Mining on Pegged Side Chains How would mining, theoretically, work in Pegged Side chains?

If mining can be done on these side chains, then it seems like too many coins could be created. And once they were used in transactions, how could they be accounted for to know which coins can and which coins can't be moved back to the main chain?

If mining cannot be done on side chains, then it seems like the side chain system could be very insecure, unless there is another way to secure the system.
Sidechains cannot create the same asset that is pegged to Bitcoins to use as a reward for mining. Obviously, it would be problematic if anyone could put in a certain amount of Bitcoins into a sidechain, and get out more/less than what was originally put in. 

However, there are many other ways to reward miners. Transaction fees is one example that is also used in Bitcoin. The sidechains paper lists some alternative reward mechanisms in section 6.1 such as demurrage (percentage of held coins are redistributed automatically to miners) and creation of a seperate unpegged asset on the side chain to reward miners.