Type
ArticleAuthors
Moshkov, Mikhail
KAUST Department
Applied Mathematics and Computational Science ProgramComputational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Date
2023-02-14Permanent link to this record
http://hdl.handle.net/10754/674928
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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 the decision trees solving the recognition and the membership problems deterministically and nondeterministically. In the case of the recognition problem, for a given word from L(n), we should recognize it using queries, each of which, for some i∈{1,…,n}, returns the ith letter of the word. In the case of the 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 the 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 the decision trees is either bounded from above by a constant or grows linearly. We study the joint behavior of the minimum depths of the considered four types of decision trees and describe five complexity classes of binary subword-closed languages.Citation
Moshkov, M. (2023). Decision Trees for Binary Subword-Closed Languages. Entropy, 25(2), 349. https://doi.org/10.3390/e25020349Sponsors
Research funded by the King Abdullah University of Science and Technology.Publisher
MDPI AGJournal
EntropyarXiv
2201.01493Additional Links
https://www.mdpi.com/1099-4300/25/2/349ae974a485f413a2113503eed53cd6c53
10.3390/e25020349
Scopus Count
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