
10. Show that the family of linear languages is not closed under concatenation. theory of computation
Show that the family of context-free languages is closed under reversal.
3. Show that the family of regular languages is closed under the given operations below The nor of two languages by nor(L, L2) = {w: w E L1 and w E L2} The cor (complementary) of two languages by cor(Li, L2) = {w: w E L1 or w E L2} a. b.
3. Show that the family of regular languages is closed under the given operations below The nor of two languages by nor(L, L2) = {w: w E L1...
Automata Question
(3) Show that the family of deterministic context-free languages is not closed under union and intersection.
Automata, Languages and Computation
Using the languages L1 = { (10)* 1(1+0) + (10)*} and L2 = { a(a*) }, construct an ei NFA that accepts the concatenation of the languages L1L2.
Using the languages L1 = { (10)* 1(1+0) + (10)*} and L2 = { a(a*) }, construct an ei NFA that accepts the concatenation of the languages L1L2.
1. i. Show that P is closed under intersection. (This means that if languages J and L are both in P, then so is J ∩ L.) ii. Show that JL (the concatenation of J and L) is in P. (Here J and L are in P as in part (i), and JL = { xy | x ∈ J and y ∈ L }. ) Here you should calculate the complexity of your P-time algorithm for JL. iii. Show...
Explain the
answer
QUESTION 8 The classes of languages P and NP are closed under certain operations, and not closed under others, just like classes such as the regular languages or context-free languages have closure properties. Decide whether P and NP are closed under each of the following operations. 1. Union. 2. Intersection. 3. Intersection with a regular language. 4. Concatenation 5. Kleene closure (star). 6. Homomorphism. 7. Inverse homomorphism. Then, select from the list below the true statement. OP...
1. (10 points) Show that the Turing Decidable languages are closed under complementation. If L is Turing Decidable then so is the complement -L. 1. (10 points) Show that the Turing Decidable languages are closed under complementation. If L is Turing Decidable then so is the complement -L.
7. (1 point) The collection of recognizable languages is closed under: A. union. B. concatenation. C. star. D. intersection. E. All of the above. Page 3 of 8 8. (1 point) L is decided by a deterministic) TM containing 100 tapes in time t(n) where n denotes the length of an input string. Which one of the following represents the time complexity of an equivalent single tape (deterministic) TM which decides L? A. Oft(n) 100). B. Oſt(n)). C. O(t(n)99). D....
Show that the class of context-free languages is not closed under difference. Use either of the following facts: a. The class of context-free languages is not closed under intersection. b. The language {ww | w ∈ {a,b}*} is not a CFL.
Prove that the class of regular languages is closed under intersection. That is, show that if ? and ? are regular languages, then ? ∩ ? = {? | ? ∈ ? ??? ? ∈ ?} is also regular. Hint:givenaDFA? =(?,Σ,?,?,?)thatrecognizes?andaDFA? =(?,Σ,?,?,?)that11111 22222 recognizes ?, construct a new DFA ? = (?, Σ, ?, ?0, ?) that recognizes ? ∩ ? and justify why your construction is correct.