I think there are special cases, like Yao's millionaire problem, where you compute a simple predicate to compare two numbers. I do not know whether such a notio

I think there are special cases, like Yao's millionaire problem, where you compute a simple predicate to compare two numbers. I do not know whether such a notion will save you much, though. Because as soon as you can compute a simple instruction like SUBLEQ you have a Turing complete scheme.