论文信息 - A Necessary Condition for the Rationality of the Zeta Function of a Regular Language

A Necessary Condition for the Rationality of the Zeta Function of a Regular Language

Abstract We show that if the zeta function of a regular language L is rational, then there exist cyclic languages L 1 and L 2 such that the generating function of L is the difference of the generating functions of L 1 and L 2 . We show also that it is decidable whether or not the zeta function of a given regular language is rational. If it is rational, it can be computed effectively.

Juha Honkala | J. Honkala

[1] Arto Salomaa,et al. Automata-Theoretic Aspects of Formal Power Series , 1978, Texts and Monographs in Computer Science.

[2] Donald E. Knuth,et al. The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[3] Jean Berstel,et al. Zeta Functions of Recognizable Languages , 1988, ICALP.

[4] N. Koblitz. p-adic Numbers, p-adic Analysis, and Zeta-Functions , 1977 .

[5] Arto Salomaa. Jewels of formal language theory , 1981 .