🤖 AI Summary
This study addresses the lack of systematic analysis regarding the normativity and minimality of weak simulation equivalence and coupled similarity—two simulation-induced behavioral equivalences. For the first time, the theory of canonical and minimal quotients is extended to these equivalences. The work proposes an abstraction construction based on labeled transition systems (LTSs), integrating simulation preorders with complexity-theoretic analysis to establish the existence of unique canonical representatives and achieve simultaneous minimization of states and transitions. Furthermore, it proves that the associated minimization problems are NP-complete, thereby filling a significant theoretical gap in the field.
📝 Abstract
Quotients have only been studied for a handful of equivalences in the linear time-branching time spectrum, for which there are results pertaining to canonicity and minimality. We extend these results to weak simulation equivalence and coupled similarity, two closely related equivalences induced by simulation preorders. We describe abstract procedures for transforming an LTS into a unique representative of its equivalence class, and for transforming an LTS into an equivalent state- and transition-minimal LTS. Moreover, we show the minimisation problem is NP-complete.