You didn't say what sort of OS your working with, or what sort of process "program_a" is... Did you look into something like this:

open( PROC, "| program_a" );
sleep $n;
close PROC;
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Or maybe program_a isn't a pipeline sort of process -- you could try something like the following -- note that

open( PROC, "| command" )
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returns the process-id of the command that is launched. It's not pretty, and not portable outside of *n*x, but it worked for me (maybe you need better time resolution on the wait; if so, good luck):

$spid = open( SH, "| /bin/sh" );
select SH; $|++;
print "program_a &\n";
$slept = 0;
until ( $ps =~ m{\b$spid\s+$$\s+/bin/sh\b} &&
        $ps =~ m{\b\d+\s+$spid\s+program_a\b} ) {
    sleep 1;  $slept++;
    $ps = `/bin/ps -o pid -o ppid -o comm`;
}
if ($ps =~ m{\b(\d+)\s+$spid\s+sleep\s}) {
    $cpid = $1;
    sleep ($n-$slept) if ( $n>$slept );
    print SH "kill -9 $cpid\n";
} else {
    print "Damn! Lost the kid.\n";
}
close SH;
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If I put parens around the target pid in the "until ()" match, $1 shows up empty outside that block, so I have to do the match again.