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Unformatted text preview: (d) to obtain the initial state of add a new state and addtransitions too all states which were ﬁnal states in . The newly added state is the initial state of . (e) there is only one ﬁnal state, namely the state which was initial state in Why this works: A word is accepted in if there is a path from the initial state to the ﬁnal state. But given the construction this means that in there is a path from the initial state to one of the ﬁnal states. Therefore if if . The above argument works the other way around, therefore implies . This proves that 3. 3 points Design a nondeterministic ﬁnite automaton for the following language. has 101 as a substring 1 1 0,1 0,1...
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 Summer '99
 Paturi
 Regular expression, Nondeterministic finite state machine, 30 Minutes, initial state

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