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# Boolean differential equations

Author: Bernd Steinbach; Christian Posthoff San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, ©2013. Synthesis lectures on digital circuits and systems, #42. eBook : Document : EnglishView all editions and formats The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean Algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits. Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The solution of such a BDE is a set of Boolean functions. This is a significant extension of Boolean equations, which have sets of Boolean vectors as solutions. In the simplest BDE a derivative operation of the BDC on the left-hand side is equal to a logic function on the right-hand side. The solution of such a simple BDE means to execute an operation which is inverse to the given derivative. BDEs can be applied in the same fields as the BDC, however, their possibility to express sets of Boolean functions extends the application field significantly.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version: Document, Internet resource Internet Resource, Computer File Bernd Steinbach; Christian Posthoff Find more information about: Bernd Steinbach Christian Posthoff 9781627052429 1627052429 1627052410 9781627052412 853278140 Part of: Synthesis digital library of engineering and computer science. 1 online resource (xii, 146 pages) : illustrations. 1. Basics of the binary Boolean algebra -- 1.1 Introduction -- 1.2 Boolean space, Boolean functions, and operations -- 1.3 Boolean functions and operations -- 1.4 Boolean equations -- 1.5 Systems of equations and inequalities -- 1.6 Solutions with regard to variables -- 1.7 XBOOLE -- 1.7.1 Concept and properties -- 1.7.2 XBOOLE monitor -- 1.7.3 XBOOLE problem program -- 1.7.4 XBOOLE library. 2. Summary of the Boolean differential calculus -- 2.1 Introduction -- 2.2 Simple derivative operations -- 2.3 Vectorial derivatives -- 2.4 -- m-fold derivative operations. 3. Boolean differential equations -- 3.1 Introduction -- 3.2 Boolean differential equations of a single simple derivative -- 3.3 Boolean differential equations of a single vectorial derivative -- 3.4 Boolean differential equations restricted to all vectorial derivatives -- 3.4.1 Essence of Boolean differential equations -- 3.4.2 Classes of solution functions -- 3.4.3 Separation of function classes -- 3.4.4 Separation of function classes using XBOOLE -- 3.5 Boolean differential equations for each set of solution functions -- 3.5.1 Separation of functions -- 3.5.2 Separation of functions using XBOOLE -- 3.6 Boolean differential equations of all derivative operations -- 3.6.1 Examples -- 3.6.2 Extension to all simple derivative operations -- 3.6.3 Extension to all vectorial derivative operations -- 3.6.4 Extension to all m-fold derivative operations -- 3.6.5 Methods of transformations as preprocessing step -- 3.7 Most general Boolean differential equations. 4. Solutions of the exercises -- Bibliography -- Authors' biographies -- Index. Synthesis lectures on digital circuits and systems, #42. Bernd Steinbach, Christian Posthoff.

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Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The  Read more...

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