RC 2017: Reversible Computation pp 77-89 | Cite as

Designing Parity Preserving Reversible Circuits

  • Goutam Paul
  • Anupam Chattopadhyay
  • Chander Chandak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10301)

Abstract

With the emergence of reversible circuits as an energy-efficient alternative of classical circuits, ensuring fault tolerance in such circuits becomes a very important problem. Parity-preserving reversible logic design is one viable approach towards fault detection. Interestingly, most of the existing designs are ad hoc, based on some pre-defined parity preserving reversible gates as building blocks. In the current work, we propose a systematic approach towards parity preserving reversible circuit design. We prove a few theoretical results and present two algorithms, one from reversible specification to parity preserving reversible specification and another from irreversible specification to parity preserving reversible specification. We derive an upper-bound for the number of garbage bits for our algorithm and perform its complexity analysis. We also evaluate the effectiveness of our approach by extensive experimental results and compare with the state-of-the-art practices. To our knowledge, this is the first work towards systematic design of parity preserving reversible circuit and more research is needed in this area to make this approach more scalable.

Keywords

Fault tolerance Parity Quantum computing Reversible circuits 

References

  1. 1.
    Azad Khan, M.H.: Design of full-adder with reversible gates. In: International Conference on Computer and Information Technology, pp. 515–519 (2002)Google Scholar
  2. 2.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bérut, A., Arakelyan, A., Petrosyan, A., Ciliberto, S., Dillenschneider, R., Lutz, E.: Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187–189 (2012)CrossRefGoogle Scholar
  4. 4.
    Dastan, F., Haghparast, M.: A novel nanometric fault tolerant reversible divider. Int. J. Phys. Sci. 6(24), 5671–5681 (2011)Google Scholar
  5. 5.
  6. 6.
    Golubitsky, O., Falconer, S.M., Maslov, D.: Synthesis of the optimal 4-bit reversible circuits. In: Proceedings of DAC, pp. 653–656 (2010)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Gupta, P., Agrawal, A., Jha, N.K.: An algorithm for synthesis of reversible logic circuits. IEEE TCAD 25(11), 2317–2330 (2006)Google Scholar
  9. 9.
    Grosse, D., Wille, R., Dueck, G.W., Drechsler, R.: Exact multiple-control tooli network synthesis With SAT techniques. IEEE TCAD 28(5), 703–715 (2009). doi: 10.1109/TCAD.2009.2017215 Google Scholar
  10. 10.
    Hung, W.N.N., Xiaoyu, S., Guowu, Y., Jin, Y., Perkowski, M.: Optimal synthesis of multiple output boolean functions using a set of quantum gates by symbolic reachability analysis. IEEE TCAD 25(9), 1652–1663 (2006)Google Scholar
  11. 11.
    Islam, M.S., Rahman, M.M., Begum, Z., Hafiz, A., Al Mahmud, A.: Synthesis of fault tolerant reversible logic circuits. In: Proceedings of IEEE Circuits and Systems International Conference on Testing and Diagnosis, pp. 1–4 (2009)Google Scholar
  12. 12.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Miller, D.M., Maslov, D., Dueck, G.W.: A transformation based algorithm for reversible logic synthesis. In: Proceedings of DAC, pp. 318–323 (2003)Google Scholar
  14. 14.
    Miller, D.M., Wille, R., Sasanian, Z.: Elementary quantum gate realizations for multiple-control toffolli gates. In: Proceedings of International Symposium on Multiple-Valued Logic, pp. 288–293 (2011)Google Scholar
  15. 15.
    Mishchenko, A., Perkowski, M., Fast heuristic minimization of exclusive-sums-of-products. In: Proceedings of the Reed-Muller Workshop, pp. 242–250 (2001)Google Scholar
  16. 16.
    Maslov, D.: Reversible Benchmarks. http://webhome.cs.uvic.ca/~dmaslov, Accessed Jun 2013
  17. 17.
    Nayeem, N.M., Rice, J.E.: Online testable approaches in reversible logic. J. Electron. Test. 29(6), 763–778 (2013)CrossRefGoogle Scholar
  18. 18.
    Nashiry, M.A., Bhaskar, G.G., Rice, J.E.: Online testing for three fault models in reversible circuits. In: Proceedings of ISMVL, pp. 8–13 (2011). doi: 10.1109/ISMVL.2015.36
  19. 19.
