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Logic synthesis using EXOR gates

Research Project

Project/Area Number 02805046
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 情報工学
Research InstitutionKyushu Institute of Technology

Principal Investigator

SASAO Tsutomu  Kyushu Institute of Technology Department of Computer Science and Technology, Associate Professor, 情報工学部, 助教授 (20112013)

Co-Investigator(Kenkyū-buntansha) 神田 徳夫  徳山工業高等専門学校, 情報電子工学科, 助教授 (10099864)
SASAO Tsutomu  Kyushu Institute of Technology Department of Computer Science and Technology, As (20112013)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1991: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1990: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsLogic Design / AND-EXOR Circuits / Logic Minimization / Multi-Level Logic Synthesis / Reed-Muller Expansion / 多段論理回路 / 論理合成
Research Abstract

Automatic logic synthesis tools are extensively used in LSI design. Most logic synthesis tools use AND and OR gates as basic logic elements. Arithmetic and error correcting circuits can be realized with many fewer gates if EXOR gates are available as well as AND and OR gates. Such circuits can be derived from AND-EXOR two-level circuits. So the minimization of Exclusive-OR sum-of-products expressions(ESOPs), which corresponds to the minimization of AND-EXOR two-level circuits, is important. ESOPs require fewer products than SOPs to realize randomly generated functions and symmetric functions. To realize an arbitrary function of 6 variables, an ESOP requires only 16 products, whereas an SOP requires 32 products. Although there exists a class of functions whose ESOP realizations require more production SOPS, the ESOP's are important tool in efficient logic design. The number of products in AND-OR two-level circuits can be reduced by adding decoders to the inputs(i. e., AND-OR PLAs with t … More wo-bit decoders). In a similar way, the number of products in AND-EXOR two-level circuits can be reduced by adding decoders to the inputs(i. e., AND-EXOR PLAs with two-bit decoders). We compared the number products and literals to represent arithmetic functions of 8-inputs by AND-OR circuits and AND-EXOR circuits with one and two-bit decoders, where a one-bit decoder generates true and complemented variables. Circuits based on ESOPs required fewer gates than the ones based on SOPS. The minimization of AND-EXOR circuits with decoders can be done by the minimization of ESOPs with multiple-valued inputs.
The first result is EXMIN2, a heuristic simplification algorithm for AND-EXOR expression with multiple-valued inputs. The algorithm iteratively reduces the number of the products in ESOPs as the first objective, and then reduces the number of the literals as the second objectives. Experimental results show that ESOPs usually require fewer products and connections than SOPs to represent arithmetic functions. The-second result is a design method for AND-OR-EXOR circuits. In the most technologies, EXORs are more expensive than ORs. To reduce the cost, we developed a method to replace some of the EXORs with ORs in ESOPs without increasing the number of the products. Less

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (34 results)

All Other

All Publications (34 results)

