Find another good example of a model behavior with two distinct but indistinguishable mechanisms.
Find an automatic way to extend the Fermat test into a correct primality test. Slightly more formally, I’d like to have a program which turns (model, explanation of mechanism, advice) --> (mechanism distinguisher), where the advice is shorter than the model+explanation, and where running it on the Fermat test with appropriate advice gives you a proper primality test.
Identify a crisp sense in which primes vs Carmichael numbers aren’t really distinct mechanisms (but sensor tampering would be). If this happens then maybe the only reason the Fermat test feels like a good example is that I’m mischaracterizing it.
Right now I’m trying to either:
Find another good example of a model behavior with two distinct but indistinguishable mechanisms.
Find an automatic way to extend the Fermat test into a correct primality test. Slightly more formally, I’d like to have a program which turns (model, explanation of mechanism, advice) --> (mechanism distinguisher), where the advice is shorter than the model+explanation, and where running it on the Fermat test with appropriate advice gives you a proper primality test.
Identify a crisp sense in which primes vs Carmichael numbers aren’t really distinct mechanisms (but sensor tampering would be). If this happens then maybe the only reason the Fermat test feels like a good example is that I’m mischaracterizing it.