Enumeration of irreducible binary words
Discrete Applied Mathematics
Overlap-free words and finite automata
Theoretical Computer Science
Overlap-free words on two symbols
Automata on Infinite Words, Ecole de Printemps d'Informatique Théorique,
Counting Overlap-Free Binary Words
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Polynomial versus exponential growth in repetition-free binary words
Journal of Combinatorial Theory Series A
Computationally Efficient Approximations of the Joint Spectral Radius
SIAM Journal on Matrix Analysis and Applications
Growth of repetition-free words: a review
Theoretical Computer Science - The art of theory
An upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices
Theoretical Computer Science
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
On the Complexity of Computing the Capacity of Codes That Avoid Forbidden Difference Patterns
IEEE Transactions on Information Theory
Polynomial-Time Computation of the Joint Spectral Radius for Some Sets of Nonnegative Matrices
SIAM Journal on Matrix Analysis and Applications
Joint Spectral Characteristics of Matrices: A Conic Programming Approach
SIAM Journal on Matrix Analysis and Applications
Growth properties of power-free languages
DLT'11 Proceedings of the 15th international conference on Developments in language theory
An experimental study of approximation algorithms for the joint spectral radius
Numerical Algorithms
| Hi-index | 5.23 |
Overlap-free words are words over the binary alphabet A={a,b} that do not contain factors of the form xvxvx, where x@?A and v@?A^*. We analyze the asymptotic growth of the number u"n of overlap-free words of length n as n-~. We obtain explicit formulas for the minimal and maximal rates of growth of u"n in terms of spectral characteristics (the joint spectral subradius and the joint spectral radius) of certain sets of matrices of dimension 20x20. Using these descriptions we provide new estimates of the rates of growth that are within 0.4% and 0.03% of their exact values. The best previously known bounds were within 11% and 3%, respectively. We then prove that the value of u"n actually has the same rate of growth for ''almost all'' natural numbers n. This average growth is distinct from the maximal and minimal rates and can also be expressed in terms of a spectral quantity (the Lyapunov exponent). We use this expression to estimate it. In order to obtain our estimates, we introduce new algorithms to compute the spectral characteristics of sets of matrices. These algorithms can be used in other contexts and are of independent interest.