Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups
Theoretical Computer Science
On bispecial factors of the Thue-Morse word
Information Processing Letters
Some combinatorial properties of Sturmian words
Theoretical Computer Science
Handbook of formal languages, vol. 1
Automata for matching patterns
Handbook of formal languages, vol. 2
Information Processing Letters
Regular Article: Forbidden Words in Symbolic Dynamics
Advances in Applied Mathematics
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Data Structures and Algorithms
Data Structures and Algorithms
Automata on Infinite Words, Ecole de Printemps d'Informatique Théorique,
Minimal Forbidden Words and Symbolic Dynamics
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Binary Patterns in Infinite Binary Words
Formal and Natural Computing - Essays Dedicated to Grzegorz Rozenberg [on occasion of his 60th birthday, March 14, 2002]
Forbidden Factors and Fragment Assembly
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Binary patterns in infinite binary words
Formal and natural computing
Information Processing Letters
Theoretical Computer Science - The art of theory
Word assembly through minimal forbidden words
Theoretical Computer Science
Theoretical Computer Science
Reconstruction of a word from a multiset of its factors
Theoretical Computer Science
On the Construction of an Antidictionary with Linear Complexity Using the Suffix Tree
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Information Processing Letters
A characterization of bispecial sturmian words
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
On the structure of bispecial Sturmian words
Journal of Computer and System Sciences
Hi-index | 5.23 |
Given a finite or infinite word v, we consider the set M(v) of minimal forbidden factors of v. We show that the set M(v) is of fundamental importance in determining the structure of the word v. In the case of a finite word w we consider two parameters that are related to the size of M(w): the first counts the minimal forbidden factors of w and the second gives the length of the longest minimal forbidden factor of w. We derive sharp upper and lower bounds for both parameters. We prove also that the second parameter is related to the minimal period of the word w. We are further interested to the algorithmic point of view. Indeed, we design linear time algorithm for the following two problems: (i) given w, construct the set M(w) and, conversely, (ii) given M(w), reconstruct the word w. In the case of an infinite word x, we consider the following two functions: gx that counts, for each n, the allowed factors of x of length n and fx that counts, for each n, the minimal forbidden factors of x of length n. We address the following general problem: what information about the structure of x can be derived from the pair (gx,fx)? We prove that these two functions characterize, up to the automorphism exchanging the two letters, the language of factors of each single infinite Sturmian word.