Equivalence of monitorability notions (Aceto et al. vs. Bauer et al.)

Determine whether the monitorability definition used by Aceto et al.—a formula is monitorable if and only if a monitor can be synthesised in their modal μ-calculus framework—is equivalent to the monitorability definition used by Bauer et al. for LTL3, which characterises non-monitorability via the existence of ugly prefixes in the good/bad/ugly prefix classification of finite traces.

Background

The paper discusses two approaches to monitorability. Bauer et al. define good and bad prefixes for LTL properties, and introduce ugly prefixes; the presence of ugly prefixes indicates non-monitorability under their LTL3-based perspective.

Aceto et al. present a positive notion of monitorability in a modal μ-calculus framework by synthesising monitors; a formula is monitorable precisely when such a monitor can be constructed. The authors note the resemblance between these semantics and formula progression and conjecture that these monitorability notions coincide.