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lfa:2023:lab05 [2023/11/06 17:10] alexandra.udrescu01 |
lfa:2023:lab05 [2023/11/11 12:29] (current) alexandra.udrescu01 |
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| 5.1.1. Identify a pair of states which are **indistinguishable**. (Solve the exercise for the 2 given DFAs.) | 5.1.1. Identify a pair of states which are **indistinguishable**. (Solve the exercise for the 2 given DFAs.) | ||
| - | /* | + | |
| <hidden DFA 1> | <hidden DFA 1> | ||
| <note tip> | <note tip> | ||
| Line 32: | Line 32: | ||
| </note> | </note> | ||
| </hidden> | </hidden> | ||
| - | */ | + | |
| 5.1.2. Identify a pair of final or non-final states which are **distinguishable**. The pair must be distinguished by a word different from the empty word. (Solve the exercise for the 2 given DFAs.) | 5.1.2. Identify a pair of final or non-final states which are **distinguishable**. The pair must be distinguished by a word different from the empty word. (Solve the exercise for the 2 given DFAs.) | ||
| - | /* | + | |
| <hidden DFA 1> | <hidden DFA 1> | ||
| <note tip>** DFA 1** | <note tip>** DFA 1** | ||
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| </hidden> | </hidden> | ||
| - | */ | + | |
| 5.1.3. Compute the table of indistinguishable states for the DFA. (Solve the exercise for the 2 given DFAs.) | 5.1.3. Compute the table of indistinguishable states for the DFA. (Solve the exercise for the 2 given DFAs.) | ||
| - | /* | + | |
| <hidden DFA 1><note tip> | <hidden DFA 1><note tip> | ||
| ** DFA 1 ** | ** DFA 1 ** | ||
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| </note> | </note> | ||
| </hidden> | </hidden> | ||
| - | */ | + | |
| ===== 5.2. Minimisation ====== | ===== 5.2. Minimisation ====== | ||
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| 5.2.1. Minimise the DFA. (Solve the exercise for the 2 given DFAs.) | 5.2.1. Minimise the DFA. (Solve the exercise for the 2 given DFAs.) | ||
| - | /* | + | |
| <hidden DFA 1> | <hidden DFA 1> | ||
| ** DFA 1 ** | ** DFA 1 ** | ||
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| {{ :lfa:2022:lfa2022_lab5_dfa2_min.png?400 |}} | {{ :lfa:2022:lfa2022_lab5_dfa2_min.png?400 |}} | ||
| </hidden> | </hidden> | ||
| - | */ | + | |
| 5.2.2. How can we algorithmically determine if two minimal DFAs accept the same language? | 5.2.2. How can we algorithmically determine if two minimal DFAs accept the same language? | ||
| - | /* | + | |
| <hidden><note tip> | <hidden><note tip> | ||
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| </note></hidden> | </note></hidden> | ||
| - | */ | + | |
| 5.2.3. Determine if the following regexes are **equivalent**: $math[(1\cup\epsilon)(00^*1)^*0^*] and $math[(10\cup 0)^*(01 \cup 1)^*(0 \cup \epsilon)] | 5.2.3. Determine if the following regexes are **equivalent**: $math[(1\cup\epsilon)(00^*1)^*0^*] and $math[(10\cup 0)^*(01 \cup 1)^*(0 \cup \epsilon)] | ||
| - | /* | + | |
| <hidden> | <hidden> | ||
| <note tip>The two languages are not equivalent because of word "110" which is accepted by the second regex, but rejected by the first regex.</note> | <note tip>The two languages are not equivalent because of word "110" which is accepted by the second regex, but rejected by the first regex.</note> | ||
| </hidden> | </hidden> | ||
| - | */ | + | |
| 5.2.4. Remember exercise 3.3.4 from Lab3. Show that the two regexes are equivalent: $ E1 = ((ab^*a)^+b)^* $ and $ E2 = (a(b\mid aa)^*ab)^* $ | 5.2.4. Remember exercise 3.3.4 from Lab3. Show that the two regexes are equivalent: $ E1 = ((ab^*a)^+b)^* $ and $ E2 = (a(b\mid aa)^*ab)^* $ | ||
| - | /* | + | |
| <hidden> | <hidden> | ||
| <note tip> | <note tip> | ||
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| </note></hidden> | </note></hidden> | ||
| - | */ | + | |
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| <note important>Brzozowski minimisation: **minDfa(A) = toDfa(reverse(toDfa(reverse(A))))**</note> | <note important>Brzozowski minimisation: **minDfa(A) = toDfa(reverse(toDfa(reverse(A))))**</note> | ||
| - | /* | + | |
| <hidden> | <hidden> | ||
| <note tip> | <note tip> | ||
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| </hidden> | </hidden> | ||
| - | */ | + | |
| ===== Conclusion ===== | ===== Conclusion ===== | ||