Zeta Functions of Recognizable Languages
نویسندگان
چکیده
LITP 4 place Jussieu 75005 Paris Abs t rac t Motivated by symbolic dynamics and algebraic geometry over finite fields, we define cyclic languages and the zeta function of a language. The main result is that the zeta function of a cyclic language which is recognizable by a finite automaton is rational. I. In t roduct ion Motivated by algebraic geometry over finite fields and symbolic dynamics, we call zeta function of a formal language L the function
منابع مشابه
A Stronger Recognizability Condition for Two-dimensional Languages
The paper presents a condition necessarily satisfied by (tiling system) recognizable two-dimensional languages. The new recognizability condition is compared with all the other ones known in the literature (namely three conditions), once they are put in a uniform setting: they are stated as bounds on the growth of some complexity functions defined for two-dimensional languages. The gaps between...
متن کاملRecognizability of Pomset Languages with Event Reenement
In the present paper, we contribute to the theory of recognizable pom-set (or partial word) languages from an algebraic point of view. By substitutions in pomsets labelled with variables and pomset contexts, we deene the syntactic equivalence of a pomset language, and use nite index ones to deene recognizable languages. We show that the induced recognizable pomset languages have extended closur...
متن کاملOn accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function
The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number of items, in this paper, we look at the Riemann Hypothesis using a new applied approach to infinity allowing one to easily execute numerical computations with...
متن کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کاملClasses of two-dimensional languages and recognizability conditions
The paper deals with some classes of two-dimensional recognizable languages of “high complexity”, in a sense specified in the paper and motivated by some necessary conditions holding for recognizable and unambiguous languages. For such classes we can solve some open questions related to unambiguity, finite ambiguity and complementation. Then we reformulate a necessary condition for recognizabil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1988