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Improvements to the Equivalence Checking of Reversible Circuits

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New Data Structures and Algorithms for Logic Synthesis and Verification

Abstract

Reversible circuits implement invertible logic functions. They are of great interest to cryptography, coding theory, interconnect design, computer graphics, quantum computing, and many other fields.

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Notes

  1. 1.

    Toffoli gates have bee briefly introduced in Chap. 2. Here, their functionality is presented for the sake of clarity.

  2. 2.

    This holds since self-inverse reversible gates such as Toffoli gates, CNOT gates, NOT gates, etc. are considered here.

References

  1. D. Kamalika, I. Sengupta, Applications of reversible logic in cryptography and coding theory, in Proceedings of the 26th International Conference on VLSI Design (2013)

    Google Scholar 

  2. K. Czarnecki et al., Bidirectional transformations: a cross-discipline perspective, in Theory and Practice of Model Transformations, ed. by R.F. Paige (Springer, Berlin, 2009), pp. 260–283

    Chapter  Google Scholar 

  3. R. Wille, R. Drechsler, C. Oswald, A. Garcia-Ortiz, Automatic design of low-power encoders using reversible circuit synthesis, in Design, Automation and Test in Europe (DATE) (2012), pp. 1036–1041

    Google Scholar 

  4. S.L. Sunil, C.D. Yoo, T. Kalker, Reversible image watermarking based on integer-to-integer wavelet transform. IEEE Trans. Inf. Forensics Secur. 2(3), 321–330 (2007)

    Article  Google Scholar 

  5. M. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010)

    Book  MATH  Google Scholar 

  6. R. Wille, R. Drechsler, Towards a Design Flow for Reversible Logic (Springer, Berlin, 2010)

    Book  MATH  Google Scholar 

  7. R. Drechsler, R. Wille, From truth tables to programming languages: Progress in the design of reversible circuits, in International Symposium on Multiple-Valued Logic (2011), pp. 78–85

    Google Scholar 

  8. M. Saeedi, I.L. Markov, Synthesis and optimization of reversible circuits–a survey. ACM Comput. Surv. (CSUR) 45(2), 21 (2013)

    Article  MATH  Google Scholar 

  9. R. Wille et al., Equivalence checking of reversible circuits, in 39th IEEE International Symposium on Multiple-Valued Logic (2009)

    Google Scholar 

  10. S.P. Jordan, Strong equivalence of reversible circuits is coNP-complete. Quantum Inf. Comput. 14(15–16), 1302–1307 (2014)

    MathSciNet  Google Scholar 

  11. CryptoMiniSAT tool. http://www.msoos.org/cryptominisat2/

  12. M. Soos, Enhanced Gaussian Elimination in DPLL-based SAT Solvers POS@SAT (2010)

    Google Scholar 

  13. T. Toffoli, Reversible computing, in Automata, Languages and Programming, ed. by W. de Bakker, J. van Leeuwen (Springer, Heidelberg, 1980), p. 632. (Technical Memo MIT/LCS/TM-151, MIT Lab. for Comput. Sci.)

    Google Scholar 

  14. E.F. Fredkin, T. Toffoli, Conservative logic. Int. J. Theor. Phys. 21(3/4), 219–253 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Peres, Reversible logic and quantum computers. Phys. Rev. A 32, 3266–3276 (1985)

    Article  MathSciNet  Google Scholar 

  16. A. Biere, M. Heule, H. van Maaren (eds.) Handbook of Satisfiability, vol. 185 (IOS Press, Amsterdam, 2009)

    Google Scholar 

  17. M. Davis, G. Logemann, D. Loveland, A machine program for theorem proving. Commun. ACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Yamashita, I.L. Markov. Fast equivalence-checking for quantum circuits, in Proceedings of the 2010 IEEE/ACM International Symposium on Nanoscale Architectures (IEEE Press, Piscataway, 2010)

    Google Scholar 

  19. M. Soos, K. Nohl, C. Castelluccia, Extending SAT solvers to cryptographic problems, Theory and Applications of Satisfiability Testing-SAT 2009 (Springer, Berlin, 2009), pp. 244–257

    Book  Google Scholar 

  20. D. Brand, Verification of large synthesized designs, in Proceedings of the ICCAD (1993), pp. 534–537

    Google Scholar 

  21. G.S. Tseitin, On the Complexity of Derivation in Propositional Calculus, Automation of Reasoning (Springer, Berlin, 1983)

    Google Scholar 

  22. Reversible CEC flow and experiments of this work. http://lsi.epfl.ch/RCEC

  23. R. Wille, D. Große, L. Teuber, G.W. Dueck, R. Drechsler, RevLib: an online resource for reversible functions and reversible circuits, in International Symposium on Multiple-Valued Logic, RevLib is (2008). http://www.revlib.org, pp. 220–225

  24. MiniSat: open-source SAT solver. http://minisat.se

  25. D.M. Miller, R. Wille, G.W. Dueck, Synthesizing reversible circuits for irreversible functions, in: Euromicro Conference on Digital System Design (DSD) (2009), pp. 749–756

    Google Scholar 

  26. R. Wille, O. Keszöcze, R. Drechsler, Determining the minimal number of lines for large reversible circuits, in Design, Automation and Test in Europe (DATE) (2011)

    Google Scholar 

  27. Y. Hamadi et al., ManySAT: a parallel SAT solver. J. Satisf. Boolean Model. Comput. 6, 245–262 (2008)

    MATH  Google Scholar 

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Correspondence to Luca Gaetano Amaru .

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Amaru, L.G. (2017). Improvements to the Equivalence Checking of Reversible Circuits. In: New Data Structures and Algorithms for Logic Synthesis and Verification. Springer, Cham. https://doi.org/10.1007/978-3-319-43174-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-43174-1_6

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