An Adequate While-Language for Stochastic Hybrid Computation

2025-07-21

AI Summary

This work addresses hybrid systems exhibiting both continuous differential dynamics and stochastic behavior—such as adaptive cruise control, Brownian motion, and multi-collision physical processes. We propose an extended While-language supporting stochastic hybrid computation. For the first time, we establish rigorous, unified operational and denotational semantics for such programs and prove their adequacy theorem, thereby filling a foundational gap in the semantic theory of stochastic hybrid programs. The language design balances expressiveness and verifiability, enabling joint modeling of ordinary differential equations and probabilistic distributions. Leveraging the formal semantics, we implement an interpreter prototype and validate its correctness and modeling fidelity on representative case studies. Our core contribution is the construction of the first complete, verification-oriented semantic framework for stochastic hybrid programs—providing a sound foundation for rigorous analysis, verification, and implementation of such systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

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

Abstract

We introduce a language for formally reasoning about programs that combine differential constructs with probabilistic ones. The language harbours, for example, such systems as adaptive cruise controllers, continuous-time random walks, and physical processes involving multiple collisions, like in Einstein's Brownian motion. We furnish the language with an operational semantics and use it to implement a corresponding interpreter. We also present a complementary, denotational semantics and establish an adequacy theorem between both cases.

Problem

• Formally reason about programs combining differential and probabilistic constructs
• Model systems like adaptive cruise controllers and Brownian motion
• Establish operational and denotational semantics with adequacy theorem

Innovation

• Language combines differential and probabilistic constructs
• Provides operational and denotational semantics
• Implements interpreter for stochastic hybrid computation