Synthesising correct concurrent runtime monitors

This paper studies the correctness of automated synthesis for concurrent monitors. We adapt a subset of the Hennessy–Milner logic with recursion (a reformulation of the modal μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-calculus) to specify safety properties for Erlang programs. We also define an automated translation from formulas in this sub-logic to concurrent Erlang monitors that detect formula violations at runtime. Subsequently, we formalise a novel definition for monitor correctness that incorporates monitor behaviour when instrumented with the program being monitored. Finally, we devise a sound technique that allows us to prove monitor correctness in stages; this technique is used to prove the correctness of our automated monitor synthesis.