Linear sifting of decision diagrams and its application in synthesis

Index Generation Functions: Recent Developments

“…However, for other functions, linearization are not so effective. Reductions of the sizes of BDDs using linear transformations were considered in [8], [1], [5]. In these cases, the methods are useful for error-correcting circuits (C499, C1355, C1908) in addition to totally and partially symmetric functions including adders (C7552).…”

A Balanced Decision Tree Based Heuristic for Linear Decomposition of Index Generation Functions

“…2, finding the optimum linear decomposition in Example 3 can be considered as constructing an ordered binary decision tree with the smallest height that divides a set of indices into singletons by compound variables y 1 and y 2 . Although there exist heuristics to construct optimum decision trees and diagrams based on linear functions [1], [3], their objective function for optimization is essentially different from that of Problem 1. Even if the existing heuristics could be applied to Problem 1, they are not always efficient.…”

Ternary Fixed Polarity Linear Kronecker Transforms and Their Comparison With Ternary Reed–muller Transform

“…[1][2][3][4][5][6]8,9,[11][12][13][14][15][16] The renewed interest in applications of spectral methods in design of VLSI digital circuits is caused by their efficiency in technology mapping problems 7 and in linear sifting of decision diagrams. 10 Extension of the linearly sifted decision diagrams called Function-driven Decision Diagrams (FDDs) based on using simple balanced (including nonlinear) Boolean functions has been proposed. 17 The experimental results shown in Ref.…”

“…1,3 Spectral techniques based on Walsh, Haar, Arithmetic and Reed-Muller transforms have been used in digital logic design for more than thirty years. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] These techniques have been used for switching function classification, disjoint decomposition, identification of symmetries, parallel and serial linear decomposition, spectral translation synthesis (extraction of linear pre-and post-filters), multiplexer synthesis, threshold logic synthesis, state assignment and testing, and evaluation of logic complexity. [1][2][3][4][5][6]8,9,[11][12][13][14][15][16] The renewed interest in applications of spectral methods in design of VLSI digital circuits is caused by their efficiency in technology mapping problems 7 and in linear sifting of decision diagrams.…”