Abstract
Quantum-Dot Cellular Automata (QCA) is a promising nanotechnology that has been recognized as one of the top emerging technologies in future computers. Size density of several orders of magnitude smaller than Complementary Metal-Oxide Semiconductor, fast switching time and extremely low power, has caused QCA to become a topic of intense research. The majority gate and the inverter gate together make a universal set of Boolean primitives in QCA technology. Reducing the number of required primitives to implement a given Boolean function is an important step in designing QCA logic circuits. Previous research has shown how to use genetic programming to minimize the number of gates implementing a given Boolean function with one output. In this paper, we first show how to minimize the gates for the given Boolean truth tables with an arbitrary number of outputs using genetic programming. Then, another criterion, reduction of the delay of the implementing circuit is considered. Multi-objective genetic programming is applied to simultaneously optimize both objectives. The results demonstrate the proposed approach is promising and worthy of further research.
Similar content being viewed by others
References
International technology roadmap for semiconductors (ITRS). [Online]. Available: http://www.itrs.net
K. Hennessy, C.S. Lent, Clocking of molecular quantum-dot cellular automata. J Vac Sci Technol B Microelectron Process Phenom 19, 1752–1755 (2001)
C.S. Lent, B. Isaksen, M. Lieberman, Molecular quantum-dot cellular automata. J. Am. Chem. Soc. 125, 1056–1063 (2003)
C.S. Lent, P.D. Tougaw, A device architecture for computing with quantum dots. Proceed IEEE 85, 541–557 (1997)
P.D. Tougaw, C.S. Lent, Logical devices implemented using quantum cellular automata. J. Appl. Phys. 75, 1818–1825 (1994)
T. Oya, T. Asai, T. Fukui, Y. Amemiya, A majority-logic nanodevice using a balanced pair of single-electron boxes. J Nanosci Nanotech 2, 333–342 (2002)
T. Oya, T. Asai, T. Fukui, Y. Amemiya, A majority-logic device using an irreversible single-electron box. IEEE Trans. Nanotechnol. 2, 15–22 (2003)
Fahmy HA, Kiehl RA (1999) Complete logic family using tunnelingphase-logic devices. In: Proceedings of the international conferences on microelectronics, pp 22–24
C.S. Lent, P.D. Tougaw, W. Porod, Bistable saturation of in coupled quantum dot for quantum cellular automata. Appl. Phys. Lett. 62, 714–716 (1993)
P.D. Tougaw, C.S. Lent, W. Porod, Bistable saturation in coupled quantum dot cells. J. Appl. Phys. 74, 3558–3566 (1993)
M. Karnaugh, The map method for synthesis of combinational logic circuits. Trans Am Inst Electr Eng 72, 593–599 (1953)
Zhang R, Walus K, Wang W, Jullien G (2004) A method of majority logic reduction for quantum cellular automata. IEEE Trans Nainventerechnol 3
Akers SB (1962) Synthesis of combinational logic using three-input majority gates. In: Proceedings of the 3rd annual symposium switching circuit theory and logical design, pp 149–157
H.S. Miller, R.O. Winder, Majority logic synthesis by geometric methods. IRE Trans Electron Comput EC-11, 89–90 (1962)
Walus K, Schulhof G, Jullien GA, Zhang R, Wang W (2004) Circuit design based on majority gates for applications with quantum-dot cellular automata. In: 38th Asilomar conference on signals, systems and computers, Vol 2, pp 1354–1357
Huo Z, Zhang Q, Huo Z, Zhang Q (2006) Logic optimization for majority gate-based nanoelectronic circuits. In: Proceedings of the international symposium on circuits and systems (ISCAS), pp 1307–1310
Zhang R, Jha NK (2007) Threshold/majority logic synthesis and concurrent error detection targeting nanoelectronic implementations. In: Proceedings of the 16th ACM great lakes symposium on VLSI
Bonyadi MR, Azghadi SMR, Rad NM, Navi K, Afjei E (2007) Logic optimization for majority gate-based nanoelectronic circuits based on genetic algorithm. In: Proceedings of the international conference on electrical engineering, ICEE, pp 1–5
Houshmand M, Khayyat SH, Rezayee R (2009) Genetic algorithm based logic optimization for multi-output majority gate-based nano-electronic circuits. In: Proceedings of 2009 IEEE international conference on intelligent computing and intelligent systems (ICIS 2009)
Houshmand M, Saleh RR, Houshmand M (2011) Logic minimization for QCA circuits using genetic algorithm. In: Advances in intelligence and soft computing, Vol 96, pp 393–403
I. Amlani, Experimental demonstration of a leadless quantum-dot cellular automata cell. Appl. Phys. Lett. 77, 738–740 (2000)
A. Konaka, D.W. Coitb, A.E. Smith, Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91, 992–1007 (2006)
Lent CS, Tougaw PD (1997) A device architecture for computing with quantum dots. In: Institute of electrical and electronics engineering, pp 541–557
O.P.V. Neto, M.A.C. Pacheco, C.R.H. Barbosa, Neural network simulation and evolutionary synthesis of QCA circuits. IEEE Trans. Comput. 56, 191–201 (2007)
Antonelli DA, Chen DZ, Dysart TJ, Hu XS, Kahng AB, Kogge PM, Murphy RC, Niemier MT (2004) Quantum-dot cellular automata (QCA) circuit partitioning: problem modeling and solutions. In: DAC 2004, San Diego
S. Zhao, L. Jiao, Multi-objective evolutionary design and knowledge discovery of logic circuits based on an adaptive genetic algorithm. Genet Program Evol Mach 7, 195–210 (2006)
Horowitz E, Sahni S (1983) Fundamentals of data structures. W H Freeman & Co (SD)
Y.W. Leung, Y.P. Wang, Multiobjective programming using uniform design and genetic algorithm. IEEE Trans Syst Man Cybernet 30, 293–304 (2000)
K.C. Tan, E.F. Khor, T.H. Lee, Multiobjective evolutionary algorithms and applications (Springer, Berlin, 2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rezaee, R., Houshmand, M. & Houshmand, M. Multi-objective optimization of QCA circuits with multiple outputs using genetic programming. Genet Program Evolvable Mach 14, 95–118 (2013). https://doi.org/10.1007/s10710-012-9173-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10710-012-9173-6