L = { w belongs {0,1}* | w contain '110' and doesn't contain '010'}
I need to construct DFA that receives L.
How can I draw a DFA that will do the both of conditions?
hints will be a great help.
A finite state machine (or automaton) consists of:
The machine starts in the starting state, and then reads each symbol in turn. When it reads a symbol, it uses the transition table to decide which is the next state. When it reaches the end, it announces success if the current state is in the accepting set; otherwise, it announces failure.
In a deterministic finite-state automaton (DFA), the transition table is single-valued and complete; that is, every entry is filled in with exactly one state. (Constructing a DFA usually involves adding a "sink state", which is non-accepting and has a self-transition on every symbol. This state is used to handle inputs which cannot be at the beginning of an accepted input.)
If you have a DFA which recognises a language L, you can construct a DFA for the complement of L by simply replacing the set of accepting states with the set of non-accepting states. So if you have a DFA which recognises any input containing 010, you can construct a DFA which recognises any input which does not contain 010 by using just changing the accepting state list.
If you have two DFAs which recognise the languages L 1 and L 2 , you can construct a new DFA which recognises only those strings in both L 1 and L 2 -- that is, the intersection L 1 ∩ L 2 -- using the Cartesian product of the two DFAs. In the new machine:
So if you can construct DFAs for:
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