regular expression and equivalent right linear grammar

Question

I have some question regarding regular expressions and right linear grammer.

I know that for any regular expression there is an equivalent right linear grammer.

Is that sentence is right also for right linear grammar that has no any epsilon rules?

Answer 1

You can systematically remove epsilon rules from a grammar, unless there is an epsilon production for the start symbol. So the statement is true for regular grammars without epsilon productions other than possibly for the start symbol. Equivalently, it's true for regular expressions which don't match epsilon.