Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis

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 ofn-bit circuits reaches near2×n!. 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.

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Bidirectional matrix-based algorithm for 4-qubit reversible logic circuits synthesis

IEEE Congress on Evolutionary Computation ◽

10.1109/cec.2010.5586417 ◽

2010 ◽

Author(s):

Dong Wang ◽

Hanwu Chen ◽

Wanning Zhu

Keyword(s):

Logic Circuits ◽

Reversible Logic

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Effective Hash-Based Algorithm for Reversible Logic Circuits Synthesis with Minimum Cost

2008 Fourth International Conference on Natural Computation ◽

10.1109/icnc.2008.191 ◽

2008 ◽

Author(s):

Zhiqiang Li ◽

Hanwu Chen ◽

Baowen Xu ◽

Xiaoyu Song ◽

Xiling Xue

Keyword(s):

Minimum Cost ◽

Logic Circuits ◽

Reversible Logic

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Analyzing Fault Models for Reversible Logic Circuits

2006 IEEE International Conference on Evolutionary Computation ◽

10.1109/cec.2006.1688609 ◽

2006 ◽

Cited By ~ 20

Author(s):

Jing Zhong ◽

J.C. Muzio

Keyword(s):

Logic Circuits ◽

Reversible Logic ◽

Fault Models

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Computing the Atom Graph of a Graph and the Union Join Graph of a Hypergraph

Algorithms ◽

10.3390/a14120347 ◽

2021 ◽

Vol 14 (12) ◽

pp. 347

Author(s):

Anne Berry ◽

Geneviève Simonet

Keyword(s):

Real Number ◽

Time Complexity ◽

Matrix Multiplication ◽

Efficient Algorithms ◽

Join Graph ◽

Current Value ◽

Minimal Separator

The atom graph of a graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all possible atom trees of this graph. We provide two efficient algorithms for computing this atom graph, with a complexity in O(min(nωlogn,nm,n(n+m¯)) time, where n is the number of vertices of G, m is the number of its edges, m¯ is the number of edges of the complement of G, and ω, also denoted by α in the literature, is a real number, such that O(nω) is the best known time complexity for matrix multiplication, whose current value is 2,3728596. This time complexity is no more than the time complexity of computing the atoms in the general case. We extend our results to α-acyclic hypergraphs, which are hypergraphs having at least one join tree, a join tree of an hypergraph being defined by its hyperedges in the same way as an atom tree of a graph is defined by its atoms. We introduce the notion of union join graph, which is the union of all possible join trees; we apply our algorithms for atom graphs to efficiently compute union join graphs.

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