On the consistency of stronger lower bounds for NEXP

Neil Thapen

doi:10.48550/arxiv.2504.03320

April 4, 2025Open Access

On the consistency of stronger lower bounds for NEXP

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Key Points

Stronger conjectures about NEXP showing consistency could reshape our understanding of complexity theory.
Key findings reveal that NEXP not in EXP / poly and NEXP not in coNEXP may hold under new theories.
Consistent observations extend reach of bounded arithmetic theory in complexity considerations.
Implications point towards a richer framework for understanding universal number-sorting within these bounds.

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Implication

This research extends earlier findings on NEXP, indicating new consistency with stronger theories in complexity theory.

Abstract

It was recently shown by Atserias, Buss and Mueller that the standard complexity-theoretic conjecture NEXP not in P / poly is consistent with the relatively strong bounded arithmetic theory V^0_2, which can prove a substantial part of complexity theory. We observe that their approach can be extended to show that the stronger conjectures NEXP not in EXP / poly and NEXP not in coNEXP are consistent with a stronger theory, which includes every true universal number-sort sentence.

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Neil Thapen (2025) studied this question.

synapsesocial.com/papers/690e8b6ca5b062d7a4e7364d https://doi.org/10.48550/arxiv.2504.03320

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On the consistency of stronger lower bounds for NEXP

Key Points

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Implication

Abstract

Discussion

Cite This Study

On the consistency of stronger lower bounds for NEXP

Key Points

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Implication

Abstract

Discussion

Cite This Study

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