# Adventures in Monitorability: From Branching to Linear Time and Back Again

arXiv: https://arxiv.org/abs/1902.00435 · HTML: https://mlsanity.com/paper/1902.00435/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Towards Partial Monitoring: It is Always too Soon to Give Up](https://mlsanity.com/paper/2110.12585/) (2021)
- [Analyzing the Narration Gap in LLM-Solver Loops](https://mlsanity.com/paper/2606.19588/) (2026)

## Abstract (arXiv)

This paper establishes a comprehensive theory of runtime monitorability for Hennessy-Milner logic with recursion, a very expressive variant of the modal μ-calculus. It investigates the monitorability of that logic with a linear-time semantics and then compares the obtained results with ones that were previously presented in the literature for a branching-time setting. Our work establishes an expressiveness hierarchy of monitorable fragments of Hennessy-Milner logic with recursion in a linear-time setting and exactly identifies what kinds of guarantees can be given using runtime monitors for each fragment in the hierarchy. Each fragment is shown to be complete, in the sense that it can express all properties that can be monitored under the corresponding guarantees. The study is carried out using a principled approach to monitoring that connects the semantics of the logic and the operational semantics of monitors. The proposed framework supports the automatic, compositional synthesis of correct monitors from monitorable properties.