Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
Language theory and molecular genetics: generative mechanisms suggested by DNA recombination
Handbook of formal languages, vol. 2
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Partial words and a theorem of Fine and Wilf revisited
Theoretical Computer Science
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
Partial words and the critical factorization theorem
Journal of Combinatorial Theory Series A
Codes, orderings, and partial words
Theoretical Computer Science
Discrete Applied Mathematics
DNA'04 Proceedings of the 10th international conference on DNA computing
Information Processing Letters
A generalization of Thue freeness for partial words
Theoretical Computer Science
Overlap-freeness in infinite partial words
Theoretical Computer Science
An Answer to a Conjecture on Overlaps in Partial Words Using Periodicity Algorithms
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Combinatorial queries and updates on partial words
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Avoiding large squares in partial words
Theoretical Computer Science
Unary pattern avoidance in partial words dense with holes
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Avoiding abelian powers in partial words
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Periodicity algorithms for partial words
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Avoiding abelian squares in partial words
Journal of Combinatorial Theory Series A
Abelian square-free partial words
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Avoidable binary patterns in partial words
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Hard counting problems for partial words
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Periodicity algorithms and a conjecture on overlaps in partial words
Theoretical Computer Science
Connecting partial words and regular languages
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Repetition-freeness with Cyclic Relations and Chain Relations
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
The hardness of counting full words compatible with partial words
Journal of Computer and System Sciences
Regular languages of partial words
Information Sciences: an International Journal
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The paper approaches the classical combinatorial problem of freeness of words, in the more general case of partial words. First, we propose an algorithm that tests efficiently whether a partial word is k-free or not, for a given k. Then, we show that there exist arbitrarily many k-free infinite partial words, over a binary alphabet, containing an infinite number of holes, for k=3. Moreover, we present an efficient algorithm for the construction of a cube-free partial word with a given number of holes, over a binary alphabet. In the final section of the paper, we show that there exists an infinite word, over a four-symbol alphabet, in which we can substitute randomly one symbol with a hole, and still obtain a cube-free word; we show that such a word does not exist for alphabets with fewer symbols. Further, we prove that in this word we can replace arbitrarily many symbols with holes, such that each two consecutive holes are separated by at least two symbols, and obtain a cube-free partial word. This result seems interesting because any partial word containing two holes with less than two symbols between them is not cube-free. Finally, we modify the previously presented algorithm to construct, over a four-symbol alphabet, a cube-free partial word with exactly n holes, having minimal length, among all the possible cube-free partial words with at least n holes.