Perceptrons: expanded edition
Journal of the ACM (JACM)
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Randomized algorithms
On the learnability of Zn-DNF formulas (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Primality and identity testing via Chinese remaindering
Journal of the ACM (JACM)
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Deterministic polynomial identity testing in non-commutative models
Computational Complexity
Improved algorithms for path, matching, and packing problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster Algebraic Algorithms for Path and Packing Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Finding paths of length k in O∗(2k) time
Information Processing Letters
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The complexity of testing monomials in multivariate polynomials
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Algorithms for testing monomials in multivariate polynomials
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
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This paper presents a summary of our initial work on developing a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum-product expansion. The complexity aspects of this problem and its variants are investigated with two objectives. One is to understand how this problem relates to critical problems in complexity, and if so to what extent. The other is to exploit possibilities of applying algebraic properties of polynomials to the study of those problems. A series of results about @P@S@P and @P@S polynomials is obtained in this paper, laying a basis for further study along this line. Several randomized and deterministic algorithms are devised for testing multilinear monomials or p-monomials in certain respective types of polynomials, where p is prime.