OutputP Membership of Minimal Hypergraph Transversal Enumeration

Determine whether enumerating the minimal transversals of a hypergraph belongs to OutputP.

Background

The paper compares enumeration on ordinary compiled representations with enumeration after applying the dual-rail encoding. It notes that enumerating prime-implicant explanations of an arbitrary model of an OBDD is at least as hard as enumerating the minimal transversals of a hypergraph. The complexity status of the latter enumeration problem is identified as unresolved, making its membership in OutputP an explicit open question relevant to the tractability of explanation enumeration.

References

In contrast, it showed that enumerating the prime implicant explanations of an arbitrary model of an $\mathtt{OBDD}$ ($\mathtt{Enum_{srs}[OBDD]}$) is at least as hard as enumerating the minimal transversals of a hypergraph, an enumeration problem whose membership to OutputP is a longstanding open question in complexity theory.

— Solving Hard XAI Queries Based on a Compiled Dual-Rail Encoding  (2609.04931 - Ledaguenel et al., 4 Sep 2026) in Section 4, paragraph “Enumeration”