Generalized algebraic structures for the representation of discrete systems Original Research Article

General algebraic structures are introduced and used to develop representations for discrete systems. Properties of the structures and mappings between the structures are derived. The first general structure presented is based on a free monoid of m-tuples of mappings. A second general structure is presented that is based on a commutative ring of functions with finite support. These structures are specialized to obtain representations for three models of discrete systems: finite-state machines, Petri nets, and inhibitor nets. Uniqueness of the representations is established, and examples of representations for each type of system are given.