Inputs that provide conflicting signatures can be blacklisted using an approach analogous to colored coins.
So a previous owner of a coin will always have the power to burn the coin, no matter where and when it is sent. If the time is long enough even a single satoshi may taint a huge amount of coins. He may profit through a leveraged short before the attack.
Yes, exactly.
However,
1) If you restrict txns to map no more than one input to each output, then you cannot use a satoshi to taint a huge amount of coins. Essentially this restriction implies that there is nothing prunable in the blockchain. If you do this, x satoshi inputs would taint exactly x satoshi outputs, no more and no less. [I added this to the list of necessary mods to PoA].
2) Taint is not burning the coin. it affects the algorithm used to compare competing candidate chains. It does not affect eligibility for minting rewards, txn rules, etc.. It only comes in to play when multiple competing chain are present. Under normal circumstances, it has no effect on behavior. [It could, but I haven't said that it does. If we allow such effects, it would be necessary to be very careful to limit their potential impact.] I think tainted coins would trade at parity with untainted coins. Who cares enough about voting on the winning chain to pay extra for the privilege of having their vote counted?
3) If you use a fully deterministic system related to Nxt's proposed transparent forging, then you can limit risk of taint to a very small number of coins. Essentially you could limit risk of taint to single satoshis if you allow for 100% deterministic mining.
My plan is to go on to specific details on (3) after questions on the thread die down. Maybe tomorrow or the day after that.
I think you are a nxt developer, so you might find this interesting.
Finally about attacks. To execute a double-spending attack you would set aside a majority of 'clean' sleeper coins. You could not mine or spend these sleeper coins on the main chain. Once they are used for mining or spent, then they become useless for attack purposes. You would then reveal the sleeper coins all in one go by mining on an attack chain. This only works if you control a majority of 'clean satoshis', so that you can overtake the main chain as a solo miner. It is essentially a legitimate exercise of authority associated with 51% ownership. It is intended behavior.
You are right though that you can use past ownership of coins to swing things in your favor to some degree. Essentially, you would want to taint as many coins as possible to increase the influence of your clean coins. Unless you have handled 100% of satoshi's over the chain's lifespan, however, you can't taint every single satoshi out there.