a. 1. The initial value of the counters is 0;
2. Counters are increased when a new page associated with that frame;
3. Counters are decreased when one of the pages associated with that frame is no longer requires;
4. First, search for the page frame with the smallest counter, and then use FIFO to select the page to be replaced.
b. There are 14 page faults occur for the new algorithm for the reference string.
c.
1 2 3 4 5 3 4 1 6 7 8
1 1 1 1 1 6 6 8
2 2 2 5 5 5 5
3 3 3 3 7 7
4 4 4 4 4