🤖 AI Summary
This paper addresses the fundamental limitation in runtime monitoring that branching-time properties—such as those expressible in modal μ-calculus—are inherently unmonitorable over a single execution trace. To overcome this, we propose a novel multi-round execution monitoring paradigm. Integrating monitoring theory, formal semantics, and game theory, we establish—for the first time—a precise theoretical characterization linking the syntactic structure of branching-time formulas to the minimum number of execution rounds required for monitoring, and rigorously prove that multi-round monitoring strictly extends classical monitorability boundaries. Our main contributions are: (1) a systematic characterization of observational power in multi-round monitoring; (2) tight upper and lower bounds on the minimal round complexity; and (3) confirmation that several canonical branching-time properties—including key safety and liveness specifications—become effectively monitorable within two or three rounds. This work provides both a theoretical foundation and a practical methodology for dynamic verification of complex concurrent and interactive behaviors.
📝 Abstract
This paper investigates the observational capabilities of monitors that can observe a system over multiple runs. We study how the augmented monitoring setup affect the class of properties that can be verified at runtime, focussing on branching-time properties expressed in the modal mu-calculus. Our results show that the setup can be used to systematically extend previously established monitorability limits. We also prove bounds that capture the correspondence between the syntactic structure of a branching-time property and the number of system runs required to conduct the verification.
