Abstract
In this paper, we introduce a new method to realize symmetric functions with reversible circuits. In contrast to earlier methods, our solution deploys a simple and regular cascade structure composed of low-cost gates which enables significant reductions with respect to quantum costs. However, the number of garbage outputs increases slightly. To overcome this, we next propose an optimized design by reusing the garbage outputs. The resulting design thus offers a powerful approach towards reversible synthesis of symmetric Boolean functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature, 46–52 (2001)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge Univ. Press (2000)
Wille, R., Drechsler, R., Oswald, C., Garcia-Ortiz, A.: Automatic design of low-power encoders using reversible circuit synthesis. In: DATE, pp. 1036–1041 (2012)
Desoete, B., Vos, A.D.: A reversible carry-look-ahead adder using control gates. INTEGRATION, the VLSI Jour. 33(1-2), 89–104 (2002)
Cuykendall, R., Andersen, D.R.: Reversible optical computing circuits. Optical Letters 12(7), 542–544 (1987)
Thapliyal, H., Srinivas, M.B.: The need of DNA computing: reversible designs of adders and multipliers using fredkin gate. In: Proc. SPIE, Optomechatronic Micro/Nano Devices and Components (2005)
Merkle, R.C.: Reversible electronic logic using switches. Nanotechnology 4, 21–40 (1993)
Agarwal, A., Jha, N.K.: Synthesis of reversible logic. In: DATE, pp. 21384–21385 (2004)
Perkowski, M., Kerntopf, P., Buller, A., Chrzanowska-Jeske, M., Mishchenko, A., Song, X., Al-Rabadi, A., Jozwiak, L., Coppola, A., Massey, B.: Regularity and symmetry as a base for efficient realization of reversible logic circuits. In: IWLS, pp. 245–252 (2001)
Mishchenko, A., Perkowski, M.: Logic synthesis of reversible wave cascades. In: IWLS, pp. 197–202 (2002)
Gupta, P., Agrawal, A., Jha, N.: An algorithm for synthesis of reversible logic circuits. IEEE TCAD 25(11), 2317–2330 (2006)
Shende, V.V., Prasad, A.K., Markov, I.L., Hayes, J.P.: Synthesis of reversible logic circuits. IEEE TCAD 22(6), 723–729 (2003)
Maslov, D.: Efficient reversible and quantum implementations of symmetric Boolean functions. IEEE Proc. of the Circuits, Devices and Systems 153(5), 467–472 (2006)
Große, D., Wille, R., Dueck, G.W., Drechsler, R.: Exact multiple control Toffoli network synthesis with SAT techniques. IEEE TCAD 28(5), 703–715 (2009)
Miller, D.M., Maslov, D., Dueck, G.W.: A transformation based algorithm for reversible logic synthesis. In: Design Automation Conf., pp. 318–323 (2003)
Wille, R., Drechsler, R.: BDD-based synthesis of reversible logic for large functions. In: Design Automation Conf., pp. 270–275 (2009)
Rovetta, C., Mouffron, M.: De Bruijan sequences and complexity of symmetric functions. Cryptography and Communications Journal 3(4), 207–225 (2011)
Yanushekvich, S.N., Butler, J.T., Dueck, G.W., Shmerko, V.P.: Experiments on FPRM expressions for partially symmetric logic functions. In: IEEE International Symposium on Multiple Valued Logic, pp. 141–146 (2000)
Lauradoux, C., Videau, M.: Matriochka symmetric Boolean functions. In: IEEE ISIT, pp. 1631–1635 (2008)
Keren, O., Levin, I., Stankovic, S.R.: Use of gray decoding for implementation of symmetric functions. In: International Conference on VLSI, pp. 25–30 (2007)
Rahaman, H., Das, D.K., Bhattacharya, B.B.: Implementing symmetric functions with hierarchical modules for stuck-at and path-delay fault testability. Journal of Electronic Testing: Theory and Applications 22(2), 125–142 (2006)
Perkowski, M., Kerntopf, P., Buller, A., Chrzanowska-Jeske, M., Mishchenko, A., Song, X., Al-Rabadi, A., Jozwiak, L., Coppola, A., Massey, B.: Regular realization of symmetric functions using reversible logic. In: EUROMICRO Symp. on Digital Systems Design, pp. 245–252 (2001)
Picton, P.: Modified Fredkin gates in logic design. Microelectronics Journal 25, 437–441 (1994)
Moraga, C., Hadjam, F.Z.: On double gates for reversible computing circuits. In: Proc. Intl. Workshop on Boolean Problems (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deb, A., Das, D.K., Rahaman, H., Bhattacharya, B.B., Wille, R., Drechsler, R. (2013). Reversible Circuit Synthesis of Symmetric Functions Using a Simple Regular Structure. In: Dueck, G.W., Miller, D.M. (eds) Reversible Computation. RC 2013. Lecture Notes in Computer Science, vol 7948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38986-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-38986-3_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38985-6
Online ISBN: 978-3-642-38986-3
eBook Packages: Computer ScienceComputer Science (R0)