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Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis

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  • Zhiqiang Li
  • Hanwu Chen
  • Guowu Yang
  • Wenjie Liu

Abstract

Owing to the exponential nature of the memory and run-time complexity, many methods can only synthesize 3-bit reversible circuits and cannot synthesize 4-bit reversible circuits well. We mainly absorb the ideas of our 3-bit synthesis algorithms based on hash table and present the efficient algorithms which can construct almost all optimal 4-bit reversible logic circuits with many types of gates and at mini-length cost based on constructing the shortest coding and the specific topological compression; thus, the lossless compression ratio of the space of -bit circuits reaches near . This paper presents the first work to create all 3120218828 optimal 4-bit reversible circuits with up to 8 gates for the CNT (Controlled-NOT gate, NOT gate, and Toffoli gate) library, and it can quickly achieve 16 steps through specific cascading created circuits.

Suggested Citation

  • Zhiqiang Li & Hanwu Chen & Guowu Yang & Wenjie Liu, 2013. "Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, April.
    • Handle: RePEc:hin:jnljam:291410
    DOI: 10.1155/2013/291410
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