From G\"odel incompleteness to the consistency of circuit lower bounds

Albert Atserias; Moritz Müller

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arXiv · 2604.25251

From G\"odel incompleteness to the consistency of circuit lower bounds

Albert Atserias·Moritz Müller

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Abstract

We prove that the bounded arithmetic theory $S^1_2$ is consistent with EXP $\not\subseteq$ P/poly. More generally, we show that certain separations of $V^1_2$ from a theory $T$ imply the consistency of $T$ with EXP $\not\subseteq$ P/poly. For $T=S^1_2$, Takeuti (1988) established such a separation using a variant of G\"odel's consistency statement. Analogous results hold for PSPACE $\not\subseteq$ P/poly but the required separations of theories are yet unknown. Finally, we give magnification results for the hardness of proving almost-everywhere versions of these lower bounds.

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BibTeX RIS

Albert Atserias, Moritz Müller. 2026-04-28. From G\"odel incompleteness to the consistency of circuit lower bounds. https://arxiv.org/abs/2604.25251

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