Ideas that @maxc on ethresear.ch is working on:
One of the thoughts I’ve had about Truebit is if the multiple rounds of interactive verification are really necessary. Would just one round suffice If you could just check-point the trace of the execution at multiple steps.
I was also wondering if it would be possible to parallelise verification, if for instance, you used witnesses everytime you read in state to the evm and stored the whole machine state at each check-point rather than just the merkle root.
An alternative is to break up a transaction into multiple transactions after say a certain number of steps have been read.
Note that most of the topics in this compendium are concerned with phase 2 and later, or are outdated.