Question

In all the answers always explain their correctness (or prove it if necessary)

Question 2: Give a deterministic automata for the following languages. The Alphabet Σ = {0, 1} 1. 01". Namely, the strings that start with some number m (it may be that m = 0) of 0 and then some another number n (n may be zero) of 1. 2. The set of all strings with 3 consecutive 0 3. The Language so that every 3 consecutive characters have at least one 0

Answer 1

It is reverse to the previous position and we can't accept string The DFA is rightarrow If we get a consecutive is then simply move to read state and after that no string will be accepted, for that we need a states(q_0,q_1,q_2) and dead state(q_d) rightarrow In every 3 consecutives character's we can have at least as zero \r\n rightarrow If we get one zero after that we can have two is, means upto two is we have accept the string. for that we need 3 final states(q_3,q_4,q_5) rightarrow If we get another 1 in state q_5 then it means we get 3 consecutive is so we moved to dead state.

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