Let Σ = {0,1}and define a language L over Σ as L = {0n10n10n : n...
Let Σ = {0,1}and define a language L over Σ as L = {0n10n10n : n ≥1} Show that L is not context-free. Remark: Compare this with language S1 onpage106,which is context free. Hint: Let p be the pumping constant and consider the string s = 0p10p10p. Write s as in the Pumping Lemma. Either vy has no zeros,or it has at leas tone zero;consider theses cases separately.
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John Doe claims that the language L, of all strings over the alphabet Σ = {...
John Doe claims that the language L, of all strings over the alphabet Σ = { a, b } that contain an even number of occurrences of the letter ‘a’, is not a regular language. He offers the following “pumping lemma proof”. Explain what is wrong with the “proof” given below. “Pumping Lemma Proof” We assume that L is regular. Then, according to the pumping lemma, every long string in L (of length m or more) must be “pumpable”. We...
Let Σ {0, 1, 2} Use the Pumping Lemma to show that the language L defined...
Let Σ {0, 1, 2} Use the Pumping Lemma to show that the language L defined below is not regular L-(w: w Σ*, w is a palindrome} Note that a palindrome is a word, number, or other sequence of characters which reads the same backward as forward, such as mom or eye.
Give a context free grammar for the language L where L = {a"bam I n>:O and...
Give a context free grammar for the language L where L = {a"bam I n>:O and there exists k>-o such that m=2"k+n) 3. Give a nondeterministic pushdown automata that recognizes the set of strings in L from question 3 above. Acceptance should be by accept state. 4. 5 Give a context-free grammar for the set (abc il j or j -k) ie, the set of strings of a's followed by b's followed by c's, such that there are either a...
6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having...
6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having twice as many O's as it has l’s. For example, Lo contains the strings 001, 001010, 010100100. Use the Pumping Lemma to show that Lo is not regular. wice as many o's as it has I's
Prove that, if L is a regular language over the alphabet Σ=(0,1), then L': { ax...
Prove that, if L is a regular language over the alphabet Σ=(0,1), then L': { ax | x E L } is also regular for any a E Σ
Consider the application of the Pumping Lemma to prove that the language over Σ = {a,b,c}...
Consider the application of the Pumping Lemma to prove that the language over Σ = {a,b,c} shown below is not regular: L = {aibjck: i ≥ j ≥ k ≥ 0} First, we choose an input string w = apbpcp=xyz, 1|xy| p, |y|=k≥1, where p is the critical length. Next, create another string w´ L to produce a contradiction. Which of the following string will produce a contradiction? e) w´ = xz f) w´ = xyz g) w´ = xy2z h)...
(d) Let L be any regular language. Use the Pumping Lemma to show that In >...
(d) Let L be any regular language. Use the Pumping Lemma to show that In > 1 such that for all w E L such that|> n, there is another string ve L such that lvl <n. (4 marks) (e) Let L be a regular language over {0,1}. Show how we can use the previous result to show that in order to determine whether or not L is empty, we need only test at most 2" – 1 strings. (2...
Let Σ = { a } , and consider the language L = { a n...
Let Σ = { a } , and consider the language L = { a n : n is a prime number } = { a 2 , a 3 , a 5 , a 7 , a 11 , . . . } . Is L a regular language? Why or why not? (Hint: L contains a 11 , a 17 , a 23 , a 29 , but not a 77 since 77 is divisible by 11. ....
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0 < n < m} is not context-free. 2. (6 pts) Use the pumping lem...
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0 < n < m} is not context-free.
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w...
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w | the length of w is at least 2 and has the same symbol in its 2nd and last positions} (b)Draw the state diagram for an NFA for accepting the following language over alphabet {0,1} (Use as few states as possible): {w | w is of the form 1*(01 ∪ 10*)*} (c)If A is a language with alphabet Σ, the complement of A is...
Let Σ {0, 1, 2} Use the Pumping Lemma to show that the language L defined below is not regular L-(w: w Σ*, w is a palindrome} Note that a palindrome is a word, number, or other sequence of characters which reads the same backward as forward, such as mom or eye.
Give a context free grammar for the language L where L = {a"bam I n>:O and there exists k>-o such that m=2"k+n) 3. Give a nondeterministic pushdown automata that recognizes the set of strings in L from question 3 above. Acceptance should be by accept state. 4. 5 Give a context-free grammar for the set (abc il j or j -k) ie, the set of strings of a's followed by b's followed by c's, such that there are either a...
6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having twice as many O's as it has l’s. For example, Lo contains the strings 001, 001010, 010100100. Use the Pumping Lemma to show that Lo is not regular. wice as many o's as it has I's
(d) Let L be any regular language. Use the Pumping Lemma to show that In > 1 such that for all w E L such that|> n, there is another string ve L such that lvl <n. (4 marks) (e) Let L be a regular language over {0,1}. Show how we can use the previous result to show that in order to determine whether or not L is empty, we need only test at most 2" – 1 strings. (2...
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0 < n < m} is not context-free.
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0
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