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• W2978323306 abstract "We consider the problem of computing succinct encodings of lists of generators for invariant rings for group actions. Mulmuley conjectured that there are always polynomial sized such encodings for invariant rings of $SL_n(C)$-representations. We provide simple examples that disprove this conjecture (under standard complexity assumptions). We develop a general framework, denoted emph{algebraic circuit search problems}, that captures many important problems in algebraic complexity and computational invariant theory. This framework encompasses various proof systems in proof complexity and some of the central problems in invariant theory as exposed by the Geometric Complexity Theory (GCT) program, including the aforementioned problem of computing succinct encodings for generators for invariant rings." @default.
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• W2978323306 date "2019-10-02" @default.
• W2978323306 modified "2023-09-27" @default.
• W2978323306 title "Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings" @default.
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