What if the Zerocoin protocol specified that the mining algorithm should be changed every so often?
While not impossible for ASIC mining to occur, creating a moving target for ASIC miner manufacturers would make it much less appealing to them. At least, in my opinion.
We have not ruled out doing this. I’m personally very keen on reserving the option to change the proof of work. Even the possibility of doing so may be sufficient to discourage ASIC vendors from putting up the R&D investment, and to limit their potential customer base, if we make clear that we’re serious about ASIC resistance.
Bitcoin would require a choice between double-SHA-256 and a new proof-of-work algorithm for compatibility. Zcash doesn’t require that, because it is starting with an algorithm that is as “egalitarian” as we can make it. There’s no need to incur complexity when we don’t know that there’s any problem with Equihash.
As for increasing the memory requirement, we can fairly easily do that. Let’s see how the parameters we will use at launch work out first.