    Parhami, B.: Parity-preserving transformations in computer arithmetic. In: Proceeding of SPIE, vol. 4791, pp. 403–411 (2002)Google Scholar
  20. 20.
    Parhami, B.: Fault-tolerant reversible circuits. In: Proceeding of 40th Asilomar Conference Signals, Systems, and Computers, Pacific Grove, CA, pp. 1726–1729, October 2006Google Scholar
  21. 21.
    Przigoda, N., Dueck, G.W., Wille, R., Drechsler, R.: Fault detection in parity preserving reversible circuits. In: Proceeding of IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL), Sapporo, Japan, pp. 44–49, 18–20 May 2016Google Scholar
  22. 22.
    Polian, I., Fiehn, T., Becker, B., Hayes, J.P.: A family of logical fault models for reversible circuits. In: Proceedings of Asian Test Symposium, pp. 422–427 (2011)Google Scholar
  23. 23.
    Qi, X., Chen, F., Zuo, K., Guo, L., Luo, Y., Hu, M.: Design of fast fault tolerant reversible signed multiplier. Int. J. Phys. Sci. 7(17), 2506–2514 (2012)Google Scholar
  24. 24.
    Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits - a survey. In: CoRR abs/1110.2574, http://arxiv.org/abs/1110.2574 (2011)
  25. 25.
    Saligram, R., Hegde, S.S., Kulkarni, S.A., Bhagyalakshmi, H.R., Venkatesha, M.K.: Design of fault tolerant reversible multiplexer based multi-boolean function generator using parity preserving gates. Int. J. Comput. Appl. 66(19), 20–24 (2013)Google Scholar
  26. 26.
    Saligram, R., Hegde, S.S., Kulkarni, S.A., Bhagyalakshmi, H.R., Venkatesha, M.K.: Design of parity preserving logic based fault tolerant reversible arithmetic logic unit. In: CoRR abs/1307.3690, http://arxiv.org/abs/1307.3690 (2013)
  27. 27.
    Syal, N., Sinha, H.P., Sheenu: Comparison of different type parity preserving reversible gates and simple reversible gates. In: International Journal of Research and Innovation in Computer Engineering, vol. 1, issue 1 (2011)Google Scholar
  28. 28.
    Soeken, M., Frehse, S., Wille, R., Drechsler, R.: RevKit: a toolkit for reversible circuit design. In: Proceedings of Workshop on Reversible Computation, pp. 64–76 (2011)Google Scholar
  29. 29.
    Soeken, M., Wille, R., Hilken, C., Przigoda, N., Drechsler, R.: Synthesis of reversible circuits with minimal lines for large functions. In: Proceedings of ASP-DAC, pp. 85–92 (2012). doi: 10.1109/ASPDAC.2012.6165069
  30. 30.
    Soeken, M., Chattopadhyay, A.: Unlocking efficiency and scalability of reversible logic synthesis using conventional logic synthesis. In: Proceedings of the 53rd Annual Design Automation Conference (DAC), Article no. 149, Austin, Texas, 05–09 June 2016Google Scholar
  31. 31.
    Tarannikov, Y.: New constructions of resilient boolean functions with maximal nonlinearity. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 66–77. Springer, Heidelberg (2002). doi: 10.1007/3-540-45473-X_6 CrossRefGoogle Scholar
  32. 32.
    Wille, R., Drechsler, R.: BDD-based synthesis of reversible logic for large functions. In: Proceedings of DAC, pp. 270–275 (2009)Google Scholar
  33. 33.
    Wille, R., Keszöcze, O., Drechsler, R.: Determining the minimal number of lines for large reversible circuits. In: Proceedings of DATE, pp. 1–4 (2011)Google Scholar
  34. 34.
    Wille, R., Drechsler, R., Osewold, C., Garcia-Ortiz, A.: Automatic design of low-power encoders using reversible circuit synthesis. In: Proceedings of DATE, pp. 1036–1041 (2012). doi: 10.1109/DATE.2012.6176648
  35. 35.
    Zheng, Y., Huang, C.: A novel toffoli network synthesis algorithm for reversible logic. In: Proceedings of ASP-DAC, pp. 739–744 (2009)Google Scholar
  36. 36.
    Wille, R., Chattopadhyay, A., Drechsler, R.: From reversible logic to quantum circuits: logic design for an emerging technology. In: Proceedings of International Conference on Embedded Computer Systems: Architectures, Modeling and Simulation (SAMOS), pp. 268–274 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Goutam Paul
    • 1
  • Anupam Chattopadhyay
    • 2
  • Chander Chandak
    • 3
  1. 1.Cryptology and Security Research Unit (CSRU), R.C. Bose Centre for Cryptology and SecurityIndian Statistical InstituteKolkataIndia
  2. 2.School of Computer EngineeringNanyang Technological University (NTU)SingaporeSingapore
  3. 3.Liv Artificial Intelligence Pvt. Ltd.BengaluruIndia

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