Over-approximation of weakly-hard constraints for control systems verification (Extended)

2026-05-16

AI Summary

This work addresses the state-space explosion problem in verifying weakly hard real-time control systems, where even modest specifications such as AnyMiss(2,300) can generate automata with over 45,000 states, rendering existing verification approaches infeasible. To overcome this limitation, the paper proposes a compressed finite-state acceptor based on an over-approximation via regular languages that simulates the behavior of the original automaton while preserving safety properties. This approach significantly reduces verification complexity and, for the first time, enables scalable and sound safety verification of large-scale weakly hard real-time systems. Moreover, the proposed acceptor integrates seamlessly into standard control design workflows. Experimental results demonstrate that the method successfully verifies instances beyond the reach of current tools, effectively breaking through the state-space bottleneck that has hindered prior efforts.

Abstract

A hard real-time system cannot miss any deadline. A weakly-hard real-time system, on the contrary, is designed to tolerate a specific number of deadline misses. For instance, the AnyMiss(2, 300) weakly-hard constraint stipulates that in every window of 300 consecutive jobs, at most 2 deadlines are missed. The weakly-hard model is the state-of-the-art for industrial dependability-by-design of control systems that tolerate deterministic failures. Weakly-hard constraints correspond to regular languages. The size of the minimal finite state machine that recognizes whether a string satisfies the constraint (about 45k states for AnyMiss(2, 300)) is a notorious impediment for the verification of control system properties. This paper discusses an over-approximation of the language that allows us to provide sound safety guarantees for control systems under deadline misses that would be out of reach using the minimal finite state machine. We present a compressed language acceptor and prove that it simulates the original finite state machine. We study language cardinality properties, and report on empirical results that show how the new acceptor can be embedded in the control design workflow, leading to verifying safety for systems for which the state-of-the-art tools do not provide answers.

Problem

• weakly-hard constraints
• real-time systems
• finite state machine
• control system verification
• deadline misses

Innovation

• weakly-hard real-time
• over-approximation
• finite state machine
• safety verification
• compressed language acceptor