Hierarchies within TFNP: building blocks and collapses
Surendra Ghentiyala, Zeyong Li

TL;DR
This paper explores the internal structure of TFNP subclasses, introduces hierarchies with oracle access, and proves collapses of these hierarchies, providing new tools for classifying problems like prime generation.
Contribution
It defines TFNP classes with oracle gates, proves certain hierarchies collapse, and offers a new framework for classifying and separating problems within TFNP.
Findings
Several TFNP subclasses are self-low, leading to hierarchy collapses.
Hierarchies such as PPA^PPA and PLS^PLS collapse to their base classes.
Prime number generation is in PPP^PPP under GRH.
Abstract
In all well-studied subclasses (e.g. etc.), the canonical complete problem takes as input a polynomial-size circuit whose input-output behavior implicitly encodes an exponentially large object , i.e. is the succinct (polynomial-size) representation of the exponential size object . The goal is to find some particular substructure in which can be confirmed in polynomial time using queries to . We initiate the study of classes of the form where both and are subclasses. In particular, we define complete problems for these classes that take as input a circuit which is allowed oracle gates to another class. Beyond introducing definitions for oracle problems, our specific technical…
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