# Construct a DFA for the following regular expression: a*b*c*a(a+b) Constructing a Deterministic Finite Automata for Regular Expression

Constructing a Deterministic Finite Automata for Regular Expression

A deterministic finite automata (DFA) can be constructed for the regular expression a*b*c*a(a+b). Five components make up a DFA for regular Expressions: state, symbol, transition function (Gorunescu 2017, 2017). The states in this DFA would be Q0, Q1 and q2, while the symbols would be A, B, and C. The start state would then be q0. And the last state, would be the q2. The transition function would be depicted by the following diagram (Khan and Labouardy, 2021):   egin{figure} includegraphics[scale=.83]{a_b_c.jpg} caption{DFA for Regular Expression a*b*c*a(a+b)} end{figure}  The DFA begins at q0 as the start state. If the symbol ‘a’ is seen, then the state moves from q0 to q1; if the symbol ‘b’ is seen, then the state moves from q1 to q2; if the symbol ‘c’ is seen, then the state moves back to q0; if the symbols ‘a’ and ‘b’ are seen again, then the state moves back to q0. The state is considered to have accepted the specified regular expression once it reaches the q2 state. The DFA accepts strings that conform to the regular expression.   References  Gorunescu, F. (2017). Finite Automata. Encyclopedia of Information Science and Technology, 4th edition. pp. 4554-4560). IGI Global.  Khan, S., & Labouardy, H. (2021). Deterministic Finite Automata to Pattern Recognition Automata, Languages and Programming, pp. 304-309). Springer, Cham.Cont…

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