A multi-objective synthesis methodology in quantum-dot cellular automata technology

Quantum-dot Cellular Automata (QCA) has been widely advocated in nanotechnology as a response to the physical limits associated with complementary metal oxide semiconductor (CMOS) technology in atomic scales. Some of its peculiar features are its smaller size, higher speed, higher switching frequency, lower power consumption, and higher scale integration. In this technology, the majority and NOT gates are employed for the production of the functions as these two gates together make a universal set of Boolean primitives in QCA technology. An important step in the generation of Boolean functions using the majority gate is reducing the number of involved gates. In this paper, a multi-objective synthesis methodology (with the objective priority of gate counts, gate levels and the number of NOT gates) is presented for finding the minimal number of possible majority gates in the synthesis of Boolean functions using the proposed Majority Specification Matrix (MSM) concept. Moreover, based on MSM, a synthesis flow is proposed for the synthesis of multi-output Boolean functions. To reveal the efficiency of the proposed method, it is compared with a meta-heuristic method, multi-objective Genetic Programing (GP). Besides, it is applied to synthesize MCNC benchmark circuits. The results are indicative of the outperformance of the proposed method in comparison to multi-objective GP method. Also, for the MCNC benchmark circuits, there is an average reduction of 10.5% in the number of levels as well as 16.8% and 33.5% in the number of majority and NOT gates, as compared to the best available method respectively.

[1]  H. S. Miller,et al.  Majority-Logic Synthesis by Geometric Methods , 1962, IRE Trans. Electron. Comput..

[2]  Bahram Honary,et al.  Construction of low-density parity-check codes based on balanced incomplete block designs , 2004, IEEE Transactions on Information Theory.

[3]  Hossam A. H. Fahmy,et al.  Complete logic family using tunneling-phase-logic devices , 2000, ICM'99. Proceedings. Eleventh International Conference on Microelectronics (IEEE Cat. No.99EX388).

[4]  J. E. Brewer,et al.  Extending the road beyond CMOS , 2002 .

[5]  Bahram Honary,et al.  On construction of low density parity check codes , 2004 .

[6]  P. D. Tougaw,et al.  A device architecture for computing with quantum dots , 1997, Proc. IEEE.

[7]  G.A. Jullien,et al.  A method of majority logic reduction for quantum cellular automata , 2004, IEEE Transactions on Nanotechnology.

[8]  P. D. Tougaw,et al.  Logical devices implemented using quantum cellular automata , 1994 .

[9]  Adrian M. Ionescu,et al.  Nanoelectronics Research for Beyond CMOS Information Processing , 2010, Proc. IEEE.

[10]  Saied Hosseini Khayat,et al.  Genetic algorithm based logic optimization for multi- output majority gate-based nano-electronic circuits , 2009, 2009 IEEE International Conference on Intelligent Computing and Intelligent Systems.

[11]  Nisha Sarwade,et al.  A REVIEW OF CONSTRUCTION METHODS FOR REGULAR LDPC CODES , 2012 .

[12]  Yun Shang,et al.  An Optimized Majority Logic Synthesis Methodology for Quantum-Dot Cellular Automata , 2010, IEEE Transactions on Nanotechnology.

[13]  Peng Wang,et al.  Minimal majority gate mapping of 4-variable functions for quantum cellular automata , 2011, 2011 11th IEEE International Conference on Nanotechnology.

[14]  Tetsuya Asai,et al.  A majority-logic device using an irreversible single-electron box , 2003 .

[15]  Rutuja Shedsale,et al.  A REVIEW OF CONSTRUCTION METHODS FOR REGULAR LDPC CODES , 2012 .

[16]  C. Lent,et al.  Molecular quantum-dot cellular automata , 2003, 2003 Third IEEE Conference on Nanotechnology, 2003. IEEE-NANO 2003..

[17]  Rui Zhang,et al.  Majority and Minority Network Synthesis With Application to QCA-, SET-, and TPL-Based Nanotechnologies , 2007, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[18]  P. D. Tougaw,et al.  Bistable saturation in coupled quantum‐dot cells , 1993 .

[19]  G. Jullien,et al.  Circuit design based on majority gates for applications with quantum-dot cellular automata , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[20]  C. Lent,et al.  Clocking of molecular quantum-dot cellular automata , 2001 .

[21]  Mahboobeh Houshmand,et al.  Logic Minimization of QCA Circuits Using Genetic Algorithms , 2011 .

[22]  Sheldon B. Akers,et al.  Synthesis of combinational logic using three-input majority gates , 1962, SWCT.

[23]  Mahboobeh Houshmand,et al.  Multi-objective optimization of QCA circuits with multiple outputs using genetic programming , 2012, Genetic Programming and Evolvable Machines.

[24]  Gary H. Bernstein,et al.  Experimental demonstration of a leadless quantum-dot cellular automata cell , 2000 .

[25]  Qishan Zhang,et al.  Logic optimization for majority gate-based nanoelectronic circuits , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[26]  M. Karnaugh.  The map method for synthesis of combinational logic circuits , 1953, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[27]  James A. Hutchby,et al.  Extending the road beyond CMOS - IEEE Circuits and Devices Magazine , 2001 .

[28]  P. D. Tougaw,et al.  Bistable saturation in coupled quantum dots for quantum cellular automata , 1993 .

[29]  K. Navi,et al.  Logic Optimization for Majority Gate-Based Nanoelectronic Circuits Based on Genetic Algorithm , 2007, 2007 International Conference on Electrical Engineering.

[30]  Tetsuya Asai,et al.  A majority-logic nanodevice using a balanced pair of single-electron boxes. , 2002, Journal of nanoscience and nanotechnology.