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This paper presents a novel theoretical framework for the state spacereduction of Kripke structures. We define two equivalence relations, Kripkeminimization equivalence (KME) and weak Kripke minimization equivalence (WKME).We define the quotient system under these relations and show that theserelations are strictly coarser than strong (bi)simulation anddivergence-sensitive stutter (bi)simulation, respectively. We prove that thequotient system obtained under KME and WKME preserves linear-time andstutter-insensitive linear-time properties. Finally, we show that KME iscompositional w.r.t. synchronous parallel composition.

A Two Step Perspective for Kripke Structure Reduction