arXiv Open Access 2025

A Verifier Hierarchy

Maurits Kaptein

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Abstrak

We investigate the trade-off between certificate length and verifier runtime. We prove a Verifier Trade-off Theorem showing that reducing the inherent verification time of a language from \(f(n)\) to \(g(n)\), where \(f(n) \ge g(n)\), requires certificates of length at least \(Ω(\log(f(n) / g(n)))\). This theorem induces a natural hierarchy based on certificate complexity. We demonstrate its applicability to analyzing conjectured separations between complexity classes (e.g., \(\np\) and \(\exptime\)) and to studying natural problems such as string periodicity and rotation detection. Additionally, we provide perspectives on the \(\p\) vs. \(\np\) problem by relating it to the existence of sub-linear certificates.

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cs.LG

Penulis (1)

Maurits Kaptein

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Kaptein, M. (2025). A Verifier Hierarchy. https://arxiv.org/abs/2507.23504

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