Filters








1,981 Hits in 3.1 sec

Lower bounds on threshold and related circuits via communication complexity

V.P. Roychowdhury, A. Orlitsky, Kai-Yeung Siu
1994 IEEE Transactions on Information Theory  
Each of the bounds derived is shown to be tight for some functions and some applications t o threshold-circuit complexity are indicated.  ...  Communication-complexity definitions and arguments are used to derive linear (Q(n)) and almost-linear (Q(n/ log n)) lower bounds on the size of circuits implementing certain functions.  ...  depth-3 threshold-circuit complexity.  ... 
doi:10.1109/18.312169 fatcat:a4ydrluivbhepmjpm4rtolxaqi

Satisfiability and Derandomization for Small Polynomial Threshold Circuits

Valentine Kabanets, Zhenjian Lu, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
This generalizes the result by Chen, Santhanam and Srinivasan (CCC, 2016) who gave a SAT algorithm for constant-depth circuits of super-linear wire complexity with linear threshold function (LTF) gates  ...  We study the problems of exact and (promise) approximate counting for PTF circuits of constant depth. Satisfiability (#SAT ).  ...  Threshold circuits. It is well known that the class of constant-depth polynomial-size TC 0 circuits is equivalent to the class of constant-depth polynomial-size circuits with LTF gates [7] .  ... 
doi:10.4230/lipics.approx-random.2018.46 dblp:conf/approx/KabanetsL18 fatcat:ch4gewg3ybelzjjwutioqml6yq

Page 3865 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
While obtaining lower bounds for constant-depth circuits with threshold gates is an extremely important and much-studied prob- lem, it has proved to be extremely difficult to get very far with the general  ...  Secondly, any depth-2 AC“) circuit can be computed by polynomial-size threshold-MOD?’ circuits.  ... 

Luby--Veličković--Wigderson revisited: Improved correlation bounds and pseudorandom generators for depth-two circuits [article]

Rocco A. Servedio, Li-Yang Tan
2018 arXiv   pre-print
ε-fools these circuits.  ...  The above PRG is actually a special case of a more general PRG which we establish for constant-depth circuits containing multiple SYM or THR gates, including as a special case {SYM,THR}∘AC^0 circuits.  ...  For some sufficiently small absolute constant c > 0, there is a PRG with seed length 2 O( √ log S) + polylog(1/ε) that ε-fools the class of size-S constant-depth circuits that contain 2 √ c log S many  ... 
arXiv:1803.04553v1 fatcat:ynglyw7775fs5ho4mlu5rbrnwy

Luby-Velickovic-Wigderson Revisited: Improved Correlation Bounds and Pseudorandom Generators for Depth-Two Circuits

Rocco A. Servedio, Li-Yang Tan, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
ε-fools these circuits.  ...  The above PRG is actually a special case of a more general PRG which we establish for constant-depth circuits containing multiple SYM or THR gates, including as a special case {SYM, THR} • AC 0 circuits  ...  For some sufficiently small absolute constant c > 0, there is a PRG with seed length 2 O( √ log S) + polylog(1/ε) that ε-fools the class of size-S constant-depth circuits that contain 2 √ c log S many  ... 
doi:10.4230/lipics.approx-random.2018.56 dblp:conf/approx/ServedioT18 fatcat:knjpbzpf3zg2zpel4wrheeaqe4

Bounded Indistinguishability and the Complexity of Recovering Secrets [chapter]

Andrej Bogdanov, Yuval Ishai, Emanuele Viola, Christopher Williamson
2016 Lecture Notes in Computer Science  
circuits of size poly(n).  ...  parties so that any set of fewer than σn parties can learn nothing about the secret, any set of at least ρn parties can reconstruct the secret, and where both the sharing and the reconstruction are done by constant-depth  ...  Emanuele thanks Daniel Wichs for asking whether bounded indistinguishability fools AND, and Mark Bun and Justin Thaler for many discussions about the approximate degree literature.  ... 
doi:10.1007/978-3-662-53015-3_21 fatcat:3whk27geizdgnnjd2ny5dybaz4

Some Limitations of the Sum of Small-Bias Distributions

Chin Ho Lee, Emanuele Viola
2017 Theory of Computing  
We present two approaches to constructing ε-biased distributions D on n bits and functions f : {0, 1} n → {0, 1} such that the XOR of two independent copies (D + D) does not fool f .  ...  Suppose for every δ > 0 there exists a constant d such that NC 2 has AC 0 circuits of size 2 n δ and depth d.  ...  Depth 3 circuits, DNF formulas and AC 0 circuits Proof of Theorem 1.5.  ... 
doi:10.4086/toc.2017.v013a016 dblp:journals/toc/LeeV17 fatcat:cqpqfsv4ezb67mdb6gegnksy3q

On derandomizing algorithms that err extremely rarely

Oded Goldreich, Avi Widgerson
2014 Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14  
We also obtain results for other classes of computational devices including log-space algorithms and Arithmetic circuits.  ...  In relation to the above question, we put forward the following quantified derandomization challenge: For a class of circuits C (e.g., P/poly or AC 0 , AC 0 [2]) and a bounding function B : N → N (e.g.  ...  Constant-depth circuits (AC 0 ).  ... 
doi:10.1145/2591796.2591808 dblp:conf/stoc/GoldreichW14 fatcat:g25g7hytyrfidh4cjipix6owfy

