之前的作品展現出我們有很大的機會，可以透過在電路合成過程中加入組合反饋迴路 (Combinational Feedback Loops) 來實現更加最小化的組合電路。
然而，他們實現這項技術的方式是藉由分支界定 (branch-and-bound) 的方法探索電路中可能存在的循環依賴關係，但是這樣的方法可能不足以應付複雜的電路設計。
有別於這樣的探索方式，本文提出了一個正規的邏輯推論的演算法，藉由合併電路節點的方法來直接識別，或者更積極的創造出迴路化的電路架構。
此外，為了驗證所形成迴路是否為組合電路，我們也提出了一個以可滿足性問題為基底 (SAT-based) 的演算法來有效率地做驗證。
我們藉由在IWLS 2005 的測試電路上所進行的實驗結果，來呈現我們所提出的識別演算法的有效性和可擴展性。
與目前最新的演算法比較起來，我們的驗證演算法平均加速了354.94倍。

Prior works showed great opportunities to achieve more minimized combinational circuits by introducing combinational feedback loops during the synthesis process.
However, they achieved this by exploring possible cyclic dependencies of circuits in a branch-and-bound manner, which may not scale well for complex designs.
Instead of exploration, this paper proposes a formal algorithm using logic implication to directly identify, or more aggressively create cyclifiable structure candidates in circuits by merging nodes.
Additionally, to validate whether the formed loops are combinational, we also propose an efficient SAT-based algorithm.
The effectiveness and scalability of the identification and validation algorithms are demonstrated in the experimental results performed on a set of IWLS 2005 benchmarks.
As compared to the state-of-the-art, the validation algorithm has an average speedup of 354.94 times.

中文摘要 i
Abstract ii
Acknowledgement iii
Contents iv
List of Tables vi
List of Figures vii
1 Introduction 1
2 Preliminaries 5
2.1 An Example 5
2.2 Background 6
2.3 Node Merging 7
3 Cycliable Structure Identication 10
3.1 Candidate Cyclic Substitute Node Identication 10
3.2 Candidate Added Cyclic Substitute Node Creation 14
3.2.1 Masking ACSNs 15
3.2.2 Induced ACSNs 16
4 Cycliable Structure Validation 21
4.1 Intra-SCC Validation 22
4.2 Inter-SCC Validation 24
5 Proposed Algorithm 29
6 Experimental Results 32
7 Conclusion 40
Bibliography 41

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