The task of a criticism algorithm is to produce a statement of how a given object is understood and appraised as a work of art using some given approach to art. The task of a design algorithm is to produce an object as a work of art in response to given initial conditions using some given approach to art. For both criticism algorithms and design algorithms, the key part is the computational component (see Chapter 4). The computational component in a criticism algorithm consists of an aesthetic viewpoint and an analysis procedure. The computational component in a design algorithm consists of an aesthetic viewpoint and a synthesis procedure. In this chapter, possible structures for analysis procedures and synthesis procedures are examined in terms of the structure of aesthetic viewpoints given by the definition of aesthetic systems.