The linear time — Branching time spectrum II

Abstract

This paper studies semantic equivalences and preorders for sequential systems with silent moves, restricting attention to the ones that abstract from successful termination, stochastic and real-time aspects of the investigated systems, and the structure of the visible actions systems can perform. It provides a parameterized definition of such a preorder, such that most such preorders and equivalences found in the literature are obtained by a suitable instantiation of the parameters. Other instantiations yield preorders that combine properties from various semantics. Moreover, the approach shows several ways in which preorders that were originally only considered for systems without silent moves, most notably the ready simulation, can be generalized to an abstract setting, and how preorders that were originally only considered for for systems without divergence, such as the coupled simulation, can be extended to divergent systems. All preorders come with—or rather as—a modal characterization, and when possible also a relational characterization. The paper concludes with some pros and cons of the preorders.