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Permanent Does Not Have Succinct Polynomial Size Arithmetic Circuits of Constant Depth
[chapter]
2011
Lecture Notes in Computer Science
We show that over fields of characteristic zero there does not exist a polynomial p(n) and a constant-free succinct arithmetic circuit family {Φn} using division by constants 1 , where Φn has size at most p(n) and depth O(1), such that Φn computes the n × n permanent. A circuit family {Φn} is succinct if there exists a nonuniform Boolean circuit family {Cn} with O(log n) many inputs and size n o(1) such that that Cn can correctly answer direct connection language queries about Φn -succinctness
doi:10.1007/978-3-642-22006-7_61
fatcat:tjfzx3b6sngjzcyhqpmrdwcmqi