Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On the method of approximations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The complexity of computing symmetric functions using threshold circuits
Theoretical Computer Science
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
An exponential lower bound for depth 3 arithmetic circuits
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)
An Exact Characterization of Symmetric Functions in qAC0[2]
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Computing Elementary Symmetric Polynomials with a Subpolynomial Number of Multiplications
SIAM Journal on Computing
Testing Polynomials over General Fields
SIAM Journal on Computing
A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra
Testing low-degree polynomials over prime fields
Random Structures & Algorithms
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We show that the set of all functions is equivalent to the set of all symmetric functions (possibly over a larger domain) up to deterministic time complexity. In particular, for any function f, there is an equivalent symmetric function fsym such that f can be computed from fsym and vice-versa (modulo an extra deterministic linear time computation). For f over finite fields, fsym is (necessarily) over an extension field. This reduction is optimal in size of the extension field. For polynomial functions, the degree of fsym is not optimal. We present another reduction that has optimal degree "blowup" but is worse in the other parameters.