MATT: [demo] Optimistic execution of arbitrary programs

In this email, Johan is responding to someone named aj who pointed out a typo. Johan agrees with aj and acknowledges that it should be O(log n), where n represents the number of steps in the program. Johan explains that P doesn't matter because they never put the whole program on the blockchain; instead, they break it down into n steps. The commitment denotes only how to create the commitment.Johan goes on to explain that when they traverse the tree, the node scripts enforce that h(sub_n ode{1,2}) is consistent with the commitment in the witness. This achieves exactly what aj suggests. To achieve this, the participants agree upfront (when the contract is created) on the exact length of the trace or the depth of the tree. If the actual execution is shorter, they fill the rest with no-ops. This ensures that they know the moment the challenge protocol starts the transactions that will be played, similar to a CTV tree. If one of the participants creates a trace from a non-balanced state tree, it will be rejected by the script at that level.Johan emphasizes the importance of building the state tree in a deterministic way. They also mention that the typo has been fixed.Overall, Johan's response provides clarification and additional details about the topic being discussed.