Work

On the consistency of circuit lower bounds for non-deterministic time

Year: 2024

Type: article

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 [Formula: see text] is consistent with the conjecture that [Formula: see text], 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 [Formula: see text] replaced by the class of problems decidable in non-deterministic barely superpolynomial time such as [Formula: see text]. Additionally, we establish a magnification result on the hardness of proving circuit lower bounds.

Source: Journal of Mathematical Logic

DOI: 10.1142/s0219061324500235

Authors: Albert Atserias, Sam Buss, Moritz Müller

Institutions: Centre de Recerca Matemàtica, Universitat Politècnica de Catalunya, University of California San Diego, University of Passau

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, University of California, San Diego, Agencia Estatal de Investigación

Awards: G1070868109, G7386763261, G84477964, G8684520763