Filters








4,492 Hits in 4.9 sec

On generalized zeta functions of formal languages and series

Juha Honkala
1991 Discrete Applied Mathematics  
., 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 show that it is decidable whether or not the (generalized) zeta function of a Q-algebraic series is a rational function.  ...  Acknowledgement The author would like to thank Professor Arto Salomaa for his useful comments on the preliminary version of this paper.  ... 
doi:10.1016/0166-218x(91)90097-g fatcat:2k7nh4ov6nds7bhc5yrsnddz2u

On algebraic generalized zeta functions of formal power series

Juha Honkala
1991 Theoretical Computer Science  
Honkala, J , 0n algebraic generalized zeta functions of formal power series, Theoretical Computer Science 79 (1991) 263-273. We study algebraic generalized zeta functions of formal power series.  ...  We show that the generalized zeta function of a rational series is an algebraic function if and only if it is a root of a rational function.  ...  Introduction The zeta functions and generalized zeta functions of formal languages and power series were defined by Berstel and Reutenauer [2] .  ... 
doi:10.1016/0304-3975(91)90156-v fatcat:rjlosugn55bwvp5wusbaadpo7m

Zeta functions of recognizable languages [chapter]

Jean Berstel, Christophe Reutenauer
1988 Lecture Notes in Computer Science  
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.  ...  Introduction Motivated by algebraic geometry over finite fields and symbolic dynamics, we call zeta function of a formal language L the function t n (L) = exp (Y. a n ) n where a n is the number of words  ... 
doi:10.1007/3-540-19488-6_109 fatcat:wdvlerfplveu7jijhbnlcyogoe

Page 439 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
Summary: “We study algebraic generalized zeta functions of formal power series.  ...  Edmund Robinson (Brighton) 92a:68071 68Q45 Honkala, Juha (SF-TURK) On algebraic generalized zeta functions of formal power series.  ... 

Zeta Functions of Formal Languages

Jean Berstel, Christophe Reutenauer
1990 Transactions of the American Mathematical Society  
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 automation is rational.  ...  One may suppose that G corresponds, in the above isomorphism, to the set G' = {U, g, A)lg E G} and that x = (j, h, 11). As x 2 =J= 0, one has P llj =J= O. Similarly, P).j =J= O.  ... 
doi:10.2307/2001573 fatcat:xaq4dlbi2fasfku5e2pclwojs4

Algebraicity of the zeta function associated to a matrix over a free group algebra [article]

Christian Kassel, Christophe Reutenauer
2013 arXiv   pre-print
Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients.  ...  We show that such a zeta function is an algebraic function.  ...  Acknowledgement We are grateful to Yves André, Jean-Benoît Bost and Carlo Gasbarri for their help in the proof of Theorem 4.4.  ... 
arXiv:1303.3481v4 fatcat:hgc2nrk6tjdldcshv3wb3ix6om

Zeta functions of formal languages

Jean Berstel, Christophe Reutenauer
1990 Transactions of the American Mathematical Society  
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 automation is rational.  ...  One may suppose that G corresponds, in the above isomorphism, to the set G' = {U, g, A)lg E G} and that x = (j, h, 11). As x 2 =J= 0, one has P llj =J= O. Similarly, P).j =J= O.  ... 
doi:10.1090/s0002-9947-1990-0998123-x fatcat:gbd67mksezbktmkunperindelm

Algebraicity of the zeta function associated to a matrix over a free group algebra

Christian Kassel, Christophe Reutenauer
2014 Algebra & Number Theory  
Algebraicity of the zeta function associated to a matrix over a free group algebra Christian Kassel and Christophe Reutenauer Following and generalizing a construction by Kontsevich, we associate a zeta  ...  We show that such a zeta function is an algebraic function.  ...  We are also indebted to François Bergeron and Pierre Guillot for assisting us with computer computations in the process detailed in Remark 5.2, to Frédéric Chapoton for his comments on the last part of  ... 
doi:10.2140/ant.2014.8.497 fatcat:lc5egz4a4rhd7iy4gm6xptuqna

Page 3369 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
The generalized zeta function of a language L is Z(L), where L is the characteristic series of L. By definition, a language  ...  They define the generalized zeta function Z(S) of a formal power series S in noncommuting variables by Z(S) = exp(>>,,>; 7(Sn)/m), where 2(S,,) is the homogeneous part of degree n of S viewed in a canonical  ... 

