I have been using Avast since 5 years and the FP problems has been never solved. Among all antivirus software is the one that find more FP. On my pc, Window 8.1 I use SONGR and CDBURNER portable versions since 1 year, but who knows why, today AVAST detected the two programs as virus, I know they are both 100% virus free, but Avast is disagree.
You can report a possible FP here: http://www.avast.com/contact-us.php?subject=VIRUS-FILE
FP problems are and will be solved.