Homework Answers
For the following context-free grammar G2 = <
V2 , 
, S , P2 > generates
L2
V2 = { S,A ,B} , ={0,1 } and P2 = { S -> 0S0 | A ,A
-> 1B1 ,B -> 0B0 |00| 
}
Add Answer to:
Construct CFG
(b) (3 points) CFG: L2 = {wwR | w is a binary string and...
1. Construct a DFSM to accept the language: L = {w € {a,b}*: w contains at...
1. Construct a DFSM to accept the language: L = {w € {a,b}*: w contains at least 3 a's and no more than 3 b's} 2. Let acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E ', let W denote the string w with the...
Write a right-linear CFG for the regular languages: (∑={0,1}) a. L = { w | w...
Write a right-linear CFG for the regular languages: (∑={0,1}) a. L = { w | w is a binary string which starts and ends with the same symbol} b. L = { w | w is a binary string with at least three 0’s } c. L = { w | w is a binary string with odd number of 0’s and even number of 1’s}
Construct DFA's that recognize the following languages over the alphabet {a,b}: 1. {w|w is any string...
Construct DFA's that recognize the following languages over the alphabet {a,b}: 1. {w|w is any string except abba or aba}. Prove that your DFA recognizes exactly the specified language. 2. {w|w contains a substring either ababb or bbb}. Write the formal description for this DFA too.
For a string s ∈ {0, 1} let denote the number represented by in the binary * s2 s numeral system. For example 1110 in binary has a value of 14 . Consider the language: L = {u#w | u,w ∈ {0, 1} , u } ,...
For a string s ∈ {0, 1} let denote the number represented by in
the binary * s2 s numeral system. For example 1110 in binary has a
value of 14 . Consider the language: L = {u#w | u,w ∈ {0, 1} , u }
, * 2 + 1 = w2 meaning it contains all strings u#w such that u + 1
= w holds true in the binary system. For example, 1010#1011 ∈ L and
0011#100 ∈...
Problem 1 Create a CFG that generates each of the languages below. [10 points] [10 points]...
Problem 1 Create a CFG that generates each of the languages below. [10 points] [10 points] wR is a substring of r if there are strings y, z E {a, b)" such that r = ywR2. A = {w I w E {a, b)" has more as than bs} B = {w#r l w,xe(a, b)" and wR a. b. is a substring of r). Rememb er, c. [10 points] C = {amb"ck 1 m, n > 0 and k =...
DO NUMBER 3 2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, g...
DO NUMBER 3
2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept the language:...
DO NUMBER 4 AND 5 2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta,...
DO NUMBER 4 AND 5
2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept...
Hello, I need help solving these two computer science questions. 3. Give a CFG for each...
Hello, I need help solving these two computer science
questions.
3. Give a CFG for each of the following: (a) The language {0416 with a +b}. (b) All binary palindromes with exactly three 1's (such as 001010100). 4. Consider the following CFG with start state S: SOAS 1BS € A → OAA 1 B + 1BBO Determine the language generated by S. Justify your answer.
1. Construct a DFA that recognizes each of the following languages: a. L1 = {w €...
1. Construct a DFA that recognizes each of the following languages: a. L1 = {w € {a, b}* | w contains at least two a's and at least two b’s} b. L2 = {w € {a,b}* | w does not contain the substring abba} C. L3 = {w € {a, b}* | the length of w is a multiple of 4}
3. (PDAs) Draw state diagrams of PDAs (with as few states as you can) that recognize...
3. (PDAs) Draw state diagrams of PDAs (with as few states as you can) that recognize the following languages. Write algorithmic descriptions for your PDAs. (b) The language L2 from Problem 2(b): (i) diagram; (ii) algorithmic description. Here is the language L2: L2 = {w | w = wR which means w is a palindrome} Recall that wR represents string w written backwards. Use at most 2 variables.
1. Construct a DFSM to accept the language: L = {w € {a,b}*: w contains at least 3 a's and no more than 3 b's} 2. Let acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E ', let W denote the string w with the...
For a string s ∈ {0, 1} let denote the number represented by in
the binary * s2 s numeral system. For example 1110 in binary has a
value of 14 . Consider the language: L = {u#w | u,w ∈ {0, 1} , u }
, * 2 + 1 = w2 meaning it contains all strings u#w such that u + 1
= w holds true in the binary system. For example, 1010#1011 ∈ L and
0011#100 ∈...
Problem 1 Create a CFG that generates each of the languages below. [10 points] [10 points] wR is a substring of r if there are strings y, z E {a, b)" such that r = ywR2. A = {w I w E {a, b)" has more as than bs} B = {w#r l w,xe(a, b)" and wR a. b. is a substring of r). Rememb er, c. [10 points] C = {amb"ck 1 m, n > 0 and k =...
DO NUMBER 3
2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept the language:...
DO NUMBER 4 AND 5
2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept...
Hello, I need help solving these two computer science
questions.
3. Give a CFG for each of the following: (a) The language {0416 with a +b}. (b) All binary palindromes with exactly three 1's (such as 001010100). 4. Consider the following CFG with start state S: SOAS 1BS € A → OAA 1 B + 1BBO Determine the language generated by S. Justify your answer.
1. Construct a DFA that recognizes each of the following languages: a. L1 = {w € {a, b}* | w contains at least two a's and at least two b’s} b. L2 = {w € {a,b}* | w does not contain the substring abba} C. L3 = {w € {a, b}* | the length of w is a multiple of 4}
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