Homework Answers
Note:-when there is a single alphabet is present then that language has to be regular then the length of the strings has to be in arithmetic progession.
a)not regular
b)not regular
c)not regular
d)not regular
e)not regular
f)not regular
all has same above reason only length of the strings are not in A.P
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6. Determine whether or not the following languages on Σ-(a) are regular (a) L = {an...
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...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b)...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b) L-(angla": kメn + 1). (c) L = {anglak : n = l or l k} . (d) L = {anb : n2 1} L = {w : na (w)关nb (w)). "(f) L = {ww : w E {a, b)'). (g) L = {w"www" : w E {a,b}*}
7. Let Σ = {a}, and consider the language L = {a n : n is...
7. Let Σ = {a}, and consider the language L = {a n : n is a prime number} = {a 2 , a3 , a5 , a7 , a11 , . . .}. 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. . . ) 8. Design a Turing machine that calculates the sum of...
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there...
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
4. A regular expression for the language over the alphabet fa, b) with each string having...
4. A regular expression for the language over the alphabet fa, b) with each string having an even number of a's is (b*ab*ab*)*b*. Use this result to find regular expressions for the following languages a language over the same alphabet but with each string having odd number of a's. (3 points) a. b. a language over the same alphabet but with each string having 4n (n >- 0) a's. (3 points)
3. For each of the following languages, . State whether the language is finite or infinite....
3. For each of the following languages, . State whether the language is finite or infinite. . State whether the language is regular or nonregular. . If you claim the language is regular: give a DFA (graphical representation) that recog- nizes the language. . If you claim that the language is not regular, describe the intuition for why this is so. Consider the following languages (a) [8 marks] The language of 8 bit binary strings that begin and end with...
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. ....
a.) Exhibit an algorithm that, given any three regular languages, L,L1,L2, determines whether or not L...
a.) Exhibit an algorithm that, given any three regular languages, L,L1,L2, determines whether or not L = L1L2. b.) Describe an algorithm by which one can decide whether two regular expressions are equivalent.
Answer these questions Construct regular expressions for the following languages: i. Even binary numbers without leading...
Answer these questions
Construct regular expressions for the following languages: i. Even binary numbers without leading zeros ii, L-(a"b"(n + m) is odd) ii L fa"b"l. n 2 3, m is odd) ni m.
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...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b) L-(angla": kメn + 1). (c) L = {anglak : n = l or l k} . (d) L = {anb : n2 1} L = {w : na (w)关nb (w)). "(f) L = {ww : w E {a, b)'). (g) L = {w"www" : w E {a,b}*}
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
4. A regular expression for the language over the alphabet fa, b) with each string having an even number of a's is (b*ab*ab*)*b*. Use this result to find regular expressions for the following languages a language over the same alphabet but with each string having odd number of a's. (3 points) a. b. a language over the same alphabet but with each string having 4n (n >- 0) a's. (3 points)
3. For each of the following languages, . State whether the language is finite or infinite. . State whether the language is regular or nonregular. . If you claim the language is regular: give a DFA (graphical representation) that recog- nizes the language. . If you claim that the language is not regular, describe the intuition for why this is so. Consider the following languages (a) [8 marks] The language of 8 bit binary strings that begin and end with...
Answer these questions
Construct regular expressions for the following languages: i. Even binary numbers without leading zeros ii, L-(a"b"(n + m) is odd) ii L fa"b"l. n 2 3, m is odd) ni m.
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