Regex doesn't fetch the nested curly braces - regex

Question

Curly braces matches sometimes and doesn't in few case.
My Code:
use strict;
use warnings;
my $str1 = '$$\eqalign{&\cases{\mathdot{\bf x}=A{\bf x}+Bu\cr y=H{\bf x}}\quad{\rm with}\{\bf x}=\left(\matrix{x\cr\mathdot{x}\cr\theta\cr\mathdot{\theta}}\right),\cr&A\!=\!\!\left(\matrix{0&1&0&0\cr 0&0&-{m_{a}\over M}g&0\cr 0&0&0&1\cr 0&0&{(M\!+\!m_{a})\over Ml}g&0}\right)\!,\ B\!=\!\left(\matrix{0\cr{a\over M}\cr 0\cr-{a\over Ml}}\right)\!,\ H^{T}\!=\!\left(\matrix{1\cr 0\cr 1\cr 0}\right)\!.}$$';
my $str2 = "\\bibcite{Airdetal2013}{{2}{2017}{{{John} {et~al.}}}{{{James}, {Flexi}, {Buella}, {Curren}, {Mozes}, {Sam}, {Kandan}, {Alexander}, {Alfonsa}, {Fireknight}, {Georgen}, {Karims}, {Merloni}, {Nanda}, {Terra}, {Alvato}, {Nini}, {Winski}, {Shankar}, {Gnali}, \& {Giito}}}}";
my $regex = qr/(?:[^{}]*(?:{(?:[^{}]*(?:{(?:[^{}]*(?:{[^{}]*})*[^{}]*)})*[^{}]*)*})*[^{}]*)*/;
if($str1=~m/\{$regex\}/) { print "str1: $&\n"; }
if($str2=~m/\{$regex\}/) { print "str2: $&\n"; }
OUTPUT:
str1: {&\cases{\mathdot{\bf x}=A{\bf x}+Bu\cr y=H{\bf x}}\quad{\rm with}\ {\bf x}=\left(\matrix{x\cr\mathdot{x}\cr\theta\cr\mathdot{\theta}}\right),\cr&A\!=\!\!\left(\matrix{0&1&0&0\cr 0&0&-{m_{a}\over M}g&0\cr 0&0&0&1\cr 0&0&{(M\!+ !m_{a})\over Ml}g&0}\right)\!,\ B\!=\!\left(\matrix{0\cr{a\over M}\cr 0\cr-{a\over Ml}}\right)\!,\ H^{T}\!=\!\left(\matrix{1\cr 0\cr 1\cr 0}\right)\!.}
str2: {2}
str1 is correct output. str2 incorrect output.
Expected Output on str2 is:
str2: {{2}{2017}{{{John} {et~al.}}}{{{James}, {Flexi}, {Buella}, {Curren}, {Mozes}, {Sam}, {Kandan}, {Alexander}, {Alfonsa}, {Fireknight}, {Georgen}, {Karims}, {Merloni}, {Nanda}, {Terra}, {Alvato}, {Nini}, {Winski}, {Shankar}, {Gnali}, \& {Giito}}}}
In the sample str1 string doesn't matched with the nested curly braces. However the second sample str12 string can matched the nested curly braces.
This is my question can matched the nested curly braces. I am clueless. It would be better if someone point out my mistake.
Thanks in advance.

Answer 1

Since your actual requirements (discussed in the chat) are to match substrings starting with \bib followed with {...} substrings or any chars other than { and }, you should use a regex with a subroutine:
/\\bib(?:({(?:[^{}]++|(?1))*})|(?!\\bib)[^{}])*/g
Details:
\\bib - \bib literal text
(?:({(?:[^{}]++|(?1))*})|(?!\\bib)[^{}])* - 0+ occurrences of:
({(?:[^{}]++|(?1))*}) - Group 1 (that will be recursed with (?1)) matching
{ - a literal {
(?:[^{}]++|(?1))* - 0 or more occurrences of 1+ chars other than { and } or the whole Group 1 subpattern
} - a literal }
| - or
(?!\\bib)[^{}] - a char other than { and } not starting a \bib literal char sequence.
See the sample Perl code:
use strict;
use warnings;
use feature 'say';
my $str2 = "\\bibcite{Airdetal2013}{{2}{2017}{{{John} {et~al.}}}{{{James}, {Flexi}, {Buella}, {Curren}, {Mozes}, {Sam}, {Kandan}, {Alexander}, {Alfonsa}, {Fireknight}, {Georgen}, {Karims}, {Merloni}, {Nanda}, {Terra}, {Alvato}, {Nini}, {Winski}, {Shankar}, {Gnali}, \& {Giito}}}}";
while($str2 =~ /\\bib(?:({(?:[^{}]++|(?1))*})|(?!\\bib)[^{}])*/g) {
say "$&";
}

Answer 2

Note The edit in the question adds \\bibcite{Airdetal2013} in front. However, this doesn't change the analysis below as it doesn't change the overall nesting levels.
This has got to be possible to do in a better way. There is recursive regex offered by Wiktor Stribiżew in comments. There are modules for recursive parsing. And there are tools for parsing Latex.
However, out of curiosity ...
Your string, shortened suitably
my $str2 = "{{2}{2017}{{{John}{et~al.}}}{{{James}, ... {Gnali}, \& {Giito}}}}";
or, with C standing for a pair of curlies with something inside (no nesting)
"{ C C { { C C } { C, ... \& C } } }"
So you have three levels of nesting, to get down to the last pair {...} (no further nesting).
Your regex, spread out and with $nc = qr/[^{}]*/ (Non-Curlies), so that we can look at it
my $regex = qr/
(?: $nc
(?: {
(?: $nc
(?: {
(?: $nc (?: { $nc } )* $nc )
}
)* $nc
)*
}
)* $nc
)*/x;
I can count two levels here. (The $nc has no curlies so { $nc } matches my C above.)
Thus this regex cannot match that whole string.
How to fix it? Best, find another way so to not drown in this.
Or, write it out like above, very carefully, and add the missing level.