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I am a bit confused about the notation that is used in the book I am reading.

Let's say I have such a regular expression 

(a + b)*(aa + bb)(a + b)*

So starting from the first one, I will pick either a or b or none then I have to add aa or bb then again I will pick either a or b or none.

so some of the words below belong to this regular expression: aaa aaab bba

but for example abaa is not accepted.

However, the author gives a finite automata like that:

enter image description here

The author says the regular expression belong to this finite automata is 

(a + b)*(aa + bb)(a + b)*

Same like above. But based on the graph, abaa can be achieved. However, I cannot produce abaa with the regular expression above. What am I doing wrong exactly?

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    Your diagram has tiny writing that I cannot read. – 2017-02-08

1 Answers 1

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The confusion comes in interpreting the Kleene star. $(a+b)^\star$ means an arbitrary number of $(a+b)$'s. Hence, this is an arbitrary string, of length $0$ or longer, containing either $a$'s or $b$'s in any order.

To get $abaa$, interpret the expression first as $(a+b)(a+b)(aa+bb)$, where we take the first $(a+b)^\star$ twice and the second $(a+b)^\star$ zero times. Then, interpret this as $abaa$.

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    wow okay. I was applying * operator to the letters inside of the parantheses. thanks!! – 2017-02-08