Extract multiline output if consist certain word AND inside a bracket - perl

Question

I have an input of such:
Jun 29 16:46:13 iPhone SomeThing[79987] <Notice>: [AppName] file.x:115 DEBUG: ClassNumberOne viewControllers: (
"<UINavigationController: 0x105031a00>",
"<UINavigationController: 0x10505ba00>",
"<UINavigationController: 0x10486fe00>",
"<UINavigationController: 0x105052600>",
"<UINavigationController: 0x105065c00>"
)
Jun 29 16:46:13 iPhone SomeThing[79987] <Notice>: [AppName] file.x:151 DEBUG: ClassNumberTwo ARG2 2
There's two case to be matched here, one is of multi-line, another is of single line. The criteria is that it must have the DEBUG: keyword. For multiline, if that line has the keyword and and a (, then it should match until the end of ). Each line is separated by a newline separator. I can't figure this out. Currently I'm using a simple grep DEBUG: and that's it. But for the multi-line scenario, everything is lost beside the first one. And I'm not familiar with perl, any idea? Thanks in advance!
Note that I'm on iOS (jailbroken), thus another tool might be limited.
EDIT:
Expected output will be the whole line that matched the criteria, that's the same as the input example shown above. The actual input have tonnes of other lines that doesn't have the keyword DEBUG:, and thus will be ignored.

Answer 1

With any awk in any shell on every UNIX box:
$ awk 'f; /\)/{f=0} /DEBUG:/{print; f=/\(/}' file
Jun 29 16:46:13 iPhone SomeThing[79987] <Notice>: [AppName] file.x:115 DEBUG: ClassNumberOne viewControllers: (
"<UINavigationController: 0x105031a00>",
"<UINavigationController: 0x10505ba00>",
"<UINavigationController: 0x10486fe00>",
"<UINavigationController: 0x105052600>",
"<UINavigationController: 0x105065c00>"
)
Jun 29 16:46:13 iPhone SomeThing[79987] <Notice>: [AppName] file.x:151 DEBUG: ClassNumberTwo ARG2 2
Explanation:
awk ' # WHILE read line DO
f; # IF the flag `f` is set THEN print the current line ENDIF
/\)/{f=0} # IF the current line contains `)` THEN clear the flag ENDIF
/DEBUG:/ { # IF the current line contains `DEBUG:` THEN
print; # print the line
f=/\(/ # set the flag `f` to 1 if the line contains `(`, 0 otherwise
} # ENDIF
' file # ENDWHILE

Answer 2

Here is an example of using a Regexp in Perl (but this should probably be handled more accurately by a parser like Regexp::Grammars):
use feature qw(say);
use strict;
use warnings;
my $data = do { local $/; <> };
my #lines = $data
=~ /
^( (?:(?!$).)* DEBUG:
(?:
(?: [^(]*? $ )
|
(?: (?:(?!$).)* \( [^)]* \) .*? $ )
)
)/gmsx;
say for #lines;