On sparseness, ambiguity and other decision problems for acceptors and transducers
3rd annual symposium on theoretical aspects of computer science on STACS 86
Handbook of formal languages, vol. 1
Information Processing Letters
Polynomial versus exponential growth in repetition-free binary words
Journal of Combinatorial Theory Series A
On the structure of the counting function of sparse context-free languages
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
On the repetition threshold for large alphabets
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Finding the Growth Rate of a Regular of Context-Free Language in Polynomial Time
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Growth rates of complexity of power-free languages
Theoretical Computer Science
Growth properties of power-free languages
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Growth of power-free languages over large alphabets
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Growth of Power-Free Languages over Large Alphabets
Theory of Computing Systems
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We study combinatorial complexity (or counting function) of regular languages, describing these functions in three ways. First, we classify all possible asymptotically tight upper bounds of these functions up to a multiplicative constant, relating each particular bound to certain parameters of recognizing automata. Second, we show that combinatorial complexity equals, up to an exponentially small term, to a function constructed from a finite number of polynomials and exponentials. Third, we describe oscillations of combinatorial complexity for factorial, prefix-closed, and arbitrary regular languages. Finally, we construct a fast algorithm for calculating the growth rate of complexity for regular languages, and apply this algorithm to approximate growth rates of complexity of power-free languages, improving all known upper bounds for growth rates of such languages.