1. On the consistency of circuit lower bounds for non-deterministic time
- Author
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació, Universitat Politècnica de Catalunya. ALBCOM - Algorísmia, Bioinformàtica, Complexitat i Mètodes Formals, Atserias, Albert, Buss, Sam, Müller, Moritz, Universitat Politècnica de Catalunya. Departament de Ciències de la Computació, Universitat Politècnica de Catalunya. ALBCOM - Algorísmia, Bioinformàtica, Complexitat i Mètodes Formals, Atserias, Albert, Buss, Sam, and Müller, Moritz
- 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 V20 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. Additionally, we establish a magnification result on the hardness of proving circuit lower bounds., Albert Atserias: Supported in part by Project PID2019-109137GB-C22 (PROOFS) and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) of the Spanish State Research Agency. Sam Buss: Supported in part by Simons Foundation grant 578919., Peer Reviewed, Postprint (author's final draft)
- Published
- 2023