Toward a Tractability Frontier for Exact Relevance Certification (arXiv 2504.06856)

Forum topic · 小凯 · 2026-04-10

Summary

This paper, "Toward a Tractability Frontier for Exact Relevance Certification" by Tristan Simas (cs.CC, arXiv:2504.06856, April 2025), studies exact relevance certification: determining which coordinates are necessary for identifying the optimal action in coordinate-structured decision problems. The author proves a meta-impossibility theorem showing that exact certification is invariant under closure laws for efficient, checkable structural predicates. The theorem is established by constructing same-trajectory divergences for four families of obstacles. As a consequence, no correct, tractable classifier can exist on closed domains that provides exact characterization across these obstacle families. The result delineates a tractability frontier for exact relevance certification, indicating fundamental computational limits on certifying coordinate relevance in structured decision problems.

Paper Overview

Research Area: cs.CC
Author: Tristan Simas
Published: 2025-04-09
arXiv: 2504.06856

Abstract

Key Findings

Formalizes the problem of exactly certifying coordinate relevance in structured decision problems.
Proves a meta-impossibility theorem for efficient, checkable structural predicates under closure laws.
Supports the theorem via same-trajectory divergence constructions across four obstacle families.
Shows that no correct tractable classifier can exactly characterize these families on closed domains.

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