Are both Kleene closure(0 or more replication) and positive closure (1 or more replication) special cases of concatenation? Does the number of operands matter here: infinitely countable, vs finite?
Does closure under concatenation imply closure under Kleene and positive closures?
Do the definitions of AFLs and full AFLs from Ullman's Introduction to Automata Theory, Languages and Computation have redundancy?
Define a class of languages to be an abstract family of languages
(AFL) if it is a trio and also closed under union, concatenation, and
positive closure.Call a class of languages a full AFL if it is a full trio and closed
under union, concatenation, and Kleene closure.
Thanks.
Best Answer
Closure under concatenation does not imply closure under $L \to L^*$ (Kleene closure) and $L \to L^+$ (positive closure): just take the class of finite languages as a counterexample.