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lfa:lab04-regexp-nfa [2020/10/29 11:26] pdmatei [NFAs to DFAs] |
lfa:lab04-regexp-nfa [2021/11/02 18:02] (current) roxana_elena.stiuca [3. The subset construction] |
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| - | ====== Regular Expressions and NFA Exercises ====== | + | ====== 5. Regex to DFA conversion ====== |
| - | ==== Regular Expression to NFA ===== | + | ==== 5.1. Nondeterministic Finite Automata ==== |
| - | 1. What language does $ (1 \cup \varepsilon)(00^*1)^*0^*$ generate? | + | |
| - | 2. Convert the previous regex to an NFA. | + | 5.1.1. Consider the following NFA: |
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| - | ==== NFAs ===== | + | |
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| - | 3. Consider the following NFA: | + | |
| {{:lfa:lab03-nfa2.png|}} | {{:lfa:lab03-nfa2.png|}} | ||
| - | What are all reachable configurations from (0,ABBA) ? | + | What are all reachable configurations from (0,abba) ? |
| - | 4. What is the accepted language of the previous NFA? | + | 5.1.2. What is the accepted language of the previous NFA? |
| - | 5. Write an NFA //without// $ \varepsilon$-transitions, which accepts the language $ L = \{abc,abd,aacd\}$ over the alphabet $ \Sigma = \{a,b,c,d\}$. | + | 5.1.3. Write an NFA //without// $ \varepsilon$-transitions, which accepts the language $ L = \{abc,abd,aacd\}$ over the alphabet $ \Sigma = \{a,b,c,d\}$. |
| - | 6. Consider the following NFA: | + | 5.1.4. Consider the following NFA: |
| {{:lfa:lab02-nfa2.png|}} | {{:lfa:lab02-nfa2.png|}} | ||
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| What are all reachable configurations from $ (0,abbabbb)$? | What are all reachable configurations from $ (0,abbabbb)$? | ||
| - | ==== NFAs to DFAs ===== | ||
| - | 7. Write the $ \varepsilon$-closure ($ E(q)$) for each state q in the NFA from exercise 6. | + | ==== 2. Regex to NFA ===== |
| + | 5.2.1. What language does $ (1 \cup \varepsilon)(00^*1)^*0^*$ generate? | ||
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| + | 5.2.2. Convert the previous regex to an NFA. | ||
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| + | ==== 3. The subset construction ===== | ||
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| + | 5.3.1. Write the $ \varepsilon$-closure ($ E(q)$) for each state q in the NFA from exercise 5.1.4. | ||
| - | 8. Convert the NFA from exercise 3 to a DFA. | + | 5.3.2. Convert the NFA from exercise 5.1.1 to a DFA. |
| - | 9. Convert the NFA from exercise 6 to a DFA. | + | 5.3.3. Convert the NFA from exercise 5.1.4 to a DFA. |
| - | 10. Convert the NFA from exercise 2 to a DFA. | + | 5.3.4. Convert the NFA from exercise 5.2.2 to a DFA. |