Is Every infinite c.e.language infinite or finite union of regular languages including at least one infinite regular language?
And is every infinite c.e.language that is not indexed language(that may generated by indexed grammar) infinite union of infinite regular languages?


Third:what class of languages may be finite or infinite union of regular language. 
And similiarly, :what class of languages may be finite or infinite union of context-free languages


Finally, we try to search for the minimal and simple class of languages finite or infinite union of which is able to form every c.e.language.



Every infinite c.e.language is infinite or finite union of regular languages including at least one infinite regular language?
A polynomial - time random language will not have any infinite regular subsets, so there's a counter example to the first question. 


For a similar counterexample to the second question, we can increase the level of resource bounded randomness to something like an "EXPSPACE-random" language (since indexed languages are context-sensitive [which implies they are in EXPSPACE](https://cs.stackexchange.com/questions/273/decidable-non-context-sensitive-languages)).


