1. Some Remarks on Regular Words
- Author
-
Zoltán Ésik and Stephen L. Bloom
- Subjects
Discrete mathematics ,Combinatorics ,Prefix code ,Class (set theory) ,Finite-state machine ,Regular language ,Countable set ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Function (mathematics) ,Lexicographical order ,Computer Science::Formal Languages and Automata Theory ,Word (group theory) ,Mathematics - 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.
- Published
- 2002