Question

Let B be the language of properly nested parentheses and brackets. For example,$\left(\left[\left(\right)\left(\right)\right]\left(\right)\left[\right]\right)$is in B but $\left([\right)]$is not. Show that B is in L.

Short answer

Every pair of matching parentheses or the brackets must be of the same kind.

Step-by-step solution

Introduce nested parenthesis and L languages

"Nested" parentheses are parentheses that are contained within another parenthesis. The simplification procedure is the same as it was in the previous page simpler examples, but we must be a little more cautious as we work our way through the grouping symbols.

B is in L. 

First, repeat the preceding Exercise technique, replacing [and] with (and). After that, locate matching pairs by repeating the technique for each left parenthesis or brackets in input (by starting the count at that point).

Reject those that are of a different sort and accept the rest.

Final answer

Therefore, when completing the previously mentioned technique on each leftparenthesis/bracket, we employ an extra counter to keep track of our progress by counting how far we moved."