Affiliation:
1. University of Marne-la-Vallée, France
Abstract
The main result is a characterization of the generating sequences of the length of words in a regular language on
k
symbols. We say that a sequence
s
of integers is regular if there is a finite graph
G
with two vertices
i, t
such that
s
n
is the number of paths of length
n
from
i
to
t
in
G
. Thus the generating sequence of a regular language is regular. We prove that a sequence
s
is the generating sequence of a regular language on
k
symbols if and only if both sequences
s
= (
s
n
)
n
≥0
and
t
= (
k
n
−
s
n
)
n
≥0
are regular.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
13 articles.
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