Last talk, we saw that polynomial-time equivalence relation reducibility admits non-reductions between P equivalence relations, which is something that cannot be said about the typical reductions in complexity theory. However, since we are still dealing with polynomial-time reductions, it is not surprising that there are problems that still have implications for open questions about complexity classes.

In this talk, we examine questions purely about our reducibility notion that are equivalent to results about complexity classes, such as P=NP. Also, we introduce some of the more accessible open problems related to this area.