Quantitative Verification of Omega-regular Properties in Probabilistic Programming

2025-12-25

AI Summary

Existing probabilistic programming inference focuses solely on the posterior distribution over final states upon program termination, failing to characterize temporal evolution of behaviors or ω-regular temporal properties (e.g., “almost-surely visit infinitely often”). Method: We propose Temporal Posterior Inference (TPI), the first framework enabling quantitative posterior inference over execution traces satisfying temporal specifications. TPI integrates Rabin automaton decomposition, stochastic barrier certificate construction, and Bayesian trace inference to derive sound upper and lower bounds on the probability of ω-regular properties. Contribution/Results: Implemented in the TPInfer prototype, TPI efficiently computes tight, controllable probabilistic bounds for complex temporal properties. It ensures rigorous probabilistic guarantees while remaining computationally feasible—overcoming the fundamental limitation of conventional inference methods that disregard trace-level dynamics and restrict analysis to terminal states only.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Planning, Routing, and Scheduling: Temporal Planning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Probabilistic programming provides a high-level framework for specifying statistical models as executable programs with built-in randomness and conditioning. Existing inference techniques, however, typically compute posterior distributions over program states at fixed time points, most often at termination, thereby failing to capture the temporal evolution of probabilistic behaviors. We introduce temporal posterior inference (TPI), a new framework that unifies probabilistic programming with temporal logic by computing posterior distributions over execution traces that satisfy omega-regular specifications, conditioned on possibly temporal observations. To obtain rigorous quantitative guarantees, we develop a new method for computing upper and lower bounds on the satisfaction probabilities of omega-regular properties. Our approach decomposes Rabin acceptance conditions into persistence and recurrence components and constructs stochastic barrier certificates that soundly bound each component. We implement our approach in a prototype tool, TPInfer, and evaluate it on a suite of benchmarks, demonstrating effective and efficient inference over rich temporal properties in probabilistic models.

Problem

• Computes posterior distributions over execution traces with temporal logic
• Provides quantitative bounds on satisfaction probabilities for omega-regular properties
• Unifies probabilistic programming with temporal specifications for dynamic behaviors

Innovation

• Temporal posterior inference for probabilistic programming
• Bounds on omega-regular property satisfaction probabilities
• Stochastic barrier certificates for Rabin condition components