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Characterization of the structure-generating functions of regular sets and the DOL growth functions by Takuya Katayama; Masayuki Okamoto; Hajime Enomoto is a Computer Science article available to read on EtoBox.

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The structure-generatlng functions of regular sets and the D0L growth functions are characterized. Our result is: A rational function f(z) with integral coefficients is a structure-generating function of a regular set if and only if (1) the constant term of its denominator is 1 and that of its numerator is 0, (2) every coefficient an of its Taylor series expansion is nonnegative, and (3) every pole of the minimal absolute value offi(z) = 52~\_ 0 anM+¢ z n is of the form re, where r > 0 and e is a root of unity for any integer M/> 1 and i = 0, 1,..., M --i. Also stated are a result on the star height problem and an analogous characterization of the growth functions of D0L systems.

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Author

Takuya Katayama; Masayuki Okamoto; Hajime Enomoto

Publisher

Elsevier Science; Elsevier ; Academic Press; Elsevier BV (ISSN 0019-9958)

Published

1978

Language

EN

Field

Computer Science (Physical Sciences)