Branching Frequency and Markov Entropy of Repetition-Free Languages

Petrova, Elena A.; Shur, Arseny M.

doi:10.1007/978-3-030-81508-0_27

Cited by 2 publications

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“…The search starts with u = λ, ml = 0, count = 1. A variant of this search algorithm was used in [11] to numerically estimate the entropy of some α-free and α-A-free languages.…”

Section: Algorithmsmentioning

confidence: 99%

“…) is supposed to be infinite, it is interesting to estimate its growth. Based on the technique described in [11], we estimate the number of words of length n in AF(5, 3…”

Section: Alphabets With 2 3 4 and 5 Lettersmentioning

confidence: 99%

“…), indicated by Conjecture 1 as infinite. To detect Abelian powers, we used Algorithm 3 for the quaternary alphabet; for the ternary and binary alphabets, we worked with the reversals of AF(3, 2 + ), and AF(2,11 …”

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confidence: 99%

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Abelian Repetition Threshold Revisited

Petrova

Shur

2022

Lecture Notes in Computer Science

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Abelian repetition threshold ART(k) is the number separating fractional Abelian powers which are avoidable and unavoidable over the k-letter alphabet. The exact values of ART(k) are unknown; the lower bounds were proved in [A.V. Samsonov, A.M. Shur. On Abelian repetition threshold. RAIRO ITA, 2012] and conjectured to be tight. We present a method of study of Abelian power-free languages using random walks in prefix trees and some experimental results obtained by this method. On the base of these results, we conjecture that the lower bounds for ART(k) by Samsonov and Shur are not tight for all k = 5 and prove this conjecture for k = 6, 7, 8, 9, 10. Namely, we show that ART(k) > k−2 k−3 in all these cases.

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“…The search starts with u = λ, ml = 0, count = 1. A variant of this search algorithm was used in [11] to numerically estimate the entropy of some α-free and α-A-free languages.…”

Section: Algorithmsmentioning

confidence: 99%

“…) is supposed to be infinite, it is interesting to estimate its growth. Based on the technique described in [11], we estimate the number of words of length n in AF(5, 3…”

Section: Alphabets With 2 3 4 and 5 Lettersmentioning

confidence: 99%