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Modelling is an essential procedure in analyzing and controlling a givenlogical dynamic system (LDS). It has been proved that deterministic LDS can bemodeled as a linear-like system using algebraic state space representation.However, due to the inherently non-linear, it is difficult to obtain thealgebraic expression of a stochastic LDS. This paper provides a unifiedframework for transition analysis of LDSs with deterministic and stochasticdynamics. First, modelling of LDS with deterministic dynamics is reviewed. Thenmodeling of LDS with stochastic dynamics is considered, and non-equivalencebetween subsystems and global system is proposed. Next, the reason for thenon-equivalence is provided. Finally, consistency condition is presented forindependent model and conditional independent model.

A Remark on Evolution Equation of Stochastic Logical Dynamic Systems