Binary equality words with two $b$'s
نویسندگان
چکیده
منابع مشابه
Large Simple Binary Equality Words
Let w be an equality word of two nonperiodic binary morphisms g, h : {a, b}∗ → ∆∗. Suppose that no overflow occurs twice in w and that w contains at least 9 occurrences of a and at least 9 occurrences of b. Then either w = (ab)a, or w = ab with gcd(i, j) = 1, up to the exchange of letters a and b.
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We show that the equality set Eq(g, h) of two non-periodic binary morphisms g, h : A * → Σ * is generated by at most two words. If the rank of Eq(g, h) = {α, β} * is two, then α and β start (and end) with different letters. This in particular implies that any binary language has a test set of cardinality at most two. A nucleus of the paper was a part of my Ph.D. thesis supervised by Aleš Drápal...
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Let g and h be binary morphisms defined on {a, b}∗, and let g be periodic and h nonperiodic. It is well known that their equality language is generated by at most one nonempty word. Suppose |h(b)| ≥ |h(a)|. We show that then the equality word is equal to aba , with i, j ≥ 0. Binary equality sets are the simplest nontrivial equality languages. Nevertheless, their full description is still not kn...
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Let L be the equality set of two distinct injective morphisms g and h, and let L be generated by at least two words. Recently it was proved ([2]) that such an L is generated by two words and g and h can be chosen marked from both sides. We use this result to show that L is of the form {ab, ba}, with i ≥ 1.
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ژورنال
عنوان ژورنال: Commentationes Mathematicae Universitatis Carolinae
سال: 2018
ISSN: 0010-2628,1213-7243
DOI: 10.14712/1213-7243.2015.247