Properties of code events and homomorphisms over regular events

摘要

An event of the form (w1∪…∪ wn)*, each wi 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.