From Innermost to Full Probabilistic Term Rewriting: Almost-Sure Termination, Complexity, and Modularity

2024-09-26

arXiv.org

AI Summary

This work addresses the automated verification of almost-sure termination (AST) and complexity for Probabilistic Term Rewriting Systems (PTRS), focusing on whether innermost rewriting suffices to guarantee reliable full rewriting behavior. We first adapt the deterministic “innermost termination implies full termination” implication to the probabilistic setting, establishing the first semantic-implication-based modular sufficient condition for AST. This yields a novel theoretical bridge: innermost AST ⇒ full-system AST. Methodologically, we integrate probabilistic modeling, inductive reasoning, and semantic verification within the automated tool AProVE. Experimental evaluation demonstrates that our decision criterion significantly improves the automation of AST and complexity analysis, enabling more efficient and modular reliability verification of probabilistic programs. (128 words)

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

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies full termination or when runtime complexity and innermost runtime complexity coincide. We adapt these criteria to the probabilistic setting, e.g., we show when it suffices to analyze almost-sure termination w.r.t. innermost rewriting in order to prove full almost-sure termination of probabilistic term rewrite systems. These criteria can be applied for both termination and complexity analysis in the probabilistic setting. We implemented and evaluated our new contributions in the tool AProVE. Moreover, we also use our new results on innermost and full probabilistic rewriting to investigate the modularity of probabilistic termination properties.

Problem

• Adapting termination criteria from innermost to full probabilistic rewriting
• Proving almost-sure termination for probabilistic term rewrite systems
• Investigating modularity of probabilistic termination properties

Innovation

• Adapting innermost termination criteria to probabilistic setting
• Proving full almost-sure termination via innermost rewriting
• Implementing criteria in AProVE for probabilistic analysis