Properties of code events and homomorphisms over regular events

Abstract

An event of the form ( w 1 ∪…∪ w n ) * , each w i being a word, is called a code event by R. McNaughton and S. Papert. In this paper, first, conditions are obtained for a code event to be noncounting, locally testable, and strictly locally testable, respectively. Next it is shown that a homomorphism f: ∑ 1 * → ∑ 2 * preserves strict local testability iff f is injective and the code event f ( ∑ 1 * ) is strictly locally testable. Similar results are obtained for locally testable events and noncounting events.