Design a DFA that every 00 is immediately followed by 1
Last Updated :
28 May, 2020
DFA machines are designed to accept the specific kind of input whose output is generated by the transition of input alphabet from each state.
Approach :
- In this situation, strings all strings are acceptable except more than 3 zeros. In this kind of string no three continuous zeros are acceptable.
- Create initial state and start with minimum length of possible string do transition of its input 0 and 1 to possible states.
- according to transition ,notice the final state and mark it.
Designing DFA step by step :
Step-1:
Make a initial state,say “A”, minimum possible strings are 1 and 0 and also any number of 1 are acceptable.To do this put self loop of 1 on state “A” and make transition of input alphabet 0 to state “B”.Because only 1’s are acceptable so state “A” is termed as final state as well.
Step-2:
As single zero is acceptable in the string so make state “B” is final state.Transect input 0 from state “B” to state “C”.
Step-3:
As every 00 is immediately followed by 1 so now after state “C” do transition of input 1 from state “C” to state “A”.
Step-4:
We are left with transition of input alphabet 1 of state “B”.So make transition of 1 from state “B” to state “A”.
Step-5:
After 00 not more zero is acceptable in continuity.So transect 0 of state “C” to dead state “D”.
Step-6:
Input alphabet 0 and 1 of dead state transect to dead state itself.
Transition Table and Transition rules of above DFA –
State “A” is both final as well as the initial state, state “C” is final state, state “D” is Dead State. Initial state is depicted by —> and final state ids depicted by *.
State |
Input (0) |
Iinput (1) |
—>A* (initial and final state both) |
B |
A |
B* (final state) |
C |
A |
C |
D (dead state) |
A |
D (dead state) |
D (dead state) |
D (dead state) |
Q’: set of finite sets = {A, B, C, D}
set of input alphabets = {0, 1}
Transition Rules tells about the transition function working on each state with each input alphabet.
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