[Paper Review] StocHy: automated verification and synthesis of stochastic processes

Nathalie Cauchi, Kurt Degiorgio+1 more|arXiv (Cornell University)|Jan 29, 2019

Formal Methods in Verification28 references4 citations

TL;DR

StocHy is a C++-based software tool for automated verification and synthesis of discrete-time stochastic hybrid systems (SHS), leveraging formal abstractions as Markov chains or Markov decision processes to enable scalable, precise analysis. It achieves state-of-the-art performance in abstraction error reduction and scalability up to 12 continuous dimensions, with integrated simulation, verification, and policy synthesis engines using sparse matrices, vector calculus, and multi-threading.

ABSTRACT

StocHy is a software tool for the quantitative analysis of discrete-time stochastic hybrid systems (SHS). StocHy accepts a high-level description of stochastic models and constructs an equivalent SHS model. The tool allows to (i) simulate the SHS evolution over a given time horizon; and to automatically construct formal abstractions of the SHS. Abstractions are then employed for (ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy allows for modular modelling, and has separate simulation, verification and synthesis engines, which are implemented as independent libraries. This allows for libraries to be easily used and for extensions to be easily built. The tool is implemented in C++ and employs manipulations based on vector calculus, the use of sparse matrices, the symbolic construction of probabilistic kernels, and multi-threading. Experiments show StocHy's markedly improved performance when compared to existing abstraction-based approaches: in particular, StocHy beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy.

Motivation & Objective

• To address the limited adoption of stochastic hybrid systems (SHS) in real-world applications due to modeling complexity and computational intractability.
• To provide a modular, extensible, and scalable software stack that supports simulation, formal verification, and policy synthesis for SHS.
• To reduce abstraction error and computational cost in verifying and synthesizing policies for SHS with multiple continuous and discrete variables.
• To enable non-expert users to model and analyze complex stochastic systems through high-level, modular abstractions and automated tooling.
• To overcome the curse of dimensionality and undecidability in SHS verification and synthesis via adaptive abstraction refinement and efficient numerical computation.

Proposed method

• StocHy parses high-level state-space models and automatically constructs a standard stochastic hybrid system (SHS) model with discrete modes and continuous state variables.
• It employs symbolic construction of probabilistic kernels and sparse matrix representations to efficiently compute transition probabilities in the abstracted models.
• For verification, it uses two abstraction techniques: general Markov chains for additive disturbance models and interval Markov decision processes (IMDPs) for finite-action models with robustness guarantees.
• It implements adaptive, sequential refinement of abstractions to minimize error while maintaining computational efficiency.
• The simulation engine uses Monte Carlo methods with 5000+ sample paths, generating histograms and visualizations of state evolution and mode transitions.
• The tool integrates symbolic computation, multi-threading, and vector calculus to accelerate kernel construction and state-space exploration.

Experimental results

Research questions

• RQ1 Can automated abstraction of stochastic hybrid systems be made both precise and scalable for high-dimensional models?
• RQ2 How can formal verification and policy synthesis be efficiently integrated into a single software stack for non-expert users?
• RQ3 To what extent can sparse matrix techniques and adaptive refinement reduce abstraction error and computational cost in SHS analysis?
• RQ4 Can a modular, extensible C++ tool achieve performance comparable or superior to existing MATLAB-based tools like faust2 in verification and synthesis tasks?
• RQ5 What is the practical scalability of formal methods for SHS when applied to real-world systems with up to 12 continuous variables?

Key findings

• StocHy reduces abstraction error significantly compared to existing tools, achieving high precision even in high-dimensional models.
• The tool demonstrates scalability to models with up to 12 continuous dimensions, a significant advancement over prior approaches.
• Simulation of a CO2 control system with 5000 Monte Carlo runs completed in 48.6 seconds, with full statistical and visualization output.
• The use of sparse matrices and multi-threading enables faster abstraction generation and reduced memory usage compared to naïve implementations.
• The adaptive abstraction refinement algorithm produces smaller abstraction errors than baseline methods while maintaining computational feasibility.
• The tool outperforms state-of-the-art tools like faust2 in both precision and computational efficiency, particularly in large-scale models.