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This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edge-valued 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 M*p*-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 M*p*-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 M*p*-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.

- Publication
- IEICE TRANSACTIONS on Information Vol.E93-D No.8 pp.2059-2067

- Publication Date
- 2010/08/01

- Publicized

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.E93.D.2059

- Type of Manuscript
- Special Section PAPER (Special Section on Multiple-Valued Logic and VLSI Computing)

- Category
- Logic Design

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Shinobu NAGAYAMA, Tsutomu SASAO, Jon T. BUTLER, "A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams" in IEICE TRANSACTIONS on Information,
vol. E93-D, no. 8, pp. 2059-2067, August 2010, doi: 10.1587/transinf.E93.D.2059.

Abstract: This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edge-valued 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 M*p*-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 M*p*-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 M*p*-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.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E93.D.2059/_p

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@ARTICLE{e93-d_8_2059,

author={Shinobu NAGAYAMA, Tsutomu SASAO, Jon T. BUTLER, },

journal={IEICE TRANSACTIONS on Information},

title={A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams},

year={2010},

volume={E93-D},

number={8},

pages={2059-2067},

abstract={This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edge-valued 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 M*p*-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 M*p*-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 M*p*-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.},

keywords={},

doi={10.1587/transinf.E93.D.2059},

ISSN={1745-1361},

month={August},}

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TY - JOUR

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

T2 - IEICE TRANSACTIONS on Information

SP - 2059

EP - 2067

AU - Shinobu NAGAYAMA

AU - Tsutomu SASAO

AU - Jon T. BUTLER

PY - 2010

DO - 10.1587/transinf.E93.D.2059

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E93-D

IS - 8

JA - IEICE TRANSACTIONS on Information

Y1 - August 2010

AB - This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edge-valued 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 M*p*-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 M*p*-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 M*p*-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.

ER -