  • [Publications] Daniel Brand,笹尾 勤: "On the minimization of ANDーEXOR expressions" International Workshop on Logic Synthesis. (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Sasao: "A trasformation of multipel-valued input two-valued output functions and its application to simplification of exclusive-or sum-of products ecpressions" International Symposuim on Multiple-Valued Logic. 270-279 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 笹尾 勤,神田 徳夫: "ANDーEXOR論理式のいくつかのクラスとその複雑度について" 電子情報通信学会第二種研究会 多値論理とその応用研究会. MVL91ー4. 28-36 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 神田 徳夫,笹尾 勤: "ANDーEXOR最小論理式の積項数について" 電子情報通信学会フォ-ルトトレラントシステム研究会. FTS91ー22. 25-30 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 笹尾 勤: "On the complexity of some classes of ANDーEXOR expressions" 京都大学数理解析研究所講究録. (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Sasao: "Bounds on the average number of products in the minimum sum-of-products expressions for multiple-valued input two-valued output functions" IEEE Trans.on Comput.40. 645-651 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 笹尾 勤: "種々のANDーEXOR論理式の複雑度について" 電子情報通信学会フォ-ルトトレラントシステム研究会. FTS91ー35. 29-36 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 神田 徳夫,笹尾 勤: "4変数ANDーEXOR最小論理式とその性質" 電子情報通信学会論文誌DーI. J74Dー1. 765-773 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "EXMIN : A simplification algorithm for exclusive-or sum-of-products expressions for multiple-valued input two-valued output functions" International Symposium on Multiple-Valued Logic. Charlotte, North Carolina. 128-135 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao and D. Brand: "A non-deterministic algorithm for minimizing AND-EXOR logical expressions" National Convention of IEICE Japan. SA-3-2. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] N. Koda and T. Sasao: "On the simplification of 5-variable AND-EXOR expressions" National Convention of IEICE Japan. SA-3-3. 1990-10-2 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "Exclusive-Or sum-of-products expressions : their properties and minimization algorithms" IEICE Technical Paper. VLD90-87. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao and D. Brand: "On the minimization of AND-EXOR expressions" IEICE Technical Paper. VLD90-88. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] N. Koda and T. Sasao: "On the number of product terms of 6-variable AND-EXOR minimum expressions (in Japanese)" National Convention of IEICE Japan. A-120. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] N. Koda and T. Sasao: "AND-EXOR expressions and their equivalence classes (in Japanese)" National Convention of IEICE Japan. A-119. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao and N. Koda: "Some classes of AND-EXOR expressions and their complexity (in Japanese)" IEICE Technical Paper. MVL-91-4. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "Bounds on the average number of products in the minimum sum-of-products expressions for multiple-valued input two-valued output functions" IEEE Trans. on Comput.40, No. 5. 645-651 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] D. Brand and T. Sasao: "On the minimization of AND-EXOR expressions" International Workshop on Logic Synthesis, Research Triangle Park. NC. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "A transformation of multiple-valued input two-valued output functions and its application to simplification of exclusive-or sum-of-products expressions" International Symposium on Multiple-Valued Logic. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "On the complexity of some classes of AND-EXOR expressions" Research Report of Institute of Mathematical Analysis, Kyoto University. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] N. Koda and T. Sasao: "On the number of product terms of AND-EXOR minimum expressions (in Japanese)" IEICE Technical Paper. FTS91-22. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "On the complexity of some classes of AND-EXOR expressions" IEICE Technical Paper. FTS91-35. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] N. Koda and T. Sasao: "Four variable AND-EXOR minimum expressions and their properties (in Japanese)" Trans. IEICE Japan. J74-D-1, No. 11. 765-773 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Sasao: "Optimization of multiple-valued AND-EXOR expressions using multiple-place decision diagrams" IEICE Technical Paper. VLD91-109. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Daniel Brand,笹尾 勤: "On the minimization of ANDーEXOR expressions" International Workshop on Logic Synthesis. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Sasao: "A transformation of multipleーvalued input twoーvalued output functions and its application to simplification of exclusiveーor sumーofーproducts expressions" International Symposium on MultipleーValued Logic. 270-279 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 笹尾 勤,神田 徳夫: "ANDーEXOR論理式のいくつかのクラスとその複雑度について" 電子情報通信学会第二種研究会 多値論理とその応用研究会. MVL91ー4. 28-36 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 神田 徳夫,笹尾 勤: "ANDーEXOR最小論理式の積項数について" 電子情報通信学会フォ-ルトトレラントシステム研究会. FTS91ー22. 25-30 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 笹尾 勤: "On the complexity of some classes of ANDーEXOR expressions" 京都大学数理解析研究所講究録. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Sasao: "Bounds on the average number of products in the minimum sumーofーproducts expressions for multipleーvalued input twoーvalued output functions" IEEE Trans.on Comput.40. 645-651 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 笹尾 勤: "種々のANDーEXOR論理式の複雑度について" 電子情報通信学会フォ-ルトトレラントシステム研究会. FTS91ー35. 29-36 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 神田 徳夫,笹尾 勤: "4変数ANDーEXOR最小論理式とその性質" 電子情報通信学会論文誌DーI. J74Dー1. 765-773 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Sasao: "EXMIN:A simpflication algorithm for exclusiveーorsumーof products expression for multipleーvalued input twoーvalued output functions" Proceeding of the 20ーth International Symosium on MultipleーValued Logic. 128-135 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 笹尾 勤,神田 徳夫: "多値入力二値出力関数に於ける変換とその排他的論理和形簡単化への応用" 第13回 多値論理研究ノ-ト. VOL.13. 13 (1990)

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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