The $\mathbf{P}$-Completeness of Inverted Index Traversal: On the Complexity of Evaluating Boolean Query DAGs
arXiv:2601.18747v2 Announce Type: replace-cross Abstract: Modern AI agents increasingly rely on search infrastructure to execute complex, neuro-symbolic reasoning workflows. These workflows often compile into deeply nested, non-monotonic Boolean queries over text fields. However, standard query evaluation strategies over inverted indices face severe theoretical limits when handling these structures. Stateful iterator models (Document-at-a-Time) are structurally bounded by $\text{NC}^1$ formula evaluation, suffering a worst-case $O(2^{|Q|})$ exponential blowup in query complexity when unrolling
This paper addresses a fundamental computational bottleneck that has emerged as AI agents become more sophisticated and rely on complex search infrastructure.
The identified P-completeness implies inherent computational limits for certain types of advanced AI queries, directly impacting the scalability and performance of next-generation AI agents.
Understanding these computational limits will force a re-evaluation of current AI agent architectures and query optimization strategies for more efficient neuro-symbolic reasoning.
- · AI researchers specializing in complexity theory
- · Companies developing novel query optimization techniques
- · Developers of specialized AI agent architectures
- · AI agent developers relying on naive query evaluation
- · Systems with deeply nested Boolean query architectures
- · Traditional inverted index traversal methods
This research will lead to new algorithmic approaches for managing complex Boolean queries in AI agents.
The necessity for more efficient query processing could drive innovation in specialized hardware or distributed computing for AI search.
These foundational limits might eventually influence the design principles for general-purpose AI and autonomous systems, favoring architectures that intrinsically manage query complexity.
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Read at arXiv cs.AI