The state execution model where the chain is only being used for data availability is similar to one described here. One optimization to allow light clients to know that they’re being served the complete set of transactions for accounts they care about, is to use a Merkle tree where intermediate nodes are labelled with the range of accounts which there are transactions for in all the leafs that can be reached from that intermediate node.
The exit game described is interesting because it allows for an application A to “read” state from an application B, without requiring the users of A to read the entire state of B.
But these schemes pose a significant challenge: they complicate the fee market. Particularly, unless block producers are aware of how all of these layer-2 state schemes work (unlikely; there are just too many possible designs), if someone attempts to pay fees inside of one of these schemes then the block producer has no way to determine whether or not a fee is actually being paid.
In LazyLedger, I use a scheme where you can pay block producers in any arbitrary currency application/contract that the block producer recognizes. You submit a fee transaction using that currency application, such the transaction is only valid if some other transaction corresponding to a specified hash is included in the same block’s Merkle root of transactions, since we only care about the data availability of that transaction. The block producer must compute the state of the currency application they’re accepting fees in to check that the fee transaction is valid.
I had another idea for those schemes that allow spending money on any of the shards: What if you added in a mechanism that immediately burns the money if it was double spent? It would basically eliminate any incentive for someone to try and cheat by reverting one chart and getting their double-spending transaction in earlier.
Wouldn’t the fact that you can burn other people’s money at any time in the future mean that you can blackmail people to sending you more money or otherwise you’ll burn it? The longer you wait, the more transactions would have been made on top of your transactions, and the more money you can burn. As you also have to burn the money that your recipient sent, and so on, otherwise you have a money inflation vulnerability. If money changes hands a lot, then in the future you might be able to burn the entire supply.