Is the collection of Turing-recognizable languages closed under the operation of Union?
Show that the collection of Turing-recognizable languages is closed under the operation of union. For any two Turing-Recognizable languages L 1 and L 2, let M 1 and M 2 be the TM s that recognize them. We construct a TM M ? that recognize the union of L 1 and L 2: Run M 1 and M 2 alternately on w step by step. If either accpts, a c c e p t.
How to recognize two Turing-recognizable languages?
For any two Turing-Recognizable languages L 1 and L 2, let M 1 and M 2 be the TM s that recognize them. We construct a TM M ? that recognize the union of L 1 and L 2: Run M 1 and M 2 alternately on w step by step. If either accpts, a c c e p t. If both half and reject, r e j e c t.
Are Turing-decidable languages closed under Kleene star?
Theorem: Turing-decidable languages are closed under Kleene star. Example: w= abcd Which factorizations of w must be considered? 11 w 1 w 2 w
Are Turing recognizable languages closed under complement?
Turing recognizable languages are not closed under complement. In fact, Theorem 1better explains the situation. Theorem 1.A languageLis decidable if and only if bothLandLare Turing recognizable.