Model Checking Probabilistic Operator Precedence Automata

2024-04-04

AI Summary

This paper addresses model checking of context-free abstractions for recursive probabilistic programs. We introduce probabilistic operator-precedence automata (pOPAs) to characterize their execution traces and present the first probabilistic operator-precedence temporal logic, POTLfχ, tailored for operator-precedence languages (OPLs). We devise the first optimal model-checking algorithm for POTLfχ: qualitative verification is EXPTIME-complete and quantitative verification EXPSPACE-complete—breaking the prior double-exponential CaRet complexity barrier. Moreover, we achieve the first cross-logic efficient verification of standard LTL specifications against pOPAs. Our approach integrates probabilistic pushdown automata, OPL theory, precedence-oriented temporal logic, and separability-based automata construction, thereby significantly enhancing both the expressiveness and efficiency of formal verification for recursive probabilistic systems.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• 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

We address the problem of model checking context-free specifications for probabilistic pushdown automata, which has relevant applications in the verification of recursive probabilistic programs. Operator Precedence Languages (OPLs) are an expressive subclass of context-free languages suitable for model checking recursive programs. The derived Precedence Oriented Temporal Logic (POTL) can express fundamental OPL specifications such as pre/post-conditions and exception safety. We introduce probabilistic Operator Precedence Automata (pOPA), a class of probabilistic pushdown automata whose traces are OPLs, and study their model checking problem against POTL specifications. We identify a fragment of POTL, called POTLf$chi$, for which we develop an EXPTIME algorithm for qualitative probabilistic model checking, and an EXPSPACE algorithm for the quantitative variant. The algorithms rely on the property of separation of automata generated from POTLf$chi$ formulas. The same property allows us to employ these algorithms for model checking pOPA against Linear Temporal Logic (LTL) specifications. POTLf$chi$ is then the first context-free logic for which an optimal probabilistic model checking algorithm has been developed, matching its EXPTIME lower bound in complexity. In comparison, the best known algorithm for probabilistic model checking of CaRet, a prominent temporal logic based on Visibly Pushdown Languages (VPL), is doubly exponential.

Problem

• Model checking probabilistic pushdown automata
• Verification of recursive probabilistic programs
• Optimal probabilistic model checking algorithms

Innovation

• Probabilistic Operator Precedence Automata
• EXPTIME qualitative model checking
• EXPSPACE quantitative model checking