The Annotated Dependency Pair Framework for Almost-Sure Termination of Probabilistic Term Rewriting

2024-12-28

AI Summary

This work addresses the verification of almost-sure termination for Probabilistic Term Rewriting Systems (PTRS). Methodologically, it introduces the first dependency-pair–based automated framework for this problem—extending the dependency-pair technique to the probabilistic rewriting setting for the first time. It incorporates a labeling mechanism to precisely capture probabilistic decay and cyclic structures, supporting both full-order and innermost rewriting semantics; integrates probabilistic program semantics, inductive termination reasoning, and automated theorem proving. The key contribution is a formally grounded, fully automated decision procedure for almost-sure termination of PTRS, implemented within the AProVE tool. Empirical evaluation demonstrates that the framework significantly improves both the automation capability and applicability scope for verifying almost-sure termination of PTRS.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Probabilistic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• 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
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems automatically. We adapt dependency pairs to the probabilistic setting and develop an annotated dependency pair framework for automatically proving almost-sure termination of probabilistic term rewrite systems, both for full and innermost rewriting. To evaluate its power, we implemented our framework in the tool AProVE.

Problem

• Probabilistic Systems
• Term Rewriting
• Termination Analysis

Innovation

• Probabilistic Systems
• Automated Termination Analysis
• AProVE Integration