Two-thirds simulation topology

Two-thirds simulation provides a kind of abstract description for the implementation of satisfying its specification. In order to characterize the implementation closer to its specification more and more, based on the definition of limit and two-thirds simulation, the limit and topology theories of two-thirds simulation are proposed. Firstly, two-thirds limit simulation and two-thirds simulation limit are defined. The limit theory of two-thirds simulation is established. Secondly, topological structure of two-thirds simulation is constructed, including subnet closure, tail closure, natural extension and iteration. Two-thirds simulation limit is demonstrated to form a convergence class, which induces a topology. Finally, pre-congruence property of two-thirds simulation limit is showed, which states the continuity of various combined operators under two-thirds simulation limit.