[Proof Complexity] (no subject)

[Müller, Moritz]

Dear all,

A new paper  is available at ArXiv:

https://arxiv.org/abs/2303.01016

On the Consistency of Circuit Lower Bounds for Non-Deterministic Time
Albert Atserias, Sam Buss, Moritz Müller  

Abstract: We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory V02 is consistent with the conjecture that NEXP ⊈ P/poly, i.e., some problem that is solvable in non-deterministic exponential time does not have polynomial size circuits. We suggest this is the best currently available evidence for the truth of the conjecture. The same techniques establish the same results with NEXP replaced by the class of problems that are decidable in non-deterministic barely superpolynomial time such as NTIME(n^O(logloglog n)). Additionally, we establish a magnification result on the hardness of proving circuit lower bounds.

Comments are most welcome.

Best regards,

Moritz Müller