Question

In: Computer Science

Prove the following Closure Properties with respect to Context Free Languages. 1. Show that Context Free...

Prove the following Closure Properties with respect to Context Free Languages.

1. Show that Context Free Languages are Closed under union(∪), concatenation(·), kleene star(*).

(Hint: If L1 and L2 are Context Free languages then write Context Free grammar equivalent to L1 ∪ L2, L1 · L2, L∗ 1 )

2. Show that if L1 and L2 are Context Free Languages, then L1 ∩ L2 is not necessarily Context Free.

(Hint: Use Proof by Counter Example)

Solutions

Expert Solution


Related Solutions

Closure under Context-Free Languages Show that the following operations are closed under context-free languages: union concatentation...
Closure under Context-Free Languages Show that the following operations are closed under context-free languages: union concatentation Kleene star
Prove that all regular languages are context free. Note: Proof must proceed by structural induction on...
Prove that all regular languages are context free. Note: Proof must proceed by structural induction on regular expressions Please prove by Structural Induction. Will Upvote for correct answer. Thanks
(a) How Context Free languages are different from Regular languages. (b) What are the automata accepting...
(a) How Context Free languages are different from Regular languages. (b) What are the automata accepting those languages and how they are different from DFA and NFA. (c) How the grammar of Context Free Languages looks different from those in Regular languages.
Are the following languages over {a, b} regular? If they are then prove it. If they...
Are the following languages over {a, b} regular? If they are then prove it. If they are not prove it with the Pumping Lemma a) {ap | p is a prime number} b) {xax | x Î{a,b}*} (start by listing some strings in, not in, the language
Give context free grammars for the languages below. To avoid mistakes, I recommend using scratch paper...
Give context free grammars for the languages below. To avoid mistakes, I recommend using scratch paper to check that your grammars produce the right set of string. This question is structured so that nonterminals (and associated rules) from an earlier subquestion might be useful in a grammar for a later sub-question. That’s why, rather than “S” as the start symbol, we will used different start symbols for each part. If you do use a nonterminal from an earlier sub-question, say...
Give context free grammars for the languages below. To avoid mistakes, I recommend using scratch paper...
Give context free grammars for the languages below. To avoid mistakes, I recommend using scratch paper to check that your grammars produce the right set of string. This question is structured so that nonterminals (and associated rules) from an earlier subquestion might be useful in a grammar for a later sub-question. That’s why, rather than “S” as the start symbol, we will used different start symbols for each part. If you do use a nonterminal from an earlier sub-question, say...
Prove that if G is a context-free grammar in which every variable occurs on the left...
Prove that if G is a context-free grammar in which every variable occurs on the left side of at most one production, then G is unambiguous.
(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?}...
(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?} (20 pt.) ? = {? ∈ {?, #}∗ | ? = ??#??# ... #?? ??? ? ≥ ?, ?? ∈ ?∗ ??? ????? ?, ??? ?? ≠?? ???????? ?≠?} Hint: choose a string ? ∈ ? that contains ? #’s.
2. Prove the following properties. (b) Prove that x + ¯ xy = x + y.
2. Prove the following properties.(b) Prove that x + ¯ xy = x + y.3. Consider the following Boolean function: F = x¯ y + xy¯ z + xyz(a) Draw a circuit diagram to obtain the output F. (b) Use the Boolean algebra theorems to simplify the output function F into the minimum number of input literals.
Show that L2 = {anb2nan : n ≥ 0} is not context-free using the pumping lemma.
Show that L2 = {anb2nan : n ≥ 0} is not context-free using the pumping lemma.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT