The P-Completeness of Inverted Index Traversal: On the Complexity of Evaluating Boolean Query DAGs

Apple researchers have formally identified that evaluating complex Boolean query structures for AI agents is P-complete, meaning these tasks are computationally difficult to parallelize. This finding suggests that as AI systems increasingly depend on search infrastructure for reasoning, existing methods for processing nested queries may face significant performance limitations. Recognizing these theoretical constraints helps developers better understand the inherent bottlenecks in scaling modern neuro-symbolic search workflows.