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Randomized Polynomial-Time Equivalence Between Determinant and Trace-IMM Equivalence Tests

2020
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International Symposium on Mathematical Foundations of Computer Science
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Equivalence testing for a polynomial family {g_m}_{m ∈ ℕ} over a field 𝔽 is the following problem: Given black-box access to an n-variate polynomial f({𝐱}), where n is the number of variables in g_m for some m ∈ ℕ, check if there exists an A ∈ GL(n,𝔽) such that f({𝐱}) = g_m(A{𝐱}). If yes, then output such an A. The complexity of equivalence testing has been studied for a number of important polynomial families, including the determinant (Det) and the family of iterated matrix multiplication

doi:10.4230/lipics.mfcs.2020.72
dblp:conf/mfcs/MurthyN020
fatcat:zrtouth5vrdlxocsieonwvio4q