Monitorability for the Hennessy–Milner logic with recursion

Trace Partitioning and Local Monitoring for Asynchronous Components

“…is shown not to be monitorable in the setting of [15,16]: to detect a violation, it requires at least two witness execution traces, one showing that action s can be performed at start-up, another showing that o can be performed at start-up. Monitorability in traditional RV settings typically assumes one execution trace.…”

“…The monitor may also reach an inconclusive verdict whenever the trace exhibited by the system does not yield the necessary information for it to reach a definitive judgement. Following [15,16], this paper uses the safety fragment of the branching-time logic µHML [23,1], called sHML (Safety HML), which has been shown to be monitorable and maximally expressive w.r.t. the constraints of runtime monitoring.…”

“…As in [15,16], the semantics of sHML, defined for closed formulae (i.e., without free variables) is interpreted over Labelled Transition Systems (LTSs) -graphs modelling the branching behaviour of systems (see Fig. 3 for examples).…”

“…In [15,16], the authors show that any sHML formula is monitorable for violations exclusively (i.e., the monitor for ϕ can reach a rejection verdict whenever p / ∈ ϕ ). We note in passing that the full logic µHML contains other logical operators, such as disjunctions, ϕ ∨ φ, with the expected interpretation; [15,16] show that disjunctions such as ϕ ∨ φ are not monitorable for violations, even when the subformulae ϕ and φ are. Consult [15,16] for more details.…”

“…Recent work [15,4,8,28,16] studies the application of online RV to general specification properties describing the branching structure of the system under scrutiny. This is of particular relevance to concurrent (component) systems with multiple executions.…”