Matching is as easy as matrix inversion
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A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Journal of the ACM (JACM)
Computational Complexity of Sparse Rational Interpolation
SIAM Journal on Computing
&egr;-discrepancy sets and their application for interpolation of sparse polynomials
Information Processing Letters
SIAM Journal on Computing
On some approximation problems concerning sparse polynomials over finite fields
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
Reducing randomness via irrational numbers
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
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
Primality and Identity Testing via Chinese Remaindering
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic identity testing for multivariate polynomials
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Pseudorandom generators for low degree polynomials
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
Interpolation of depth-3 arithmetic circuits with two multiplication gates
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Polynomial Identity Testing for Depth 3 Circuits
Computational Complexity
Read-once polynomial identity testing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness-randomness tradeoffs for bounded depth arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
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
Deterministic identity testing of depth-4 multilinear circuits with bounded top fan-in
Proceedings of the forty-second ACM symposium on Theory of computing
On the hardness of the noncommutative determinant
Proceedings of the forty-second ACM symposium on Theory of computing
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
Enumeration of the monomials of a polynomial and related complexity classes
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits
SIAM Journal on Computing
Black-box identity testing of depth-4 multilinear circuits
Proceedings of the forty-third annual ACM symposium on Theory of 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
An Almost Optimal Rank Bound for Depth-3 Identities
SIAM Journal on Computing
On obtaining pseudorandomness from error-correcting codes
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
On identity testing of tensors, low-rank recovery and compressed sensing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Reconstruction of depth-4 multilinear circuits with top fan-in 2
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximate verification and enumeration problems
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
Testers and their applications
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On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
Theory of Computing Systems
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We present a randomized polynomial time algorithm to determine if a multivariate polynomial is zero using O(\log mn&dgr;) random bits where n is the number of variables, m is the number of monomials, and &dgr; is the total degree of the unknown polynomial. All other known randomized identity tests (see for example [7, 12, 1]) use &ohgr;(n) random bits even when the polynomial is sparse and has low total degree. In such cases our algorithm has an exponential savings in randomness. In addition, we obtain the first polynomial time algorithm for interpolating sparse polynomials over finite fields of large characteristic. Our approach uses an error correcting code combined with the randomness optimal isolation lemma of [8] and yields a generalized isolation lemma which works with respect to a set of linear forms over a base set.