I'm just having a little trouble understanding the precedence relationship between the concatenation and union operators in regular expressions.
Specifically (for my problem), given the regular expression:
$(aa^*+ba^*)^* . (bbb+ab^*)+(ab)^*$
Would it be correct to treat the order of operation as follows:
$((aa^*+ba^*)^* . (bbb+ab^*))+(ab)^*$
Thank you in advance.
The order of operations, for regular operations is star (highest precedence), product, union. Thus you are right, $(aa^*+ba^*)^* (bbb+ab^*)+(ab)^*$ is equivalent to $((aa^*+ba^*)^* (bbb+ab^*))+(ab)^*$. Note however that you should avoid the dot in your expressions, otherwise you should also write $a \cdot a^*$ for instance.
By the way, this is the same precedence order than for the three operations exponent, product, sum for numbers.