Liu Pyramids and Feedback Iteration Functions on Monoids

Abstract

General concepts of n-dimensional Liu pyramids on monoids and their feedback iteration functions are first created and established. Second, general concepts of initial sets and initial conditions are defined in order to connect the Liu pyramids and their feedback iteration functions. Four examples of 1-dimensional Liu pyramids and their feedback iteration functions, initial set, initial conditions are demonstrated. Then, the 2-dimensional case is discussed in detail. Finally, Liu notation is introduced and employed in the discussion of 3- and higher-dimensional cases.