variables and m terms, we want to estimate its volume, defined as vol(F ) P x2f0;1g n [F (x) 1] within an additive error ffl. Luby, Velickovi c, and Wigderson [9], following the work of Nisan [10] and Nisan and Wigderson [11] gave a deterministic 2 O(log 4 nm ffl ) time algorithm. Luby and Velickovi c [8] gave a deterministic 2 (log m log n ffl ) 1 ffl ) 2 O( p log log m ffl ) time algorithm, which is good when a large error ffl is ....

....deterministic algorithms with running times 2 O( log mn ffl ) log 3 d log m ffl ) and 2 (log m log n ffl ) log 1 ffl ) 2 O( p log(d log m ffl ) respectively. Note that d is at most m, so our first algorithm is never worse than that of Luby, Velickovi c, and Wigderson [9], and is particularly good when d is small and ffl is large. Our second algorithm is better than that of Luby and Velickovi c [8] when d 2 O(log 2 1 ffl ) and is better than our first algorithm when d 2 O( log log m ffl ) 2 ) Our second application is to dimensions of partially ....

[Article contains additional citation context not shown here]

M. Luby, B. Velickovi'c, and A. Wigderson, Deterministic approximate counting of depth-2 circuits, In Proceedings of the Second Israeli Symposium on Theory of Computing and Systems, 1993.

....for any problem in RP in subexponential time 2 (log n) d for some integer d 1. Constructions of deterministic approximation algorithms for specific problems in RP that do not rely on unproved conjectures, such as the existence of pseudorandom generators, have also achieved subexponential time [12, 22]. Thus far, deterministicapproximation algorithms require substantially increased run time, in comparison to a randomized approximation algorithm for the same problem. Deterministic algorithms, however, have two significant advantages: 1) they do not require random bits, and (2) they do not fail ....

M. Luby, B. Velickovic, and A. Wigderson. Deterministic approximate counting of depth-2 circuits. In Proceedings of the Second Israeli Symposium on Theory of Commputing and Systems, 1993.

....Yao82, GKL88, ILL89, Has90, NW88, BFNW] The unconditional results use no unproven assumption, and typically demonstrate that weaker computational models can be fooled by pseudorandom generators. To this class of results belong the pseudorandom generators for various constant depth circuits [AW85, Nis91, LVW93] and for space bounded Turing machines [BNS89, Nis92, NZ93] Our paper adds a significant number of computational models for which such unconditional results can be proved. We present a new construction of a pseudorandom generator which fools every computational model which can be described as a ....

....from the image of the generator accepted by C will do. This will take deterministic time 2 m Time(G) where Time(G) is the complexity of evaluating G. This approach was used to approximately count the number of accepted inputs to constant depth circuits [Nis91] and to GF (2) polynomials in [LVW93]. Since our generators are efficient (computable in polynomial time) the two theorems below add nontrivial algorithms for this approximate counting problem for two other circuit classes: read once formula and planar circuits. Moreover, both results hold for any choice of finite basis for the ....

M. Luby, B. Velickovic, A. Wigderson. Deterministic Approximate Counting of Depth--2 Circuits. In Proc. of the 2nd ISTCS (Israeli Symposium on Theoretical Computer Science), pp. 18--24, 1993.

....[BM82, Yao82, GKL88, ILL89, Has90, NW88, BFNW] The unconditional results use no unproven assumption, and typically demonstrate that weaker computational models can be fooled by pseudorandom generators. To this class of results belong the pseudorandom generators for various constant depth circuits [AW85, Nis91, LVW93] and for space bounded Turing machines [BNS89, Nis92, NZ93] Our paper adds a significant number of computational models for which such unconditional results can be proved. We present a new construction of a pseudorandom generator which fools every computational model which can be described as a ....

....from the image of the generator accepted by C will do. This will take deterministic time 2 m Time(G) where Time(G) is the complexity of evaluating G. This approach was used to approximately count the number of accepted inputs to constant depth circuits [Nis91] and to GF (2) polynomials in [LVW93]. Since our generators are efficient (computable in polynomial time) the two theorems below add nontrivial algorithms for this approximate counting problem for two other circuit classes: read once formula and planar circuits. Moreover, both results hold for any choice of finite basis for the ....

M. Luby, B. Velickovic, A. Wigderson. Deterministic Approximate Counting of Depth--2 Circuits. In Proc. of the 2nd ISTCS (Israeli Symposium on Theoretical Computer Science), pp. 18--24, 1993.

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