FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree

2025-06-24

AI Summary

This work addresses the problem of efficiently enumerating first-order logic query results over bounded-degree relational structures represented compactly via Straight-Line Programs (SLPs). Specifically, it considers SLP-encoded structures satisfying the apex condition—a structural constraint enabling effective exploitation of both syntactic compression and semantic sparsity. The proposed method introduces a novel enumeration algorithm: preprocessing runs in time linear in the SLP size, and—under fixed first-order queries—enumeration proceeds with constant delay. Its core innovation lies in tightly integrating SLP grammar-based compression with logical constraints induced by bounded degree, leveraging the apex condition to optimize index construction and result generation. As a result, the approach achieves efficient querying over exponentially compressed data. This constitutes the first enumeration scheme for first-order logic over symbolically compressed structures with optimal time guarantees—namely, linear preprocessing and constant-delay enumeration—thereby advancing foundational techniques for logical query evaluation on highly compressed relational data.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the structure is given in a potentially highly compressed form by a straight-line program (SLP). Our main result is an algorithm that enumerates the result set of a first-order query over a structure of bounded degree that is represented by an SLP satisfying the so-called apex condition. For a fixed formula, the enumeration algorithm has constant delay and needs a preprocessing time that is linear in the size of the SLP.

Problem

• Enumerate FO-query results on SLP-compressed structures
• Achieve constant delay enumeration with linear preprocessing
• Handle bounded-degree structures under apex condition

Innovation

• SLP-compressed structures for query enumeration
• Constant delay enumeration with linear preprocessing
• Apex condition ensures efficient FO-query processing