Introduction to finite fields and their applications
Introduction to finite fields and their applications
Matching is as easy as matrix inversion
Combinatorica
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
Interpolation and approximation of sparse multivariate polynomials over GF(2)
SIAM Journal on Computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Designing programs that check their work
Journal of the ACM (JACM)
SIAM Journal on Computing
Reducing randomness via irrational numbers
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Modern computer algebra
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Polynomial Identity Testing for Depth 3 Circuits
Computational Complexity
Hardness-randomness tradeoffs for bounded depth arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Deterministically testing sparse polynomial identities of unbounded degree
Information Processing Letters
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
The ideal membership problem and polynomial identity testing
Information and Computation
The monomial ideal membership problem and polynomial identity testing
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On the relation between polynomial identity testing and finding variable disjoint factors
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits
SIAM Journal on Computing
Blackbox identity testing for bounded top fanin depth-3 circuits: the field doesn't matter
Proceedings of the forty-third annual ACM symposium on Theory of computing
Recent results on polynomial identity testing
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Algebraic independence and blackbox identity testing
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Algorithms for testing monomials in multivariate polynomials
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
An Almost Optimal Rank Bound for Depth-3 Identities
SIAM Journal on Computing
Algebraic independence and blackbox identity testing
Information and Computation
Journal of Combinatorial Optimization
On testing monomials in multivariate polynomials
Theoretical Computer Science
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We give a simple and new randomized primality testing algorithm by reducing primality testing for number n to testing if a specific univariate identity over Zn holds.We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over Zn for any n. The running time of the algorithms is polynomial in the size of arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, for example, the Schwartz--Zippel test [Schwartz 1980; Zippel 1979], Chen--Kao and Lewin--Vadhan tests [Chen and Kao 1997; Lewin and Vadhan 1998].