Proving Circuit Lower Bounds in High Uniform Classes

Abstract

Proving circuit lower bounds in uniform classes is one of the grand challenges in computational complexity theory. Particularly, it is well known that proving superpolynomial circuit lower bounds in NP resolves the longstanding conjecture NP 6 ¼ P. Towards the final goal, a lot of work have been dedicated to approaches proving circuit lower bounds in high classes. This tutorial article overviews those proof techniques developed for circuit lower bounds in higher classes than NP such as PH, ZPP NP , MA EXP , PP, Promise-MA, NEXP, and so forth.