Chiefly Symmetric: Results on the Scalability of Probabilistic Model Checking for Operating-System Code

TL;DR

This paper explores the use of symmetry reduction to improve the scalability of probabilistic model checking for low-level operating system code, enabling analysis of larger process counts despite state explosion issues.

Contribution

It demonstrates the effectiveness of symmetry reduction in handling state explosion in probabilistic model checking of OS code with many processes.

Findings

Symmetry reduction enables analysis of models with over a hundred processes.

Inter-process dependencies influence the effectiveness of symmetry reduction.

Naive approaches face rapid state explosion as process numbers increase.

Abstract

Reliability in terms of functional properties from the safety-liveness spectrum is an indispensable requirement of low-level operating-system (OS) code. However, with evermore complex and thus less predictable hardware, quantitative and probabilistic guarantees become more and more important. Probabilistic model checking is one technique to automatically obtain these guarantees. First experiences with the automated quantitative analysis of low-level operating-system code confirm the expectation that the naive probabilistic model checking approach rapidly reaches its limits when increasing the numbers of processes. This paper reports on our work-in-progress to tackle the state explosion problem for low-level OS-code caused by the exponential blow-up of the model size when the number of processes grows. We studied the symmetry reduction approach and carried out our experiments with a simple test-and-test-and-set lock case study as a representative example for a wide range of protocols with natural inter-process dependencies and long-run properties. We quickly see a state-space explosion for scenarios where inter-process dependencies are insignificant. However, once inter-process dependencies dominate the picture models with hundred and more processes can be constructed and analysed.