Two classes of languages related to the prefix codes

Abstract

In this paper, we generalize some properties about prefix codes in [1], replacing the condition: the language L is finite with the condition: L satisfies |∪ _x∈η(L) x ⁻¹ L| < ∞. Then we give another equivalent characterization on the right dense. At last, we give the element in an ideal K = {A ∈ M | AM ∩ P = ∅} of ⟨M, ·⟩ an equivalent description.

Keywords:

• Free monoid
• Code
• Prefix code
• Primitive word

Acknowledgement

The authors would like to thank Cao Chunhua and Liu Yun for their valuable suggestions. The project is supported by NSF(10071068) of China.