1. Why do we care about minimizing DFA's ?Because, For DFA there is a nice algebraic structure that determines which states can beequivalent, the Myhill-Nerode equivalence on strings is related to minimization of DFA.2. Minimize the following DFA. What Language does it generate?DFA minimization is usually done in three steps, corresponding to the removal/merger of therelevant states. Since the elimination of nondistinguishable states is computationally the mostexpensive one, it is usually done as the last step.Minimization :Now we turn to examining how to reduce the size of a DFA such that it still recognizes the samelanguage. This is useful because some transformations and tools will generate DFAs with a largeamount of redundancy.3. Minimize the following DFA. What Language does it generate?The language { w | w contains the substring 0101, i.e., w = x0101y for some x, y } withfive states.4. Minimize the following DFA. What Language does it generate?The language {} with one state.5. Give a regular grammar that generates the same language as the DFA in problem 2.6. Give a regular grammars that generates the same language as the following regularexpressions:a. 010*r7 = 1 S1 1 r6 = 0 S2 0 r2= r6r7 S3 S2S1 r5 = 1 S4 1 r4 = 0 S5 0 r3 = (r4+r5) S6 S4| S5 r1= r3* S7 S6S7| r = r1r2 S8 S7Sb. a(ab + bc)*S AB A aaA| B Bb | S AB aaAB aaABb7. Is the following a valid argument ...

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