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lfa:2022:lab04-regexp-nfa [2022/10/28 22:35]
alexandra.udrescu01 		lfa:2022:lab04-regexp-nfa [2022/11/04 13:30] (current)
alexandra.udrescu01
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 ====== 4. Regex to DFA conversion ====== ====== 4. Regex to DFA conversion ======
- 
-<note warning>​AU va pune solutiile in acest weekend</​note>​ 
  
 ==== 4.1. Nondeterministic Finite Automata ==== ==== 4.1. Nondeterministic Finite Automata ====
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 What are all reachable configurations from (0,abba) ? What are all reachable configurations from (0,abba) ?
 +
  
 <​hidden>​ <​hidden>​
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 </​note>​ </​note>​
 </​hidden>​ </​hidden>​
 +
  
 4.1.2. What is the accepted language of the previous NFA?  4.1.2. What is the accepted language of the previous NFA? 
 +
  
 <​hidden>​ <​hidden>​
 <note tip> <note tip>
-(a $\cup$ b)* a (a $\cup$ b) (a $\cup$ b $\cup$ $\varepsilon$)+L( (a $\cup$ b)* a (a $\cup$ b) (a $\cup$ b $\cup$ $\varepsilon$) )
 </​note>​ </​note>​
 </​hidden>​ </​hidden>​
 +
  
 4.1.3. Write an NFA //without// $ \varepsilon$-transitions,​ which accepts the language $ L = \{abc,​abd,​aacd\}$ over the alphabet $ \Sigma = \{a,​b,​c,​d\}$. 4.1.3. Write an NFA //without// $ \varepsilon$-transitions,​ which accepts the language $ L = \{abc,​abd,​aacd\}$ over the alphabet $ \Sigma = \{a,​b,​c,​d\}$.
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 <​hidden>​ <​hidden>​
 +{{:​lfa:​2022:​lfa2022_lab2_ex1_4.png?​400|}}
 </​hidden>​ </​hidden>​
 +
  
 4.1.4. Consider the following NFA: 4.1.4. Consider the following NFA:
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 What are all reachable configurations from $ (0,​abbabbb)$?​ What are all reachable configurations from $ (0,​abbabbb)$?​
 +
  
 <​hidden>​ <​hidden>​
  
-{{:​lfa:​2022:​lfa2022_lab4_ex1_4.png?​400|}}+{{:​lfa:​2022:​lfa2022_lab4_ex1_4.png?​300|}}
  
 </​hidden>​ </​hidden>​
 +
  
 ==== 2. Regex to NFA ===== ==== 2. Regex to NFA =====
 +
 4.2.1. What language does $ (1 \cup \varepsilon)(00^*1)^*0^*$ generate? 4.2.1. What language does $ (1 \cup \varepsilon)(00^*1)^*0^*$ generate?
 +
  
 <​hidden><​note tip> <​hidden><​note tip>
 L($ (1 \cup \varepsilon)(00^*1)^*0^*$) = { w $\in$ {0, 1}* | w has the property that there are no sequences of 2 or more consecutive "​1"​ } L($ (1 \cup \varepsilon)(00^*1)^*0^*$) = { w $\in$ {0, 1}* | w has the property that there are no sequences of 2 or more consecutive "​1"​ }
 </​note></​hidden>​ </​note></​hidden>​
 +
  
 4.2.2. Convert the previous regex to an NFA. 4.2.2. Convert the previous regex to an NFA.
 +
 +
 +<​hidden>​
 +{{:​lfa:​2022:​lfa2022_lab4_ex2_2_v2.png?​600|}}
 +</​hidden>​
  
  
 ==== 3. The subset construction ===== ==== 3. The subset construction =====
  
-4.3.1. Write the $ \varepsilon$-closure ($ E(q)$) for each state q in the NFA from exercise ​5.1.4.+4.3.1. Write the $ \varepsilon$-closure ($ E(q)$) for each state q in the NFA from exercise ​4.1.4. 
  
 <​hidden><​note tip> <​hidden><​note tip>
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 </​note></​hidden>​ </​note></​hidden>​
  
-4.3.2. Convert the NFA from exercise ​5.1.1 to a DFA.+ 
 +4.3.2. Convert the NFA from exercise ​4.1.1 to a DFA. 
  
 <​hidden>​ <​hidden>​
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 </​hidden>​ </​hidden>​
  
-4.3.3. Convert the NFA from exercise ​5.1.4 to a DFA.+ 
 +4.3.3. Convert the NFA from exercise ​4.1.4 to a DFA. 
  
 <​hidden>​ <​hidden>​
 {{:​lfa:​2022:​lfa2022_lab4_ex3_3.png?​400|}} {{:​lfa:​2022:​lfa2022_lab4_ex3_3.png?​400|}}
 +
 +Barred transitions go to a sink state.
 </​hidden>​ </​hidden>​
  
-4.3.4. Convert the NFA from exercise ​5.2.2 to a DFA.+ 
 +4.3.4. Convert the NFA from exercise ​4.2.2 to a DFA. 
 + 
 <​hidden>​ <​hidden>​
-{{:​lfa:​2022:​lfa2022_lab4_ex3_4.png?400|}}+{{:​lfa:​2022:​lfa2022_lab4_ex3_4_v2.png?400|}} 
 + 
 +Barred transitions go to a sink state.
 </​hidden>​ </​hidden>​
 +