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4. Let = {0,1} and let A denote a language of strings that consist solely of...
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...
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet...
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that the number of 0s is divisible by 2 and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a methodical way to do this: Figure out all the final states and label each with the shortest string it accepts, work backwards from these states to...
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression...
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA a, b
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA...
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of...
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that there are no consecutive 0s, and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a way to approach the problem: First focus only building the DFA which accepts the language: As you build your DFA, label your states with an explanation of what the state actually represents in terms...
Problem 3.3: For a string x € {0,1}*, let af denote the string obtained by changing...
Problem 3.3: For a string x € {0,1}*, let af denote the string obtained by changing all 0's to l's and all l's to O's in x. Given a language L over the alphabet {0,1}, define FLIP-SUBSTR(L) = {uvFw: Uvw E L, U, V, w € {0, 1}*}. Prove that if L is regular, then FLIP-SUBSTR(L) is regular. (For example, (1011)F = 0100. If 1011011 e L, then 1000111 = 10(110) F11 € FLIP-SUBSTR(L). For another example, FLIP-SUBSTR(0*1*) = 0*1*0*1*.)...
Consider the NFA N with states labeled q1, q2 and q3, where q1 is the start...
Consider the NFA N with states labeled q1, q2 and q3, where q1 is the start state and q2 and q3 are the final (accepting) states. The transition function for N is δ(q1,a) = {q1}, δ(q1,b) = {q1,q2}, δ(q2,a) = {q3}, δ(q2,b)= ∅, δ(q3,a)= ∅, and δ(q3,b)= ∅. Let L be the language recognized by N i.e. L(N). a) Draw the state diagram for N. b) Describe in plain English what's in the language L. c) Via the construction NFA to...
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
Can you please thoroughly explain part B? Let Σ {0,1} be an alphabet. Suppose the language...
Can you please thoroughly explain part B?
Let Σ {0,1} be an alphabet. Suppose the language Ly is the set of all strings that start with a 1 and L2 is the set of all strings that end in a 1. Describe Lj U L2 and (L1 UL2)* using English. b) Decide if the given strings belong to the language defined by the given regular expression. If it does not belong, then explain why. 0(1|€)10(e|0)*11 , strings: 0110011, 0100011001111
**please note that not just 0212 120 and epsion need to work, as the other solution...
**please note that not just 0212 120 and epsion need to work, as
the other solution i found ONLY accounted for those. Any sequence
following the pattern of increase, decrease, increase, decrease
(indefinitely) must work. Thank you!
3. (10 points) Consider the following language over the alphabet [0, 1,2) L={ai . . . an I n > 0 and ai <a2,a2 > a3,a3 <G4, ) For example, 0212, 120, and ε are each strings in L; 11 and 20 are...
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 ∈...
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA a, b
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA...
Problem 3.3: For a string x € {0,1}*, let af denote the string obtained by changing all 0's to l's and all l's to O's in x. Given a language L over the alphabet {0,1}, define FLIP-SUBSTR(L) = {uvFw: Uvw E L, U, V, w € {0, 1}*}. Prove that if L is regular, then FLIP-SUBSTR(L) is regular. (For example, (1011)F = 0100. If 1011011 e L, then 1000111 = 10(110) F11 € FLIP-SUBSTR(L). For another example, FLIP-SUBSTR(0*1*) = 0*1*0*1*.)...
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
Can you please thoroughly explain part B?
Let Σ {0,1} be an alphabet. Suppose the language Ly is the set of all strings that start with a 1 and L2 is the set of all strings that end in a 1. Describe Lj U L2 and (L1 UL2)* using English. b) Decide if the given strings belong to the language defined by the given regular expression. If it does not belong, then explain why. 0(1|€)10(e|0)*11 , strings: 0110011, 0100011001111
**please note that not just 0212 120 and epsion need to work, as
the other solution i found ONLY accounted for those. Any sequence
following the pattern of increase, decrease, increase, decrease
(indefinitely) must work. Thank you!
3. (10 points) Consider the following language over the alphabet [0, 1,2) L={ai . . . an I n > 0 and ai <a2,a2 > a3,a3 <G4, ) For example, 0212, 120, and ε are each strings in L; 11 and 20 are...
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 ∈...
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