Synthesis of Safety Specifications for Probabilistic Systems

2025-11-20

AI Summary

This paper addresses the challenge of enforcing general temporal safety specifications—beyond conventional probabilistic avoidance constraints—in safety-critical probabilistic systems. We propose a controller synthesis method based on Constrained Probabilistic Computation Tree Logic (CPCTL). Our approach formally reduces global safety requirements to localized constraints, establishing a rigorous synthesis framework that supports full PCTL-level safety properties. We further devise a sound and complete value-iteration algorithm for controller construction. Unlike existing methods limited to simple avoidance, our technique enables unified modeling and synthesis for complex safety properties involving both probability bounds and temporal structure—for instance, “reach a safe set within five steps with probability ≥0.95 while avoiding unsafe states forever.” Experimental evaluation demonstrates the method’s effectiveness, completeness, and scalability across standard probabilistic models.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Programming
• Planning, Routing, and Scheduling: Temporal Planning
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Security and Privacy: Large-scale security measurements
• 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

Abstract

Ensuring that agents satisfy safety specifications can be crucial in safety-critical environments. While methods exist for controller synthesis with safe temporal specifications, most existing methods restrict safe temporal specifications to probabilistic-avoidance constraints. Formal methods typically offer more expressive ways to express safety in probabilistic systems, such as Probabilistic Computation Tree Logic (PCTL) formulas. Thus, in this paper, we develop a new approach that supports more general temporal properties expressed in PCTL. Our contribution is twofold. First, we develop a theoretical framework for the Synthesis of safe-PCTL specifications. We show how the reducing global specification satisfaction to local constraints, and define CPCTL, a fragment of safe-PCTL. We demonstrate how the expressiveness of CPCTL makes it a relevant fragment for the Synthesis Problem. Second, we leverage these results and propose a new Value Iteration-based algorithm to solve the synthesis problem for these more general temporal properties, and we prove the soundness and completeness of our method.

Problem

• Developing a framework for synthesizing safe PCTL specifications
• Reducing global PCTL constraints to local synthesis conditions
• Creating value iteration algorithm for probabilistic temporal logic synthesis

Innovation

• Developed PCTL framework for safety specifications
• Introduced CPCTL fragment to simplify synthesis
• Created Value Iteration algorithm for PCTL properties