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32
Transductions and contextfree languages
 Ed. Teubner
, 1979
"... 1.1 Notation and examples......................... 3 ..."
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Cited by 292 (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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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.
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 10 (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 9 (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 .
Periodicity, Repetitions, and Orbits of an Automatic Sequence
, 2009
"... We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given kautomatic sequence is ultimately periodic. We prove that it is decidable whether a given kautomati ..."
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Cited by 8 (6 self)
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We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given kautomatic sequence is ultimately periodic. We prove that it is decidable whether a given kautomatic sequence is overlapfree (or squarefree, or cubefree, etc.) We prove that the lexicographically least sequence in the orbit closure of a kautomatic sequence is kautomatic, and use this last result to show that several related quantities, such as the critical exponent, irrationality measure, and recurrence quotient for Sturmian words with slope α, have automatic continued fraction expansions if α does.
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 7 (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 (2 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