Displaying similar documents to “Krohn-Rhodes complexity pseudovarieties are not finitely based”

Equations on partial words

Francine Blanchet-Sadri, D. Dakota Blair, Rebeca V. Lewis (2007)

RAIRO - Theoretical Informatics and Applications

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It is well-known that some of the most basic properties of words, like the commutativity () and the conjugacy (), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation has only periodic solutions in a free monoid, that is, if holds with integers , then there exists a word such that are powers of . This result, which received a lot of attention, was first proved by Lyndon...

Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

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We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When =1 we show that . In the cases when or max} we show that the first difference of the complexity function takes value in for every , and consequently we determine...

Closure properties of hyper-minimized automata

Andrzej Szepietowski (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Two deterministic finite automata are almost equivalent if they disagree in acceptance only for finitely many inputs. An automaton is hyper-minimized if no automaton with fewer states is almost equivalent to . A regular language is canonical if the minimal automaton accepting is hyper-minimized. The asymptotic state complexity () of a regular language is the number of states of a hyper-minimized automaton for a language finitely different from . In this paper we show...

A note on constructing infinite binary words with polynomial subword complexity

Francine Blanchet-Sadri, Bob Chen, Sinziana Munteanu (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Most of the constructions of infinite words having polynomial subword complexity are quite complicated, , sequences of Toeplitz, sequences defined by billiards in the cube, etc. In this paper, we describe a simple method for constructing infinite words over a binary alphabet  {  }  with polynomial subword complexity . Assuming contains an infinite number of ’s, our method is based on the gap function which gives the distances between consecutive ’s. It is known that...

Closure properties of hyper-minimized automata

Andrzej Szepietowski (2012)

RAIRO - Theoretical Informatics and Applications

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Two deterministic finite automata are almost equivalent if they disagree in acceptance only for finitely many inputs. An automaton is hyper-minimized if no automaton with fewer states is almost equivalent to . A regular language is canonical if the minimal automaton accepting is hyper-minimized. The asymptotic state complexity () of a regular language is the number of states of a hyper-minimized automaton...

Hereditary properties of words

József Balogh, Béla Bollobás (2010)

RAIRO - Theoretical Informatics and Applications

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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every  or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...

Integers in number systems with positive and negative quadratic Pisot base

Z. Masáková, T. Vávra (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We consider numeration systems with base and − , for quadratic Pisot numbers and focus on comparing the combinatorial structure of the sets Z and Z of numbers with integer expansion in base , resp. − . Our main result is the comparison of languages of infinite words and coding the ordering of distances between consecutive - and (− )-integers. It turns out that for a class of roots of − − , the languages coincide, while for other...

Undecidability of infinite post correspondence problem for instances of size 8

Jing Dong, Qinghui Liu (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The infinite Post Correspondence Problem (PCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [36 (2003) 231–245] showed that PCP is undecidable for domain alphabets of size 105, Halava and Harju [40 (2006) 551–557] showed that PCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that PCP is undecidable for domain alphabets of size 8.