Relating untimed and timed notions of justness

Establish a formal correspondence between justness defined explicitly in untimed process algebras and justness derived from time-divergent (everlasting) runs in timed extensions, including precise conditions under which they coincide.

Background

In timed settings, justness can be interpreted via runs where time grows unboundedly; in untimed settings, it is defined structurally. Clarifying their relationship will enable consistent reasoning when moving between untimed and timed models and may reduce the need for extra justness annotations in timed languages.

References

Open Problem Establish the relationship between notions of justness defined explicitly in untimed process algebra, and those derived from everlasting runs in timed extensions.

— Ensuring Liveness Properties of Distributed Systems: Open Problems  (1912.05616 - Glabbeek, 2019) in Task “Real-time”, Section “A research agenda”