The Coarsest Precongruences Respecting Safety and Liveness Properties

This paper characterises the coarsest refinement preorders on labelled transition systems that are precongruences for renaming and partially synchronous interleaving operators, and respect all safety, liveness, and conditional liveness properties, respectively.

💡 Research Summary

The paper investigates the problem of identifying the coarsest refinement preorders and equivalence relations on labelled transition systems (LTS) that both respect a given class of behavioural properties and are precongruences for a selected set of process composition operators. The authors adopt a two‑dimensional framework: a class C of properties (safety, liveness, conditional liveness, and more generally linear‑time properties) and a class O of operators (partial synchronous interleaving k_S from CSP, the abstraction/​concealment operator τ_I, and the state‑renaming operator λ_m^s).

Two fundamental requirements are imposed. First, an equivalence ≡ must preserve all properties in C: if p ≡ q then for every ϕ∈C, p satisfies ϕ iff q does. Second, ≡ must be a precongruence for every operator in O: p ≡ q implies C