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lfa:lab06-closure-properties [2022/11/17 19:15]
pdmatei 		lfa:lab06-closure-properties [2022/11/17 19:16] (current)
pdmatei
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 <​hidden>​ All strategies require building DFAs from the regexes. <​hidden>​ All strategies require building DFAs from the regexes.
- +  - You can use an existing minimisation algorithm to find the minimal DFAs. Then, label each state from each DFA from 0 to |K|. Fix an ordering of the symbols of the alphabet. Sort the transitions by symbol. Make a textual representation of each DFA which includes the number of states and the sorted transition function. ​ If the textual representations of the two DFAs are identical then they accept the same language. 
- +  ​- ​Use the indistinguishability algorithm to check if the two initial states of the two DFAs are indistinguishable. 
-1. You can use an existing minimisation algorithm to find the minimal DFAs. Then, label each state from each DFA from 0 to |K|. Fix an ordering of the symbols of the alphabet. Sort the transitions by symbol. Make a textual representation of each DFA which includes the number of states and the sorted transition function. ​ If the textual representations of the two DFAs are identical then they accept the same language. +  ​- ​Check $math[L(A_1) \subseteq L(A_2)] and $math[L(A_2) \subseteq L(A_1)]. The condition $math[L(A) \subseteq L(B)] can be restated as $math[L(A) \cap complement(L(B)) = \emptyset]. Build the complement DFA for B, and use the product construction with A. Check if the resulting DFA has any final state accessible from the initial one.
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-2. Use the indistinguishability algorithm to check if the two initial states of the two DFAs are indistinguishable. +
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-3. Check $math[L(A_1) \subseteq L(A_2)] and $math[L(A_2) \subseteq L(A_1)]. The condition $math[L(A) \subseteq L(B)] can be restated as $math[L(A) \cap complement(L(B)) = \emptyset]. Build the complement DFA for B, and use the product construction with A. Check if the resulting DFA has any final state accessible from the initial one.+
 </​hidden>​ </​hidden>​