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- W4387031651 abstract "We show that there is a language in $mathsf{S}_2mathsf{E}/_1$ (symmetric exponential time with one bit of advice) with circuit complexity at least $2^n/n$. In particular, the above also implies the same near-maximum circuit lower bounds for the classes $Sigma_2mathsf{E}$, $(Sigma_2mathsf{E}capPi_2mathsf{E})/_1$, and $mathsf{ZPE}^{mathsf{NP}}/_1$. Previously, only half-exponential circuit lower bounds for these complexity classes were known, and the smallest complexity class known to require exponential circuit complexity was $Delta_3mathsf{E} = mathsf{E}^{Sigma_2mathsf{P}}$ (Miltersen, Vinodchandran, and Watanabe COCOON'99). Our circuit lower bounds are corollaries of an unconditional zero-error pseudodeterministic algorithm with an $mathsf{NP}$ oracle and one bit of advice ($mathsf{FZPP}^{mathsf{NP}}/_1$) that solves the range avoidance problem infinitely often. This algorithm also implies unconditional infinitely-often pseudodeterministic $mathsf{FZPP}^{mathsf{NP}}/_1$ constructions for Ramsey graphs, rigid matrices, two-source extractors, linear codes, and $mathrm{K}^{mathrm{poly}}$-random strings with nearly optimal parameters. Our proofs relativize. The two main technical ingredients are (1) Korten's $mathsf{P}^{mathsf{NP}}$ reduction from the range avoidance problem to constructing hard truth tables (FOCS'21), which was in turn inspired by a result of Jev{r}'abek on provability in Bounded Arithmetic (Ann. Pure Appl. Log. 2004); and (2) the recent iterative win-win paradigm of Chen, Lu, Oliveira, Ren, and Santhanam (FOCS'23)." @default.
- W4387031651 created "2023-09-26" @default.
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- W4387031651 date "2023-09-22" @default.
- W4387031651 modified "2023-09-27" @default.
- W4387031651 title "Symmetric Exponential Time Requires Near-Maximum Circuit Size" @default.
- W4387031651 doi "https://doi.org/10.48550/arxiv.2309.12912" @default.
- W4387031651 hasPublicationYear "2023" @default.
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