Deterministic simulation in LOGSPACE
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Better expanders and superconcentrators
Journal of Algorithms
Expanders obtained from affine transformations
Combinatorica - Theory of Computing
Explicit construction of linear sized tolerant networks
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
On read-once vs. multiple access to randomness in logspace
Theoretical Computer Science - Special issue on structure in complexity theory
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
Journal of Computer and System Sciences
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Computational Complexity
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Journal of Computer and System Sciences
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Tiny families of functions with random properties: a quality-size trade-off for hashing
Proceedings of the workshop on Randomized algorithms and computation
Efficient approximation of product distributions
Random Structures & Algorithms
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
An O(log(n)4/3) space algorithm for (s, t) connectivity in undirected graphs
Journal of the ACM (JACM)
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
On the Derandomization of Space-Bounded Computations
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
On the Derandomization of Constant Depth Circuits
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Discrepancy sets and pseudorandom generators for combinatorial rectangles
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Pseudorandom generators for low degree polynomials
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Pseudorandom walks on regular digraphs and the RL vs. L problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Random Structures & Algorithms
Pseudorandom Bits for Constant-Depth Circuits with Few Arbitrary Symmetric Gates
SIAM Journal on Computing
Undirected connectivity in log-space
Journal of the ACM (JACM)
Undirected connectivity in O(log/sup 1.5/n) space
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Randomness-efficient oblivious sampling
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
A Simple Proof of Bazzi’s Theorem
ACM Transactions on Computation Theory (TOCT)
Pseudorandom Bit Generators That Fool Modular Sums
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Small-Bias Spaces for Group Products
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Polylogarithmic Independence Can Fool DNF Formulas
SIAM Journal on Computing
Polylogarithmic independence fools AC0 circuits
Journal of the ACM (JACM)
Pseudorandom generators for polynomial threshold functions
Proceedings of the forty-second ACM symposium on Theory of computing
An invariance principle for polytopes
Proceedings of the forty-second ACM symposium on Theory of computing
Fooling Functions of Halfspaces under Product Distributions
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Improved pseudorandom generators for depth 2 circuits
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Bounded Independence Fools Degree-2 Threshold Functions
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
The Coin Problem and Pseudorandomness for Branching Programs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Pseudorandom Generators for Regular Branching Programs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Pseudorandom generators for combinatorial shapes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Pseudorandom generators for group products: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
Pseudorandomness for Permutation and Regular Branching Programs
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Pseudorandom Generators for Combinatorial Checkerboards
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
Pseudorandomness for Read-Once Formulas
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Linear advice for randomized logarithmic space
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Derandomized squaring of graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Pseudorandomness
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We define a combinatorial checkerboard to be a function f : {1, . . . , m} d 驴 {1,驴1} of the form $${f(u_1,\ldots,u_d)=\prod_{i=1}^df_i(u_i)}$$ for some functions f i : {1, . . . , m} 驴 {1,驴1}. This is a variant of combinatorial rectangles, which can be defined in the same way but using {0, 1} instead of {1,驴1}. We consider the problem of constructing explicit pseudorandom generators for combinatorial checkerboards. This is a generalization of small-bias generators, which correspond to the case m = 2. We construct a pseudorandom generator that $${\epsilon}$$ -fools all combinatorial checkerboards with seed length $${O\bigl(\log m+\log d\cdot\log\log d+\log^{3/2} \frac{1}{\epsilon}\bigr)}$$ . Previous work by Impagliazzo, Nisan, and Wigderson implies a pseudorandom generator with seed length $${O\bigl(\log m+\log^2d+\log d\cdot\log\frac{1}{\epsilon}\bigr)}$$ . Our seed length is better except when $${\frac{1}{\epsilon}\geq d^{\omega(\log d)}}$$ .