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研究生: 張鶴騰
Zhang, He-Teng
論文名稱: 利用互斥對稱與內部節點的非確切投射布林配對
Exclusive-Symmetry Aware Non-exact Projective Boolean Matching with Internal Nodes Matching
指導教授: 蔡孟勳
Tsai, Meng-Hsun
共同指導: 陳盈如
Chen, Yean-Ru
學位類別: 碩士
Master
系所名稱: 電機資訊學院 - 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年: 2017
畢業學年度: 105
語文別: 英文
論文頁數: 103
中文關鍵詞: 邏輯合成布林配對設計驗證設計修復
外文關鍵詞: Logic Synthesis, Boolean Matching, Design Verification, Design Rectification
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  • 布林配對尋找兩個電路的輸入/輸出之對應/補數關係,使得兩者功能相等。這在電路修正與技術映射中很重要。先前的文獻探討了輸入/輸出數量相等的情形,但它們無法處理非確切投射布林配對,也就是輸入/輸出數量不相同的情形。我們使用了基於布林可滿足問題的方法與函數性質(對稱),以設計一套可用於非確切布林配對的技巧。我們設計的技巧可以使布林配對加速收斂。新定義的函數性質與對應的方法能移除更多的不可行解並避免過度修剪解空間。實驗顯示,不限於非確切布林配對,我們提出的方法有更好的能力解決較大的電路問題。

    Boolean matching is to determine whether two circuits can be equivalent under permutation and/or negation of their inputs and outputs. It is important in circuit rectification and technology mapping. Previous works discussed Boolean matching under the same numbers of inputs and outputs. They are inapplicable to Non-exact Projective NPNP Boolean matching (NP3), in which inputs/outputs numbers of two circuits are different. We use SAT-based method and functional properties (symmetry) to design a technique which is applicable to NP3. We design a technique to speed up convergence of Boolean matching procedure. A newly defined functional property is used to remove more infeasible solutions. Experimental data shows, besides to NP3, the proposed technique has better capability of matching circuits with large number of inputs.

    摘要 i Abstract ii 誌謝 iii Table of Contents v List of Tables vii List of Figures viii Chapter 1. Introduction 1 Chapter 2. Preliminaries 6 2.1. Boolean Function Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2. Cofactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3. Shannon Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4. Symmetry and Symmetry Group . . . . . . . . . . . . . . . . . . . . . . . 8 2.5. Boolean Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.6. Boolean Satisfiability and SAT Solver . . . . . . . . . . . . . . . . . . . . 11 2.7. Circuit Terminologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.8. Tseitin Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Chapter 3. Related Work 16 Chapter 4. From Boolean Matching To Satisfiability 20 4.1. Formula for NPNP Boolean Matching . . . . . . . . . . . . . . . . . . . . 20 4.2. Solving Boolean Matching by SAT Solver . . . . . . . . . . . . . . . . . . 23 4.2.1. Finding a Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2.2. Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.3. Post-Pruning of Solution Space . . . . . . . . . . . . . . . . . . . . 33 4.3. Non-exact Projective NPNP Boolean Matching . . . . . . . . . . . . . . . 35 4.3.1. Projective NPNP Boolean Matching . . . . . . . . . . . . . . . . . 37 4.3.2. Non-exact Projective NPNP Boolean matching . . . . . . . . . . . 40 Chapter 5. Effectively Pruning Solution Space 47 5.1. Normal Group Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2. Exclusive Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3. Matching by Internal Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.3.1. Matching Candidates . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.3.2. Internal Nodes Matching . . . . . . . . . . . . . . . . . . . . . . . 58 5.3.3. Refinement of Internal Nodes Matching with Redundant Logic . . . 65 5.4. Experiment Setup and Result . . . . . . . . . . . . . . . . . . . . . . . . . 67 iv Chapter 6. Conclusion 80 References 82 Appendix A. Periodic Boolean Reasoning 85 A.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 A.2. Periodic Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 A.3. Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 A.4. Periodic Boolean Reasoning Example . . . . . . . . . . . . . . . . . . . . 95 A.5. Experimental Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Appendix B. Experiment Data 103

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