Constructing a DFA from a Regular Expression: How to Handle * and () Operators?

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To construct a DFA from the regular expression a*(ab)*c*, one approach is to first create a non-deterministic finite automaton (NFA) and then convert it into a DFA. The expression indicates that the DFA should accept any number of 'a's followed by zero or more occurrences of the substring 'ab', and ending with any number of 'c's. Clarification was provided that the correct interpretation of the regular expression is a*(ab)*c*, not *a. The discussion emphasizes the importance of understanding the conversion process from NFA to DFA for successful construction.
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Homework Statement


Construct a DFA based on the regular express.

Regular expr = *a(ab)*c*


Homework Equations


How do you construct a DFA out of this regular expr?

The Attempt at a Solution


Here's what I think it says...

it can accept 0 or more a,c, and ordered pair of ab.



the construction of the DFA is where I am stuck.
 
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doh! yeah it's a*(ab)*c*
 
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