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This paper presents a formal approach to verify arithmetic circuits using symbolic computer algebra. Our method describes arithmetic circuits directly with high-level mathematical objects based on weighted number systems and arithmetic formulae. Such circuit description can be effectively verified by polynomial reduction techniques using Grobner Bases. In this paper, we describe how the symbolic computer algebra can be used to describe and verify arithmetic circuits. The advantageous effects of the proposed approach are demonstrated through experimental verification of some arithmetic circuits such as multiply-accumulator and FIR filter. The result shows that the proposed approach has a definite possibility of verifying practical arithmetic circuits.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.3038-3046

- Publication Date
- 2008/10/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1093/ietfec/e91-a.10.3038

- Type of Manuscript
- PAPER

- Category
- VLSI Design Technology and CAD

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Yuki WATANABE, Naofumi HOMMA, Takafumi AOKI, Tatsuo HIGUCHI, "Arithmetic Circuit Verification Based on Symbolic Computer Algebra" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 10, pp. 3038-3046, October 2008, doi: 10.1093/ietfec/e91-a.10.3038.

Abstract: This paper presents a formal approach to verify arithmetic circuits using symbolic computer algebra. Our method describes arithmetic circuits directly with high-level mathematical objects based on weighted number systems and arithmetic formulae. Such circuit description can be effectively verified by polynomial reduction techniques using Grobner Bases. In this paper, we describe how the symbolic computer algebra can be used to describe and verify arithmetic circuits. The advantageous effects of the proposed approach are demonstrated through experimental verification of some arithmetic circuits such as multiply-accumulator and FIR filter. The result shows that the proposed approach has a definite possibility of verifying practical arithmetic circuits.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.10.3038/_p

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@ARTICLE{e91-a_10_3038,

author={Yuki WATANABE, Naofumi HOMMA, Takafumi AOKI, Tatsuo HIGUCHI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Arithmetic Circuit Verification Based on Symbolic Computer Algebra},

year={2008},

volume={E91-A},

number={10},

pages={3038-3046},

abstract={This paper presents a formal approach to verify arithmetic circuits using symbolic computer algebra. Our method describes arithmetic circuits directly with high-level mathematical objects based on weighted number systems and arithmetic formulae. Such circuit description can be effectively verified by polynomial reduction techniques using Grobner Bases. In this paper, we describe how the symbolic computer algebra can be used to describe and verify arithmetic circuits. The advantageous effects of the proposed approach are demonstrated through experimental verification of some arithmetic circuits such as multiply-accumulator and FIR filter. The result shows that the proposed approach has a definite possibility of verifying practical arithmetic circuits.},

keywords={},

doi={10.1093/ietfec/e91-a.10.3038},

ISSN={1745-1337},

month={October},}

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TY - JOUR

TI - Arithmetic Circuit Verification Based on Symbolic Computer Algebra

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 3038

EP - 3046

AU - Yuki WATANABE

AU - Naofumi HOMMA

AU - Takafumi AOKI

AU - Tatsuo HIGUCHI

PY - 2008

DO - 10.1093/ietfec/e91-a.10.3038

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E91-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 2008

AB - This paper presents a formal approach to verify arithmetic circuits using symbolic computer algebra. Our method describes arithmetic circuits directly with high-level mathematical objects based on weighted number systems and arithmetic formulae. Such circuit description can be effectively verified by polynomial reduction techniques using Grobner Bases. In this paper, we describe how the symbolic computer algebra can be used to describe and verify arithmetic circuits. The advantageous effects of the proposed approach are demonstrated through experimental verification of some arithmetic circuits such as multiply-accumulator and FIR filter. The result shows that the proposed approach has a definite possibility of verifying practical arithmetic circuits.

ER -