Delayed Constraints in Narrowing for the Logic-Based Analyses of Real-Time Systems

2026-07-23

AI Summary

This work addresses the challenge of infinite state spaces in formal analysis of real-time systems arising from unbounded numbers of agents and dense time. To tackle this, the paper proposes a reduction-based symbolic verification approach that integrates rewriting modulo SMT, reductions with logical variables, delay-constraint memorization, and folding mechanisms within a unified framework. This enables terminating bounded or unbounded verification of parameterized real-time systems, such as parameterized timed automata. A prototype implementation built on the Maude rewriting engine successfully verifies a timed mutual exclusion protocol without any bound on the number of processes, demonstrating support for unified analysis across diverse real-time models and significantly enhancing both expressiveness and verification reliability.

Abstract

The formal analysis of real-time systems must address two dimensions of infiniteness: an unbounded number of agents and messages, and a potentially infinite state space induced by dense time. We present a novel narrowing-based verification method that deals with both dimensions. Our approach integrates (i) rewriting modulo SMT for symbolic representation of timing constraints, (ii) narrowing with logical variables to reason about systems with an unknown number of agents, and (iii) a constraint store over partially instantiated terms, in the style of constraint logic programming. We further introduce a folding mechanism that, under certain conditions, ensures termination of the symbolic analysis. The method has been implemented as an extension of the Maude rewriting engine. We evaluate the approach by verifying the correctness of a timed mutual exclusion protocol without imposing bounds on the number of participating processes. Moreover, we show that the framework uniformly supports the analysis of other real-time models, including parametric timed automata with unspecified components that our method can synthesize. Our results suggest that the proposed framework provides a sound and expressive basis for the symbolic verification of real-time rewrite theories.

Problem

• real-time systems
• infinite state space
• unbounded concurrency
• dense time
• formal verification

Innovation

• narrowing
• rewriting modulo SMT
• constraint logic programming
• real-time systems
• symbolic verification