Results 1  10
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21
Transductions and contextfree languages
 Ed. Teubner
, 1979
"... 1.1 Notation and examples......................... 3 ..."
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Cited by 235 (4 self)
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1.1 Notation and examples......................... 3
Improved bounds on the number of ternary squarefree words
 J. Integer Seq
"... Abstract. Improved upper and lower bounds on the number of squarefree ternary words are obtained. The upper bound is based on the enumeration of squarefree ternary words up to length 110. The lower bound is derived by constructing generalised Brinkhuis triples. The problem of finding such triples c ..."
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Cited by 15 (2 self)
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Abstract. Improved upper and lower bounds on the number of squarefree ternary words are obtained. The upper bound is based on the enumeration of squarefree ternary words up to length 110. The lower bound is derived by constructing generalised Brinkhuis triples. The problem of finding such triples can essentially be reduced to a combinatorial problem, which can efficiently be treated by computer. In particular, it is shown that the number of squarefree ternary words of length n grows at least as 65 n/40, replacing the previous best lower bound of 2 n/17. 1.
The entropy of squarefree words
 Math. Comput. Modelling
, 1997
"... Finite alphabets of at least three letters permit the construction of squarefree words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid converge ..."
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Cited by 12 (5 self)
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Finite alphabets of at least three letters permit the construction of squarefree words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters. Résumé Il est possible de construire des mots de longueur infinie sans carré sur un alphabet ayant au moins trois lettres. Nous démontrons que l’entropie du langage des mots sans carré sur un tel alphabet est strictement positive et l’encadrons par des bornes inférieure et supérieure raisonnables. Enfin, nous donnons pour l’entropie une expression approchée qui est asymptotiquement correcte et converge rapidement lorsque le nombre de lettres de l’alphabet tend vers l’infini.
An Optimal O(log log n) Time Parallel Algorithm for Detecting all Squares in a String
, 1995
"... An optimal O(log log n) time concurrentread concurrentwrite parallel algorithm for detecting all squares in a string is presented. A tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm. When p processors are available the bounds become \Theta(d n ..."
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Cited by 11 (6 self)
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An optimal O(log log n) time concurrentread concurrentwrite parallel algorithm for detecting all squares in a string is presented. A tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm. When p processors are available the bounds become \Theta(d n log n p e + log log d1+p=ne 2p). The algorithm uses an optimal parallel stringmatching algorithm together with periodicity properties to locate the squares within the input string.
New Lower Bound on the Number of Ternary SquareFree Words
 J. Integer Sequences
, 2003
"... A new lower bound on the number of nletter ternary squarefree words is presented: 110 , which improves the previous best result of 65 . ..."
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Cited by 7 (1 self)
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A new lower bound on the number of nletter ternary squarefree words is presented: 110 , which improves the previous best result of 65 .
On the Entropy and Letter Frequencies of Ternary SquareFree Words
, 2003
"... We enumerate all ternary lengthℓ squarefree words, which are words avoiding squares of words up to length ℓ, for ℓ ≤ 24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary squarefree words. We then consider ternary squar ..."
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Cited by 5 (1 self)
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We enumerate all ternary lengthℓ squarefree words, which are words avoiding squares of words up to length ℓ, for ℓ ≤ 24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary squarefree words. We then consider ternary squarefree words with fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities. We derive consequences for the free energy and entropy of ternary squarefree words.
Words avoiding reversed subwords
 J. Combin. Math. and Combin. Comput
, 2003
"... We examine words w satisfying the following property: if x is a subword of w and x  is at least k for some fixed k, then the reversal of x is not a subword of w. 1 ..."
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Cited by 4 (1 self)
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We examine words w satisfying the following property: if x is a subword of w and x  is at least k for some fixed k, then the reversal of x is not a subword of w. 1
NONREPETITIVE COLORINGS OF TREES
"... A coloring of the vertices of a graph G is nonrepetitive if no path in G forms a sequence consisting of two identical blocks. The minimum number of colors needed is the Thue chromatic number, denoted by π(G). A famous theorem of Thue asserts that π(P) = 3 for any path P with at least 4 vertices. In ..."
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A coloring of the vertices of a graph G is nonrepetitive if no path in G forms a sequence consisting of two identical blocks. The minimum number of colors needed is the Thue chromatic number, denoted by π(G). A famous theorem of Thue asserts that π(P) = 3 for any path P with at least 4 vertices. In this paper we study the Thue chromatic number of trees. In view of the fact that π(T) is bounded by 4 in this class we aim to describe the 4chromatic trees. In particular, we study the 4critical trees which are minimal with respect to this property. Though there are many trees T with π(T) = 4 we show that any of them has a sufficiently large subdivision H such that π(H) = 3. The proof relies on Thue sequences with additional properties involving palindromic words. We also investigate nonrepetitive edge colorings of trees. By a similar argument we prove that any tree has a subdivision which can be edgecolored by at most ∆ + 1 colors without repetitions on paths.