Overlap-Free Regular Languages

We define a language to be overlap-free if any two distinct strings in the language do not overlap with each other. We observe that overlap-free languages are a proper subfamily of infix-free languages and also a proper subfamily of comma-free languages. Based on these observations, we design a polynomial-time algorithm that determines overlapfreeness of a regular language. We consider two cases: A language is specified by a nondeterministic finite-state automaton and a language is described by a regular expression. Furthermore, we examine the prime overlap-free decomposition of overlap-free regular languages and show that the prime overlap-free decomposition is not unique.

• Type: Conference
• Year: 2006
• Where: COCOON
• Authors: Yo-Sub Han, Derick Wood
• Keywords: COCOON 2006, Combinatorics, Prime Overlap-free Decomposition, Proper Subfamily, Regular Languages