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On the Decidability of Membership in Matrix-exponential Semigroups

2019
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Journal of the ACM
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We consider the decidability of the membership problem for matrix-exponential semigroups: given k ∈ N and square matrices A 1 , . . . , A k , C, all of the same dimension and with real algebraic entries, decide whether C is contained in the semigroup generated by the matrix exponentials exp(A i t), where i ∈ {1, . . . , k} and t ≥ 0. This problem can be seen as a continuous analog of Babai et al.'s and Cai et al.'s problem of solving multiplicative matrix equations, and has applications to

doi:10.1145/3286487
fatcat:7p4umebcjjc6dntci53ys5dwbe