Research On Modern Digital Theory And Method

Based on the form and properties of coincidence operation, firstly, this dissertation proposes the theory of OR-Coincidence algebra system. It includes the definition of two basic operations, logical function's expansion and matrix formulation in OR-Coincidence algebra system, and the introduction of map expression--dj map, the complete research of the relations among CRM expansion^ maxteim expansion and RM expansion, iiamely tie relations among dj map, K-map and bj map, also includes the minimization of CRM expansion in fixed and mixed polarities-Meanwhile this dissertation points out the form and properties of basic symmetric function, simple symmetric function and basic CRM symmetric function in OR-Coincidence algebra system, discusses the relations and transform methods among the coefficients of the three kinds of symmetric functions.Then, the dissertation, on account of the normalized Haar transform, sets up the spectral formulation, expounds the significance, properties, map-expression (ha coefficient map), several computating methods of spectral coefficient, including the relations and transform methods among ha coefficient map, had coefficient map and K-map. We also make a detailed research of the applications of Haar transform spectral technique in the fields of logical function classification, symmetric function detection, etc. In view of Chrestenson function and three-valued Haar function, this dissertation lists the formulation and properties of three-valued spectral technique, the significance and computation of spectral coefficient, and proposes the transform method between three-valued K-map and spectral coefficient map.In addition, the dissertation discusses the tabular detection method of monotonic function and the computatiag method of some special operations.