On symmetric algorithms for bilinear forms over finite fields
Journal of Algorithms
Finding irreducible polynomials over finite fields
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Fredman-Kolmo´s bounds and information theory
SIAM Journal on Algebraic and Discrete Methods
New bounds for perfect hashing via information theory
European Journal of Combinatorics
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Journal of Combinatorial Theory Series A
On finding primitive roots in finite fields
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
Optimal linear perfect hash families
Journal of Combinatorial Theory Series A
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Some new bounds for cover-free families
Journal of Combinatorial Theory Series A
Explicit constructions of perfect hash families from algebraic curves over finite fields
Journal of Combinatorial Theory Series A
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Combinatorics, Probability and Computing
Pseudorandom generators for low degree polynomials
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Explicit constructions of separating hash families from algebraic curves over finite fields
Designs, Codes and Cryptography
Topics in Geometry, Coding Theory and Cryptography (Algebra and Applications)
Topics in Geometry, Coding Theory and Cryptography (Algebra and Applications)
On generalized separating hash families
Journal of Combinatorial Theory Series A
A bound on the size of separating hash families
Journal of Combinatorial Theory Series A
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
Improved Polynomial Identity Testing for Read-Once Formulas
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Efficiently decodable non-adaptive group testing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Bounds for separating hash families
Journal of Combinatorial Theory Series A
Finite Fields: Theory and Computation The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Nonrandom binary superimposed codes
IEEE Transactions on Information Theory
Vector sets for exhaustive testing of logic circuits
IEEE Transactions on Information Theory
Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
IEEE Transactions on Information Theory - Part 2
Curves with Many Points and Multiplication Complexity in Any Extension of Fq
Finite Fields and Their Applications
Explicit Nonadaptive Combinatorial Group Testing Schemes
IEEE Transactions on Information Theory
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We develop a new notion called tester of a class M of functions f : A → C that maps the elements α ∈ A in the domain A of the function to a finite number (the size of the tester) of elements b1,...,bt in a smaller sub-domain B ⊂ A where the property f(α) ≠ 0 is preserved for all f ∈ M. I.e., for all f ∈ M and - ∈ A if f(α) ≠ 0 then f(bi) ≠ 0 for some i. We use tools from elementary algebra and algebraic function fields to construct testers of almost optimal size in deterministic polynomial time in the size of the tester. We then apply testers to deterministically construct new set of objects with some combinatorial and algebraic properties that can be used to derandomize some algorithms. We show that those new constructions are almost optimal and for many of them meet the union bound of the problem. Constructions include, d-restriction problems, perfect hash, universal sets, cover-free families, separating hash functions, polynomial restriction problems, black box polynomial identity testing for polynomials and circuits over small fields and hitting sets.