dc.contributor.author Moshkov, Mikhail dc.date.accessioned 2022-01-12T12:36:44Z dc.date.available 2022-01-12T12:36:44Z dc.date.issued 2022-01-05 dc.identifier.uri http://hdl.handle.net/10754/674928 dc.description.abstract In 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.sponsorship Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST) dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2201.01493.pdf dc.rights Archived with thanks to arXiv dc.subject subword-closed language dc.subject recognition problem dc.subject membership problem dc.subject deterministic decision tree dc.subject nondeterministic decision tree dc.title Decision trees for binary subword-closed languages dc.type Preprint dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.identifier.arxivid 2201.01493 kaust.person Moshkov, Mikhail refterms.dateFOA 2022-01-12T12:39:49Z
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