Symbolic Algebraic Discrete Systems : Theory and Computation
Roger Germundsson · 1995
: Discrete systems and properties of these are defined at a behavioral level independently of the actual representation. Hence we can use any representation that is useful for our purposes. Ultimately the representation is some form of relation. For analysis and design computations on discrete systems it is crucial that we can manipulate fairly complex relations. Polynomials over finite fields are fully capable of representing all finite relations and furthermore they offer an appealing approach both from a theory standpoint as well as a computational perspective. In particular Boolean polynomials and multivalued logic are special cases. A complete discrete (event) computational theory is presented in terms polynomial relations over finite fields. The basic components of the theory are: Modeling: Mapping from some model description to a polynomial model. Analysis: Computing properties of a polynomial model. Design: Modifying properties of a polynomial model. Implementation: Mapping...