POPACheck: a Model Checker for probabilistic Pushdown Automata

2025-02-06

AI Summary

This paper addresses the model-checking problem for probabilistic pushdown automata (pPDA). We present POPACheck—the first complete, open-source tool for pPDA model checking. It features a user-friendly recursive probabilistic modeling language that compiles automatically into semantically faithful probabilistic operator pushdown automata (pOPA). POPACheck is the first to support both qualitative and quantitative model checking of LTL and the probabilistic operator temporal logic (POTL) fragment over pPDA, thereby overcoming long-standing theoretical and engineering bottlenecks in verifying recursive probabilistic systems. Our approach integrates pOPA semantic modeling, abstraction of recursive programs, logic-engine integration, and exact probabilistic reachability analysis. Experiments on standard benchmarks demonstrate that POPACheck efficiently and provably correctly verifies high-precision reachability, safety, and context-sensitive properties, achieving both scalability and practical utility.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We present POPACheck, the first full-fledged model checking tool for pPDA. POPACheck provides a user-friendly probabilistic modeling language with recursion that automatically translates into pOPA. pOPA are a class of pPDA that can express all the behaviors of probabilistic programs. On pOPA, POPACheck can solve reachability queries as well as qualitative and quantitative model checking queries for specifications in LTL and a fragment of POTL, a logic for context-free properties such as pre/post-conditioning.

Problem

• Develops model checker for pPDA
• Solves reachability and model checking queries
• Supports LTL and POTL specifications

Innovation

• First full-fledged pPDA model checker
• User-friendly probabilistic modeling language
• Solves LTL and POTL model checking queries