Some Remarks on Regular Words
Stephen L. Bloom
September 2002 |

## Abstract:
In the late 1970's, Courcelle introduced the class of
``arrangements'', or labeled linear ordered sets, here called just ``words''.
He singled out those words which are solutions of finite systems of fixed
point equations involving finite words, which we call the ``regular words''.
The current paper contains some new descriptions of this class of words
related to properties of regular sets of binary strings, and uses finite
automata to decide various natural questions concerning these words. In
particular we show that a countable word is regular iff it can be defined on
an ordinary regular language (which can be chosen to be a prefix code)
ordered by the lexicographical order such that the labeling function
satisfies a regularity condition. Those regular words whose underlying order
is ``discrete'' or ``scattered'' are characterized in several
ways
Available as |

Last modified: 2003-06-08 by webmaster.