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

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 NC^1 formula evaluation, suffering a worst-case O(2^|Q|) exponential blowup in query complexity when unrolling re-convergent logic. Conversely, recursive materialization models…