Consider the following finite state machine FSM_1 over the alphabet sigma = {0,

Question

Consider the following finite state machine FSM_1 over the alphabet sigma = {0, 1} S_0 is the starting state. There is no accepting state. Is this finite state machine a valid deterministic finite state machine or invalid? Justify your answer. Which state(s) should be made as (an) accepting state (s) in order for FSM_1 to recognize the languages of strings (sentences) with zero or an even number of 1? Which state(s) should be made as (an) accepting state(s) in order for FSM_1 to recognize the languages of strings (sentences) with odd length?

Explanation / Answer

3a)
Yes, we can have DFA without final state, its valid...Normally DFA with final state are called acceptor..

If we dont have final state its called transducer


3(b) : Zero or Even number of Ones :
S0 will be the final state that will accept zero or even number of ones and none other

3(b) : Strings of Odd Length :
S1 and  S2 are the final states that will contain strings of odd length

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