Skip to main content

An Asynchronous Cellular Automaton Implementing 2-State 2-Input 2-Output Reversed-Twin Reversible Elements

  • Conference paper
Cellular Automata (ACRI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5191))

Included in the following conference series:

Abstract

Reversible computers usually work in a synchronous mode, i.e., in the presence of clock signals, but in the light of the asynchronous nature of microscopic physical phenomena this may be an anomaly. The alternative, an asynchronous mode of operation, has therefore attracted attention from researchers, witness the proposal of a reversible circuit element in (Morita 2001) that works in such a mode. Simplicity of circuit elements like this is an important design objective since it correlates positively with the efficiency by which they may be realized physically. In this paper, we present two mutually inverse logic elements that compare favorably to other circuit elements in terms of their number of states and their number of input and output lines. We show that the proposed circuit elements can perform universal computation by embedding circuits made of them in asynchronous cellular automata.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bennett, C.: Logical reversibility of computation. IBM Journal of Research and Development 17(6), 525–532 (1973)

    Article  MATH  Google Scholar 

  2. Vos, A.D., Raa, B., Storme, L.: Generating the group of reversible logic gates. Journal of Physics A: Mathematical and General 35(33), 7063–7078 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Frank, M., Vieri, C., Ammer, M., Love, N., Margolus, N., Knight Jr., T.F.: A scalable reversible computer in silicon. In: Calude, C.S., Casti, J., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 183–200. Springer, Singapore (1998)

    Google Scholar 

  4. Fredkin, E., Toffoli, T.: Conservative logic. International Journal of Theoretical Physics 21(3-4), 219–253 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Margolus, N.: Physics-like models of computation. Physica D 10(1/2), 81–95 (1984)

    Article  MathSciNet  Google Scholar 

  6. Merkle, R.: Reversible electronic logic using switches. Nanotechnology 4(1), 21–40 (1993)

    Article  Google Scholar 

  7. Hauck, S.: Asynchronous design methodologies: an overview. Proc. IEEE 83(1), 69–93 (1995)

    Article  MathSciNet  Google Scholar 

  8. Patra, P., Fussell, D.: Conservative delay-insensitive circuits. In: Workshop on Physics and Computation (PhysComp 1996) (1996)

    Google Scholar 

  9. Morita, K.: A simple universal logic element and cellular automata for reversible computing. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 102–113. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Lee, J., Peper, F., Adachi, S., Mashiko, S.: On reversible computation in asynchronous systems. In: Quantum Information and Complexity, pp. 296–320. World Scientific, Singapore (2004)

    Google Scholar 

  11. Tanaka, K.: Universal reversible logic elements with 3 inputs, 3 outputs, and 2 states. Master Thesis, Hiroshima University (in Japanese) (2003)

    Google Scholar 

  12. Lee, J., Peper, F., Adachi, S., Morita, K., Mashiko, S.: Reversible computation in asynchronous cellular automata. In: Calude, C.S., Dinneen, M.J., Peper, F. (eds.) UMC 2002. LNCS, vol. 2509, pp. 220–229. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Peper, F., Isokawa, T., Kouda, N., Matsui, N.: Self-timed cellular automata and their computational ability. Future Generation Computer Systems 18(7), 893–904 (2002)

    Article  MATH  Google Scholar 

  14. Mealy, G.: A method for synthesizing sequential circuits. Bell System Technical Journal 34(5), 1045–1079 (1955)

    MathSciNet  Google Scholar 

  15. Morita, K., Shirasaki, A., Gono, Y.: A 1-tape 2-symbol reversible Turing machine. Trans. IEICE Japan E-72, 223–228 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hiroshi Umeo Shin Morishita Katsuhiro Nishinari Toshihiko Komatsuzaki Stefania Bandini

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lee, J., Peper, F., Adachi, S., Morita, K. (2008). An Asynchronous Cellular Automaton Implementing 2-State 2-Input 2-Output Reversed-Twin Reversible Elements. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-79992-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79991-7

  • Online ISBN: 978-3-540-79992-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics