A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
On Zeilberger's algorithm and its q-analogue
VII SPOA Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
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
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
A Representation Theorem for Holonomic Sequences Based on Counting Lattice Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
| Hi-index | 0.00 |
Chomsky and Schutzenberger showed in 1963 that the sequence d"L(n), which counts the number of words of a given length n in a regular language L, satisfies a linear recurrence relation with constant coefficients for n, i.e., it is C-finite. It follows that every sequence s(n) which satisfies a linear recurrence relation with constant coefficients can be represented as d"L"""1(n)-d"L"""2(n) for two regular languages. We view this as a representation theorem for C-finite sequences. Holonomic or P-recursive sequences are sequences which satisfy a linear recurrence relation with polynomial coefficients. q-Holonomic sequences are the q-analog of holonomic sequences. In this paper we prove representation theorems of holonomic and q-holonomic sequences based on position specific weights on words, and for holonomic sequences, without using weights, based on sparse regular languages.