We can write for state-3 comes = state-2 a (aa)* = (aa)*bb* a (aa)*īecause in our DFA, we have three final states so language accepted by DFA is union (+ in RE) of three RL (or three RE). State-3: comes after state-2 then first a then there is a loop via state-6.
State-2: comes after even a then b then any number of b. State-6: Just to differentiate whether odd a or even. You can write for state-5 : Yellow-b followed-by any string of a, b that is = Yellow-b (a + b)* Once you gets b after odd numbers of a(at state-5) every thing is acceptable because there is self a loop for (b,a) at state-5. NOTICE: Once first b has been come, move can't back to state-1 and state-4. Regular Expression for this state is = (aa)*a.įigure: a BLUE states = EVEN number of a, and RED states = ODD number of a has been come. Regular Expression(RE) for this state is = (aa)*. State-1: is START state and information stored in it is even number of a has been come. ( note: In my explanation any number means zero or more times and Λ is null symbol) Let's see what information stored in the DFA (refer my colorful figure). For any Regular Language(RL) a DFA is always possible.
A state stores some information in automate like ON-OFF fan switch.Ī Deterministic-Finite-Automata(DFA) called finite automata because finite amount of memory present in the form of states. In any automata, the purpose of state is like memory element.
#FINITE STATE AUTOMATA NATURAL LANGAUGE HOW TO#
How to write regular expression for a DFA
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