Representations of Elementary Functions Using Edge-Valued MDDs

Nagayama, Shinobu; Sasao, Tsutomu

doi:10.1109/ismvl.2007.49

Cited by 14 publications

(22 citation statements)

References 23 publications

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“…Theorem 1 also holds for EVMDDs because an EVMDD is obtained by merging non-terminal nodes in an EVBDD. Note that the upper bound for l-restricted Mp-monotone increasing functions shown in Theorem 1 is equal to the upper bound for totally Mp-monotone increasing functions shown in [21]. This upper bound is much smaller than the worst-case upper bound, 2 n , which is reached by EVBDDs for power functions and polynomial functions [23].…”

Section: Definition 11mentioning

confidence: 73%

“…Y+1 is an affine transformation of an M1-monotone increasing function [21]. As shown in Example 4, f (X, Y) = X Y+1 can be converted into an affine transformation of an extended 2-restricted M1-monotone increasing function.…”

Section: Example 5: 2-bit Precision Functionmentioning

confidence: 99%

“…Definition 9: An edge-valued multiple-valued decision diagram (EVMDD) [21] is an extension of an MDD [13], and represents a multiple-valued input integer function. It consists of one terminal node representing 0 and non-terminal nodes with edges having integer weights, and 0-edges always have zero weights.…”

Section: Definitionmentioning

confidence: 99%

“…Various design methods for numeric function generators (NFGs) have been developed [18]. However, most existing methods are intended for one-variable numeric functions [7], [16], [21], [25], [29]- [31], and only a few methods have been reported for specific multi-variable numeric functions [9], [10], [34]. Thus, different numeric functions require different methods.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, choosing a DD appropriate to a given class of functions is important. Although DDs suitable for onevariable numeric functions have been presented [21], [23], [29], [33], as far as we know, no study on graph-based representations for multi-variable numeric functions has been reported.…”

Section: Introductionmentioning

confidence: 99%

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A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Nagayama

Sasao

Butler

2010

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edgevalued multiple-valued decision diagram (EVMDD), and shows a systematic design method based on the EVMDD. To achieve a design, we characterize a numeric function f by the values of l and p for which f is an l-restricted Mp-monotone increasing function. Here, l is a measure of subfunctions of f and p is a measure of the rate at which f increases with an increase in the dependent variable. For the special case of an EVMDD, the EVBDD, we show an upper bound on the number of nodes needed to realize an l-restricted Mp-monotone increasing function. Experimental results show that all of the two-variable numeric functions considered in this paper can be converted into an l-restricted Mp-monotone increasing function with p = 1 or 3. Thus, they can be compactly realized by EVBDDs. Since EVMDDs have shorter paths and smaller memory size than EVBDDs, EVMDDs can produce fast and compact NFGs. key words: two-variable numeric function generators (NFGs), edgevalued multiple-valued decision diagrams (EVMDDs), edge-valued binary decision diagrams (EVBDDs), graph-based representation of numeric functions, programmable memory-based architecture

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Section: Definition 11mentioning

confidence: 73%

Section: Example 5: 2-bit Precision Functionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Nagayama

Sasao

Butler

2010

IEICE Trans. Inf. & Syst.

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Agent-based power equilibrium in a smart grid with XBOOLE

Veith

Steinbach

2017

2017 International Conference on Information and Digital Technologies (IDT)

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Representations of Two-Variable Elementary Functions Using EVMDDs and their Applications to Function Generators

Nagayama

Sasao

2008

38th International Symposium on Multiple Valued Logic (Ismvl 2008)

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This paper proposes a method to represent two-variable elementary functions using edge-valued multi-valued decision diagrams (EVMDDs), and presents a design method and an architecture for function generators using EVMDDs. To show the compactness of EVMDDs, this paper introduces a new class of integer-valued functions, l-restricted Mp-monotone increasing functions, and derives an upper bound on the number of nodes in an edge-valued binary decision diagram (EVBDD) for the l-restricted Mp-monotone increasing function. EVBDDs represent l-restricted Mpmonotone increasing functions more compactly than MTBDDs and BMDs when p is small. Experimental results show that all the two-variable elementary functions considered in this paper can be converted into l-restricted

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Representations of Elementary Functions Using Edge-Valued MDDs

Abstract: Abstract

Cited by 14 publications

References 23 publications

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Agent-based power equilibrium in a smart grid with XBOOLE

Representations of Two-Variable Elementary Functions Using EVMDDs and their Applications to Function Generators

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