Show that the class of context-free languages is not closed under difference. Use either of the...
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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.
Homework Answers
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Show that the class of context-free languages is not closed
under difference. Use either of the...
4. (Closure) Show that the class of context-free languages is closed under the star operation.
4. (Closure) Show that the class of context-free languages is closed under the star operation.
Automata Question (3) Show that the family of deterministic context-free languages is not closed under union...
Automata Question
(3) Show that the family of deterministic context-free languages is not closed under union and intersection.
Show that the class of context-free languages is closed under the regular operation union. For simplicity,...
Show that the class of context-free languages is closed under the regular operation union. For simplicity, you may assume that the alphabets of G1 and G2 are the same. [Hint: Use a constructive proof. Start with the formal definitions, G1 = (V1 ,∑, R1,S1) and G2 = (V2, ∑, R2, S2) and derive the formal definition of G∪.]
Show that the family of context-free languages is closed under reversal.
Show that the family of context-free languages is closed under reversal.
use the pumping lemma for context free languages to prove the language is not context free....
use
the pumping lemma for context free languages to prove the language
is not context free.
B = {w#t | w is a substring of t, where wit e {a,b}*}. Hint: consider s = apbº#apba.
Q.5 Are the context-free languages closed under reversal? Answer yes or no, and explain. (Reversal means...
Q.5 Are the context-free languages closed under reversal? Answer yes or no, and explain. (Reversal means to form the language containing the reverse of every string in the original.)
2. (10 points) Use the pumping lemma for context free grammars to show the following languages...
2. (10 points) Use the pumping lemma for context free grammars
to show the following languages are not context-free.
(a) (5 points)
.
(b) (5 points)
L = {w ◦ Reverse(w) ◦ w | w ∈ {0,1}∗}.
I free grammar for this language L. lemma for context free grammars to show t 1. {OʻPOT<)} L = {w • Reverse(w) w we {0,1}*). DA+hattha follaurino lano
Explain the answer QUESTION 8 The classes of languages P and NP are closed under certain...
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...
Prove that the class of regular languages is closed under intersection. That is, show that if...
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.
Automata Question
(3) Show that the family of deterministic context-free languages is not closed under union and intersection.
use
the pumping lemma for context free languages to prove the language
is not context free.
B = {w#t | w is a substring of t, where wit e {a,b}*}. Hint: consider s = apbº#apba.
2. (10 points) Use the pumping lemma for context free grammars
to show the following languages are not context-free.
(a) (5 points)
.
(b) (5 points)
L = {w ◦ Reverse(w) ◦ w | w ∈ {0,1}∗}.
I free grammar for this language L. lemma for context free grammars to show t 1. {OʻPOT<)} L = {w • Reverse(w) w we {0,1}*). DA+hattha follaurino lano
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...
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