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The Complexity of Divisibility

dc.creatorBausch, Johannes
dc.creatorCubitt, Toby
dc.date.accessioned2018-11-24T23:18:48Z
dc.date.available2016-04-08T14:40:33Z
dc.date.available2018-11-24T23:18:48Z
dc.date.issued2016-04-08
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/254895
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3343
dc.description.abstractWe address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.
dc.languageen
dc.publisherElsevier
dc.publisherLinear Algebra and its Applications
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightsAttribution 4.0 International
dc.subjectstochastic matrices
dc.subjectcptp maps
dc.subjectprobability distributions
dc.subjectdivisibility
dc.subjectdecomposability
dc.subjectcomplexity theory
dc.titleThe Complexity of Divisibility
dc.typeArticle


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