A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
The Specker--Blatter theorem does not hold for quaternary relations
Journal of Combinatorial Theory Series A
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)
Modular Counting and Substitution of Structures
Combinatorics, Probability and Computing
Analytic Combinatorics
The specker-blatter theorem revisited
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
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Chomsky and Schützenberger showed in 1963 that the sequence dL (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, or equivalently, the generating function gL(x) = Σn dL(n)xn is a rational function. In this talk we survey results concerning sequences a(n) of natural numbers which -satisfy linear recurrence relations over Z or Zm, and -have a combinatorial or logical interpretation. We present the pioneering, but little known, work by C. Blatter and E. Specker from 1981, and its further developments, including results by I. Gessel (1984), E. Fischer (2003), and recent results by T. Kotek and the author.