Small Circuits and Dual Weak PHP in the Universal Theory of p-time Algorithms
Jan Krajíček · ACM Transactions on Computational Logic · 2021
We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms that a specific p-time function extending bits to bits violates the dual weak pigeonhole principle: Every string equals the value of the function for some . The function is the truth-table function assigning to a circuit the table of the function it computes and the hypothesis is that every language in P has circuits of a fixed polynomial size .