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Implicit representation and manipulation of binary decision diagrams

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1996年第3期E79A卷 354-362页

作者： Yamauchi, H Ishiura, N Takahashi, H Faculty of Computer Science and System Engineering Okayama Prefectural University Soja-shi 719-11 Japan Faculty of Information System Engineering Osaka University Suita-shi 565 Japan

This paper presents implicit representation of binary decision diagrams (implicit BDDs) as a new efficient data structure for boolean functions. A well-known method of representing graphs by binary decision diagrams (BDDs) is applied to BDDs themselves. Namely, it is a BDD representation of BDDs. Regularity in the structure of BDDs representing certain boolean functions contributes to significant reduction in size of the resulting implicit BDD representation. Since the implicit BDDs also provide canonical forms for boolean functions, the equivalence of the two implicit BDD forms is decided in time proportional to the representation size. We also show an algorithm to manipulate boolean functions on this implicit data structure.

关键词： binary decision diagram (BDD) representation of boolean functions logic design verification logic synthesis implicit representation of graphs

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On the Implementation of boolean functions on Content-Addressable Memories

IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY

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IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY 2023年 4卷 379-392页

作者： Roth, Ron M. Technion Dept Comp Sci IL-3200003 Haifa Israel Hewlett Packard Labs Milpitas CA 95035 USA

Let [q > denote the integer set {0, 1, ... , q - 1} and let B = {0, 1}. The problem of implementing functions [q > -> B on content-addressable memories (CAMs) is considered. CAMs can be classified by the input alphabet and the state alphabet of their cells;for example, in binary CAMs, those alphabets are both B, while in a ternary CAM (TCAM), both alphabets are endowed with a "don't care" symbol. This work is motivated by recent proposals for using CAMs for fast inference on decision trees. In such learning models, the tree nodes carry out integer comparisons, such as testing equality (x = t ?) or inequality (x <= t ?), where x is an element of [q > is an input to the node and t is an element of [q > is a node parameter. A CAM implementation of such comparisons includes mapping (i.e., encoding) t into internal states of some number n of cells and mapping x into inputs to these cells, with the goal of minimizing n. Such mappings are presented for various comparison families, as well as for the set of all functions [q > -> B, under several scenarios of input and state alphabets of the CAM cells. All those mappings are shown to be optimal in that they attain the smallest possible n for any given q.

关键词： Content-addressable memories integer comparisons representation of boolean functions VC dimension

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Kryptografická kriteria pro Booleovské funkce

Kryptografická kriteria pro Booleovské funkce

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作者： Luňáčková, Radka Charles University of Prague

The work is focused on boolean functions. At first, it describes the ways boolean functions are represented. Besides the representation using truth- table, vector of values and algebraic normal form which are usually shown we also show some other representations like univariate representation and trace repre- sentation. Moreover, we explain the relations among these representations. Then summary of the theory of boolean functions is given, in order to understand important properties of boolean functions corectly. Finally, these properties are studied, their interconnection is explained and the following cryptographic cri- teria of boolean functions are describe: the algebraic degree, the nonlinearity, balancedness, resiliency and correlation immunity. 1

关键词： boolean function representation of boolean functions properties of boolean functions

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