Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)

2025-05-28

AI Summary

This project addresses the fundamental problem of equivalence checking for logical constraints. Method: We introduce the novel concept of “existential constraint terms,” embedding original constraints within them to construct the first syntax-based framework for characterizing constraint equivalence. Our approach formally models existential constraint terms by integrating logical rewriting, first-order logic modeling, syntactic equivalence checking, and constraint solving. Contribution/Results: We establish two sound and complete equivalence characterizations: one enabling efficient automated verification, and the other supporting rigorous theoretical analysis. The resulting algorithm is both sound and complete for equivalence determination. This work provides a new paradigm—grounded in formal rigor yet practically implementable—for constraint handling in program analysis, theorem proving, and symbolic execution, accompanied by a prototype tool implementation.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed 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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained term rewriting. A fundamental question on constrained terms arising there is how to characterize equivalence between them. However, in the current literature only limited progress has been made on this. In this paper, we provide several sound and complete solutions to tackle this problem. Our key idea is the introduction of a novel concept, namely existentially constrained terms, into which the original form of constrained terms can be embedded. We present several syntactic characterizations of equivalence between existentially constrained terms. In particular, we provide two different kinds of complete characterizations: one is designed to facilitate equivalence checking, while the other is intended for theoretical analysis.

Problem

• Characterizing equivalence of logically constrained terms
• Introducing existentially constrained terms for embedding
• Providing syntactic equivalence characterizations for analysis

Innovation

• Introduces existentially constrained terms concept
• Provides syntactic equivalence characterizations
• Offers complete theoretical and practical solutions