Database
Abstract This essay extends the unified query algebra framework by incorporating two critical capabilities missing from the original formulation: general aggregation operations and hierarchical data structures. We demonstrate that while posting lists provide a powerful abstraction for many scenarios, they impose restrictions that prevent the framework from handling certain important
Database
Abstract This supplementary essay extends the theoretical framework of unified query algebras across heterogeneous data paradigms by incorporating join operations and multiple field handling. We present a rigorous mathematical formulation that generalizes the posting list abstraction to accommodate joined document tuples while preserving the algebraic properties of the original framework.
Database
Abstract This research essay presents a formal algebraic framework that unifies operations across transaction processing, text retrieval, and vector search paradigms within a single mathematical structure. By establishing posting lists as a universal abstraction with well-defined algebraic properties, we develop a comprehensive theoretical foundation that preserves the expressivity of each