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dc.contributor.authorMoshkov, Mikhail
dc.date.accessioned2022-01-12T12:36:44Z
dc.date.available2022-01-12T12:36:44Z
dc.date.issued2022-01-05
dc.identifier.urihttp://hdl.handle.net/10754/674928
dc.description.abstractIn this paper, we study arbitrary subword-closed languages over the alphabet $\{0,1\}$ (binary subword-closed languages). For the set of words $L(n)$ of the length $n$ belonging to a binary subword-closed language $L$, we investigate the depth of decision trees solving the recognition and the membership problems deterministically and nondeterministically. In the case of recognition problem, for a given word from $L(n)$, we should recognize it using queries each of which, for some $i\in \{1,\ldots ,n\}$, returns the $i$th letter of the word. In the case of membership problem, for a given word over the alphabet $\{0,1\}$ of the length $n$, we should recognize if it belongs to the set $L(n)$ using the same queries. With the growth of $n$, the minimum depth of decision trees solving the problem of recognition deterministically is either bounded from above by a constant, or grows as a logarithm, or linearly. For other types of trees and problems (decision trees solving the problem of recognition nondeterministically, and decision trees solving the membership problem deterministically and nondeterministically), with the growth of $n$, the minimum depth of decision trees is either bounded from above by a constant or grows linearly. We study joint behavior of minimum depths of the considered four types of decision trees and describe five complexity classes of binary subword-closed languages.
dc.description.sponsorshipResearch reported in this publication was supported by King Abdullah University of Science and Technology (KAUST)
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2201.01493.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectsubword-closed language
dc.subjectrecognition problem
dc.subjectmembership problem
dc.subjectdeterministic decision tree
dc.subjectnondeterministic decision tree
dc.titleDecision trees for binary subword-closed languages
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.identifier.arxivid2201.01493
kaust.personMoshkov, Mikhail
refterms.dateFOA2022-01-12T12:39:49Z


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