Pseudorandom Generators for Read-Once ACC^0

Dmitry Gavinsky, Shachar Lovett, Srikanth Srinivasan
2012 2012 IEEE 27th Conference on Computational Complexity  
We give an explicit construction of a pseudorandom generator for the class of read-once constant depth circuits with unbounded fan-in AND, OR, NOT and generalized modulo m gates, where m is an arbitrary  ...  fixed constant.  ...  This amounts to constant depth circuits with arbitrary symmetric gates; which is known to also be equivalent to TC 0 , where arbitrary threshold gates are allowed [6] , [7] .  ... 
doi:10.1109/ccc.2012.37 dblp:conf/coco/GavinskyLS12 fatcat:67a6f2di4ncybh3sxhzamp57gy

Polynomial Threshold Functions: Structure, Approximation and Pseudorandomness [article]

Ido Ben-Eliezer, Shachar Lovett, Ariel Yadin
2009 arXiv   pre-print
Our second result relates to constructing pseudorandom generators fooling low-degree polynomial threshold functions.  ...  We prove that any low-degree polynomial threshold function, which can be represented as a function of a small number of linear threshold functions, can also be fooled by k-wise independence.  ...  Later, Braverman [10] proved that polylogarithmic-wise independence fools small constant depth circuits, settling a conjecture of Linial and Nisan [20] .  ... 
arXiv:0911.3473v3 fatcat:7iegsdeyo5ey5nwbx5g6jwjyr4

Shielding circuits with groups

Eric Miles, Emanuele Viola
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
We show how to efficiently compile any given circuit C into a leakage-resilient circuit C such that any function on the wires of C that leaks information during a computation C(x) yields advantage in computing  ...  This includes communication protocols, and AC 0 circuits augmented with few arbitrary symmetric gates.  ...  AC 0 with symmetric gates Recall that in §3.4, it was shown that (A 5 ) t t −Ω(log t) -fools the class of unbounded-fan-in constant-depth circuits that contain t O(log t) And/Or/Not gates and O(log 2 t  ... 
doi:10.1145/2488608.2488640 dblp:conf/stoc/MilesV13 fatcat:zohseoo4yzdyxgksrycfbxeca4

Nonuniform Kolmogorov extractors [article]

Marius Zimand
2012 arXiv   pre-print
precisely, as instantiations of more general results, we show that while O(1) amount of advice regarding the source is not enough for extracting a string with randomness rate 1 from a source string with constant  ...  Pseudo-random generator fooling bounded-size constant-depth circuits The derandomization in the proof of Theorem 4.6 is done using the Nisan-Wigderson pseudo-random generator that "fools" constant-depth  ...  Therefore, we can use the Nisan-Wigderson ( [NW94] ) pseudorandom generator NW-gen that fools bounded-size constant-depth circuits and has seeds of size polylogaritmic in the size of the output.  ... 
arXiv:1204.6696v1 fatcat:swfpfse3ungrbi57u7vnshyh5a

Fine-Grained Cryptography [chapter]

Akshay Degwekar, Vinod Vaikuntanathan, Prashant Nalini Vasudevan
2016 Lecture Notes in Computer Science  
secure against adversaries with an a-priori bounded polynomial amount of resources (time, space or parallel-time), where the honest algorithms use less resources than the adversaries they are designed to fool  ...  Previously, one-way permutations and pseudo-random generators (with linear stretch) computable in AC 0 and secure against AC 0 circuits were known from the works of Håstad and Braverman.  ...  of polylog thresholds by constant-depth circuits.  ... 
doi:10.1007/978-3-662-53015-3_19 fatcat:ueuecgreavgr3koy6pdlwfwps4

Pseudo-Derandomizing Learning and Approximation

Igor Carboni Oliveira, Rahul Santhanam, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
BPE) requires large Boolean circuits.  ...  Finally, we investigate the notion of approximate canonization of Boolean circuits.  ...  If there is a family of quick pseudorandom generators G m : {0, 1} (m) → {0, 1} m that ε-fool depth-e size-m C-circuits, for C f has depth ≤ d and size ≤ s(n), and D n is an oracle circuit of depth ≤  ... 
doi:10.4230/lipics.approx-random.2018.55 dblp:conf/approx/OliveiraS18 fatcat:gjphuxvvubakxevkekyacqxryq

Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates [article]

Alexander S. Kulikov, Vladimir V. Podolskii
2016 arXiv   pre-print
For depth 3 circuits we show that a circuit with k= O(n^2/3) can compute MAJ_n correctly on all inputs.  ...  We study the following computational problem: for which values of k, the majority of n bits MAJ_n can be computed with a depth two formula whose each gate computes a majority function of at most k bits  ...  Acknowledgments We would like to thank the participants of Low-Depth Complexity Workshop (St. Petersburg, Russia, May 21-25, 2016) for many helpful discussions.  ... 
arXiv:1610.02686v1 fatcat:74xhlc3drncynhzp4v7nnitiry
« Previous Showing results 1 — 15 out of 1,981 results