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On the decidability of membership in matrix-exponential semigroups

Abstract:

We consider the decidability of the membership problem for matrix-exponential semigroups: given k ∈ N and square matrices A1, . . . ,Ak,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(Ait), 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 reachabili...

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Publication status:
Accepted
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1145/3286487

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Computer Science
Oxford college:
St Johns College
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Computer Science
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Computer Science
Role:
Author
Publisher:
Association for Computing Machinery Publisher's website
Volume:
66
Issue:
2
Pages:
Article: 15
Publication date:
2019-05-29
Acceptance date:
2019-02-01
DOI:
ISSN:
1535-9921
Pubs id:
pubs:983520
URN:
uri:21174833-b044-4dde-80ce-d742c1944d81
UUID:
uuid:21174833-b044-4dde-80ce-d742c1944d81
Local pid:
pubs:983520

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