Power, positive closure, and quotients on convex languages

Hospodár, Michal

doi:10.1016/j.tcs.2021.02.002

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…By Corollary 7, the language L is accepted by an n-state AFA. On the other hand, each singleton set is reachable and co-reachable in the MNFA A which means that every NFA accepting L has at least 2 n + 1 states by [4,Lemma 9].…”

Section: Simulations Of Bfas and Afas By Mnfas Nfas And Dfasmentioning

confidence: 99%

Operations on Boolean and Alternating Finite Automata

Jirásková

2023

Electron. Proc. Theor. Comput. Sci.

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We examine the complexity of basic regular operations on languages represented by Boolean and alternating finite automata. We get tight upper bounds m + n and m + n + 1 for union, intersection, and difference, 2 m + n and 2 m + n + 1 for concatenation, 2 n + n and 2 n + n + 1 for square, m and m + 1 for left quotient, 2 m and 2 m + 1 for right quotient. We also show that in both models, the complexity of complementation and symmetric difference is n and m + n, respectively, while the complexity of star and reversal is 2 n . All our witnesses are described over a unary or binary alphabets, and whenever we use a binary alphabet, it is always optimal.

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Section: Simulations Of Bfas and Afas By Mnfas Nfas And Dfasmentioning

confidence: 99%

Operations on Boolean and Alternating Finite Automata

Jirásková

2023

Electron. Proc. Theor. Comput. Sci.

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“…In this paper, we study arbitrary binary languages (languages over the alphabet E = {0, 1}) that are subword closed: if a word w 1 u 1 w 2 • • • w m u m w m+1 belongs to a language, then the word u 1 • • • u m belongs to this language. Subword-closed languages have attracted the attention of researchers in the field of formal languages for many years [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Decision Trees for Binary Subword-Closed Languages

Moshkov

2023

Entropy

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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.

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