On generalized zeta functions of formal languages and series

Juha Honkala
1991 Discrete Applied Mathematics  
Honkala, .I., On generalized zeta functions of formal languages and series, Discrete Applied Mathematics 32 (1991) 141-153. We study generalized zeta functions of formal languages and series. We give necessary conditions for the rationality of the generalized zeta function. We show that it is decidable whether or not the (generalized) zeta function of a Q-algebraic series is a rational function. The same question is shown to be undecidable for context-free languages. 0166-218X/91/$03.50 0 1991 -Elsevier Science Publishers B.V. (North-Holland)
doi:10.1016/0166-218x(91)90097-g fatcat:2k7nh4ov6nds7bhc5yrsnddz2u