Affiliation:
1. Computer, Electrical and Mathematical Sciences & Engineering Division and Computational Bioscience Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
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 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.
Funder
King Abdullah University of Science and Technology
Subject
General Physics and Astronomy
Reference17 articles.
1. Deciding Atomicity of Subword-Closed Languages;Diekert;Lecture Notes in Computer Science, Proceedings of the Developments in Language Theory-26th International Conference, DLT 2022, Tampa, FL, USA, 9–13 May 2022, Proceedings,2022
2. Quotient Complexity of Closed Languages;Brzozowski;Theory Comput. Syst.,2014
3. On Free Monoids Partially Ordered by Embedding;Haines;J. Comb. Theory,1969
4. Power, positive closure, and quotients on convex languages;Theor. Comput. Sci.,2021
5. On the State Complexity of Scattered Substrings and Superstrings;Okhotin;Fundam. Inform.,2010
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