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Additional info for Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook

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Logic design of nanodevices is being developed in two directions: Using advanced logic design techniques and methods from other disciplines, in particular, fault-tolerant computing. Development of a new theory and technique for logic design in spatial dimensions. The first direction adapts architectural approaches such as array-based logic, parallel and distributed architectures, methods from fault-tolerant computing and adaptive structures such as neural networks. The design of nanostructure topologies based on decision diagram techniques is considered in Chapter 34.

Decision tables are used to formalize many approaches and to represent data [1, 13, 16]. Multivalued counterpart of decision tables are used to represent multivalued relations (see, for example, [12]). Decision trees and diagrams. Decision trees were introduced first to represent discrete sets in 1935 by Kurepa [9]. The applications of decision trees include decision table programming [13, 16], databases, pattern recognition [1], taxonomy and identification [6], and analysis of algorithms [17]. A particular case, binary decision trees are used in many areas of data mining and processing.

It follows that x1 x2 ∨ x1 x2 = x1 . The edges 1x and x1 define in a unique way the function f , hence we can write f = {1x, x1}. This corresponds to the function f = x1 ∨x2 . 9a). 3 Decision trees and diagrams Decision trees can be derived from a functional equation or truth table. This provides a canonical representation of functions in graphical form, so that for a fixed variable order there is a bijection between switching functions and decision diagrams. The definitions for decision trees and diagrams are given in Chapter 2.

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