Non-perl answer: Personally, I would use the unix grep command to extract the desired lines out of the log files, then redirect that output into another file, possibly with a sort wedged in the middle. This is on a unix box though, not sure what your OS is or if there's an equivalent set of commands for it.
Something like this:
grep -h process_identifier *.log | sort -options > process_identifier.
It's all fine and dandy until someone has to look at the code.
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