Kleene's theorem can be used to turn a transition graph (TG) into a regular expression. Which one of the following regular expressions would generate a language that would be equivalent to the language described by the following TG? Highlight 91 a 92 a a, b a, b 93

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Topic : Theoretical Computer Sciences and Computer Engineering

Question 4

A) and B)

Kleene's theorem can be used to turn a transition graph (TG) into a regular expression. Which one of the following regular expressions would generate a
language that would be equivalent to the language described by the following TG?
Highlight
91
1. b*a(aa + ab)*a
2. b*a[a + (a + b)]a
3. b*aa + ab
4. b*(aa+ba)*a
a
90/1
1. 0111
2. 00111
3. 10111
4. 11101
a
a
9₁/0
a
b
Given the Moore machine below, which one of the following represents the output that would be printed if the machine were fed the input string abba?
Highlight
9₁/1
92
94
b
a
b
a, b
a, b
9₂/1
+
93
a, b
Transcribed Image Text:Kleene's theorem can be used to turn a transition graph (TG) into a regular expression. Which one of the following regular expressions would generate a language that would be equivalent to the language described by the following TG? Highlight 91 1. b*a(aa + ab)*a 2. b*a[a + (a + b)]a 3. b*aa + ab 4. b*(aa+ba)*a a 90/1 1. 0111 2. 00111 3. 10111 4. 11101 a a 9₁/0 a b Given the Moore machine below, which one of the following represents the output that would be printed if the machine were fed the input string abba? Highlight 9₁/1 92 94 b a b a, b a, b 9₂/1 + 93 a, b
Consider the following FA with the regular expression r:
O 1.
O 2.
O 3.
-W1
4.
b
W2
la
By applying Kleene's theorem, an FA must be built for the regular expression r*. In the process a transition
table is compiled. We compile a suitable transition table by using the algorithm provided in Cohen page 129.
New state
+Z₁ = W₁
Z₂ = W₁
Z3 = W2
+Z4 = W₁ Or W3
+Z5 =W₁ or W2 or W3
New state
Z₁ = W1
b
Z2 = W₂
+Z3 = W₁ Or W3
+Z4 =W₁ or W₂ or W3
New state
+Z₁ = W₁
Z2 = W2
+Z3 = W₁ Or W3
+Z4 =W₁ or W2 or W3
New state
Z₁ = W1
Z₂ = W₂
+Z3 = W3
Z2
Z₂
Read an a
Z₂
+Z4
+Z4
Z₁
Read an a
Z₁
+Z3
+Z3
+21
Read an a
+Z₁
+Z3
+Z3
a, b
Read an a
+W3
Z₁
Z₁
+Z3
Read an b
Z3
Z3
+Z4
+Z5
+Z5
Read an b
Z2
+Z3
+Z4
+Z4
Read an b
Z₂
+Z3
+Z4
+Z4
Read an b
Z2
+Z3
+Z3
Transcribed Image Text:Consider the following FA with the regular expression r: O 1. O 2. O 3. -W1 4. b W2 la By applying Kleene's theorem, an FA must be built for the regular expression r*. In the process a transition table is compiled. We compile a suitable transition table by using the algorithm provided in Cohen page 129. New state +Z₁ = W₁ Z₂ = W₁ Z3 = W2 +Z4 = W₁ Or W3 +Z5 =W₁ or W2 or W3 New state Z₁ = W1 b Z2 = W₂ +Z3 = W₁ Or W3 +Z4 =W₁ or W₂ or W3 New state +Z₁ = W₁ Z2 = W2 +Z3 = W₁ Or W3 +Z4 =W₁ or W2 or W3 New state Z₁ = W1 Z₂ = W₂ +Z3 = W3 Z2 Z₂ Read an a Z₂ +Z4 +Z4 Z₁ Read an a Z₁ +Z3 +Z3 +21 Read an a +Z₁ +Z3 +Z3 a, b Read an a +W3 Z₁ Z₁ +Z3 Read an b Z3 Z3 +Z4 +Z5 +Z5 Read an b Z2 +Z3 +Z4 +Z4 Read an b Z₂ +Z3 +Z4 +Z4 Read an b Z2 +Z3 +Z3
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