Boolean Differential Calculus
| Autor: | ChristianPosthoff, BerndSteinbach |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Product term Parity function Two-element Boolean algebra Boolean circuit Boolean expression Computer Science::Computational Complexity Electrical and Electronic Engineering Boolean algebras canonically defined Stone's representation theorem for Boolean algebras Complete Boolean algebra Hardware_LOGICDESIGN Mathematics |
| Zdroj: | Synthesis Lectures on Digital Circuits and Systems. 12:1-215 |
| ISSN: | 1932-3174 1932-3166 |
| DOI: | 10.2200/s00766ed1v01y201704dcs052 |
| Popis: | The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces 𝔹 and 𝔹ⁿ, Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The ... |
| Databáze: | OpenAIRE |
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