Here is a possible such extension to Peercoin’s proof-of-stake algorithm:

[ol][li]The target inflation varies by the square of the ratio between the number of transactions in each of the two last intervals between self-adjustments.[/li]

[li]The number of transactions expected until the next self-adjustment is the same found in the previous interval between self-adjustments.[/li]

[li]The transaction fee results from dividing the target inflation by the number of transactions expected until the next self-adjustment.[/li]

[li]The remaining inflation or deflation adds to the target inflation and subtracts from the transaction fee.[/li][/ol]

For example, with a fixed money supply of 21,000,000 PPC:

[ol][li]When the algorithm starts:

[list type=decimal]

[li]The money supply is 21,000,000 PPC.[/li]

[li]The target inflation is 0.0001%, or 21,000,000*0.000001=21 PPC.[/li]

[li]The number of expected transactions is 1,000.[/li]

[li]The transaction fee is 21/1,000=0.021.[/li]

[/list][/li]

[li]The network meets the target inflation:

[list type=decimal]

[li]The actual number of transactions was 800:

[list type=decimal]

[li]The paid fees totaled 800*0.021=16.8.[/li]*

[li]There is an excess money supply of 21−16.8=4.2 PPC.[/li]

[/list][/li]

[li]The number of expected transactions becomes 800, so the target inflation becomes 0.000001((800/1,000)^2)=0.00000064:

[list type=decimal]

[li]The target inflation will be (21,000,000*0.00000064)−4.2=9.24 PPC.[/li]

[li]The transaction fee will be (9.24+4.2)/800=0.0168 PPC.[/li]

[/list][/li]

[/list][/li]

[li]Again, the network meets the target inflation:

[list type=decimal]

[li]The actual number of transactions was 1,000:

[list type=decimal]

[li]The paid fees totaled 1,000*0.0168=16.8 PPC.[/li]*

[li]There is an excess money supply of 9.24+4.2−16.8=−3.36 PPC.[/li]

[/list][/li]

[li]The number of expected transactions becomes 1,000, so the target inflation becomes 0.00000064((1,000/800)^2)=0.000001:

[list type=decimal]

[li]The target inflation will be (21,000,000*0.000001)−(−3.36)=24.36 PPC.[/li]

[li]The transaction fee will be (24.36+(−3.36))/1,000=0.021 PPC.[/li]

[/list][/li]

[/list][/li]

[li]Again, the network meets the target inflation:

[list type=decimal]

[li]The actual number of transactions was 1,000:

[list type=decimal]

[li]The paid fees totaled 1,000*0.021=21 PPC.[/li]*

[li]There is an excess money supply of 24.36+(−3.36−21)=0 PPC.[/li]

[/list][/li]

[li]The number of expected transactions becomes 1,000, so the target inflation becomes 0.000001((1,000/1,000)^2)=0.000001:

[list type=decimal]

[li]The target inflation will be (21,000,000*0.000001)−0=21 PPC.[/li]

[li]The transaction fee will be (21+0)/1,000=0.021 PPC.[/li]

[/list][/li]

[/list][/li]

[li]Again, the network meets the target inflation:

[list type=decimal]

[li]The actual number of transactions was 1,200:

[list type=decimal]

[li]The paid fees totaled 1,200*0.021=25.2 PPC.[/li]*

[li]There is an excess money supply of 21+(0−25.2)=−4.2 PPC.[/li]

[/list][/li]

[li]The number of expected transactions becomes 1,200, so the target inflation becomes 0.000001((1,200/1,000)^2)=0.00000144:

[list type=decimal]

[li]The target inflation will be (21,000,000*0.00000144)−(−4.2)=34.44 PPC.[/li]

[li]The transaction fee will be (34.44+(−4.2))/1,200=0.0252 PPC.[/li]

[/list][/li]

[/list][/li]

[li]Etc.[/li][/ol]