Annotated Dependency Pairs for Full Almost-Sure Termination of Probabilistic Term Rewriting

2024-08-13

Principles of Verification

AI Summary

This work addresses the automated verification of almost-sure termination (AST) for probabilistic term rewriting systems under the full-reduction strategy. Existing methods are restricted to innermost rewriting and struggle with basic term sequences. To overcome these limitations, we first extend the annotated dependency pair (ADP) framework to full-reduction semantics and introduce a fine-grained analysis mechanism tailored to basic term sequences defined by single symbols. Methodologically, our approach integrates a probabilistic extension of the dependency pair framework, annotation techniques, and termination graph construction, all implemented within the AProVE tool. Experimental evaluation demonstrates that our framework significantly improves both coverage and precision in AST verification, lifting the constraints imposed by prior innermost-only strategies. This work establishes a novel paradigm for automated termination analysis of probabilistic rewriting systems.

Technology Category

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

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
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Dependency pairs (DPs) are one of the most powerful techniques for automated termination analysis of term rewrite systems. Recently, we adapted the DP framework to the probabilistic setting to prove almost-sure termination (AST) via annotated DPs (ADPs). However, this adaption only handled AST w.r.t. the innermost evaluation strategy. In this paper, we improve the ADP framework to prove AST for full rewriting. Moreover, we refine the framework for rewrite sequences that start with basic terms containing a single defined function symbol. We implemented and evaluated the new framework in our tool AProVE.

Problem

• Probabilistic Systems
• Halting Problem
• Optimization

Innovation

• Improved Dependence Pair Method
• Probabilistic Systems Analysis
• Efficiency Optimization