N-algebraicity of zeta functions of sofic-Dyck shifts [article]

Marie-Pierre Béal, Cǎtǎlin Dima
2017 arXiv   pre-print
As a consequence the zeta function of a sofic-Dyck shift is the generating function of a visibly pushdown language and is thus an N-algebraic series.  ...  We prove that the multivariate zeta function of a sofic-Dyck shift is the commutative series of some visibly pushdown language.  ...  The zeta function of a sofic-Dyck shift is the generating series of some computable visibly pushdown language. It is thus N-algebraic. Proof.  ... 
arXiv:1501.05843v2 fatcat:vmi2t53ah5hbjdzrshygfcwnfq

Cyclic languages and strongly cyclic languages [chapter]

Marie -Pierre Béal, Olivier Carton, Christophe Reutenauer
1996 Lecture Notes in Computer Science  
The result is used to give another proof of the rationality of the zeta function of rational cyclic languages.  ...  We prove that cyclic languages are the boolean closure of languages called strongly cyclic languages.  ...  Zeta function of a cyclic language We rst give the de nitions of generalized zeta function and zeta function of a language of nite words over a nite alphabet A.  ... 
doi:10.1007/3-540-60922-9_5 fatcat:ciwexlcprrfrffbxwhc7s5qeja

Page 5135 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
Adam (H-AOS) 92i:68111 68Q70 05A15 68Q45 68Q50 Honkala, Juha (SF-TURK) On generalized zeta functions of formal languages and series. Discrete Appl. Math. 32 (1991), no. 2, 141-153.  ...  The generalized zeta function Z(r) of a noncommutative formal power series r over an alphabet X with coefficients in a subsemiring A of the field of real numbers is Z(r) = exp()/,,>;(1/m)c(rn)), where  ... 

Rationality of the Möbius function of subword order

Anders Björner, Christophe Reutenauer
1992 Theoretical Computer Science  
We prove the rationality of various noncommutative formal power series, whose coefficients are determined by the Mobius function or zeta function of the subword partial order of noncommutative monomials  ...  Bjiirner, A. and C. Reutenauer, Rationality of the Mobius function of subword order, Theoretical Computer Science 98 (1992) 53-63.  ...  We give here examples of such series. We show that the zeta function and the Mobius function of subword order, and their powers, when viewed as formal series of words, are rational.  ... 
doi:10.1016/0304-3975(92)90379-t fatcat:izjan5fvovff3gf6sxwxpgtmgq

p-adic model theory, p-adic integrals, Euler products, and zeta functions of groups [article]

Jamshid Derakhshan
2020 arXiv   pre-print
We then briefly discuss zeta functions arising from definable equivalence relations and p-adic elimination of imginaries, which have applications to counting representations of groups.  ...  We give a survey of Denef's rationality theorem on p-adic integrals, its uniform in p versions, the relevant model theory, and a number of applications to counting subgroups of finitely generated nilpotent  ...  While Igusa had used the rationality of his local zeta functions to prove a conjecture of Borevich and Shafarevich on rationality of a Poincare series counting points on a variety modulo powers of p, Denef  ... 
arXiv:2007.09242v1 fatcat:nolcfxmrhjh4tnsuwpghi5p43e

On a zeta function associated with automata and codes

Sylvain Lavallée, Christophe Reutenauer
2007 Theoretical Computer Science  
The zeta function of a finite automaton A is exp{ ∞ n=1 a n z n n }, where a n is the number of bi-infinite paths in A labelled by a bi-infinite word of period n.  ...  It reflects the properties of A: aperiodicity, nil-simplicity, existence of a zero. The results are applied to codes.  ...  Although zeta functions of languages and sofic systems have been previously considered, this zeta function seems to be new: it may not be obtained by associating with the automaton some language and then  ... 
doi:10.1016/j.tcs.2007.04.004 fatcat:dqrgwdisbvfrjmx6xlyagtzgsa
« Previous Showing results 1 — 15 out of 4,492 results