I would like the new AV enginge to remember the last scan so that the next scan will take less time. Something like kasperksky`s “scan new and changed files only”.
I dont know how to explain it better as my english aint good enough.
(I read in the rules that I should add a poll to my request. I dont know how to do that. Anyone??)
I know what you mean. 
But I think a current version of CIS is scanning very fast.
I agree. It is very fast. It was just a thought though. 
Is it something like SFI (Stateful File Inspection) featured since Version 3.9.95478.509 : 15th May, 2009?
I dont know what SFI is. But I think of a way that the AV keeps a record of which files it has scanned.
The first scan will scan your whole computer, the next will scan only the files that has been changed since the first scan or new files added to your computer.
SFI (Antivirus Tasks > Common Tasks > Scanner Settings > Real Time Scanning | Stateful) is an option of realtime module that behaves that way in order to not unnecessarily scan the same files (AFAIK until a signature update) if they were not modified since the last scan.
The necessity of rescanning after a signature update probably limit performance benefits of such approaches to repeated scans in narrow time-frames.
Yes. I think stateful scanning is useless when it comes to scheduled scans. Unless you have scans scheduled every 20 minutes, there is always going to be a virus DB update between scans, so stateful gains you nothing in this respect.