Disproving (Positive) Almost-Sure Termination of Probabilistic Term Rewriting via Random Walks

2026-02-18

AI Summary

Existing approaches struggle to automatically disprove (positive) almost-sure termination of probabilistic term rewriting systems. This work proposes a novel method that extends qualitative cycle detection to quantitative analysis by embedding a random walk model into computation paths, thereby integrating cycle existence with expected step count estimation to automatically refute non-terminating behaviors. The approach is fully implemented in the tool AProVE and successfully applied to various classes of probabilistic term rewriting systems, significantly enhancing both the automation capability and applicability of termination analysis.

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

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• 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

Abstract

In recent years, numerous techniques were developed to automatically prove termination of different kinds of probabilistic programs. However, there are only few automated methods to disprove their termination. In this paper, we present the first techniques to automatically disprove (positive) almost-sure termination of probabilistic term rewrite systems. Disproving termination of non-probabilistic systems requires finding a finite representation of an infinite computation, e.g., a loop of the rewrite system. We extend such qualitative techniques to probabilistic term rewriting, where a quantitative analysis is required. In addition to the existence of a loop, we have to count the number of such loops in order to embed suitable random walks into a computation, thereby disproving termination. To evaluate their power, we implemented all our techniques in the tool AProVE.

Problem

• probabilistic term rewriting
• almost-sure termination
• termination analysis
• random walks
• non-termination

Innovation

• probabilistic term rewriting
• almost-sure termination
• random walks
• termination disproving
• quantitative analysis