Abstract
Reversible computing is a paradigm of computation that reflects physical reversibility, and is considered to be important when designing a logical devices based on microscopic physical law in the near future. In this paper, we focus on a problem how universal computers can be built from primitive elements with very simple reversible rules. We introduce a new reversible logic element called a “rotary element”, and show that any reversible Turing machine can be realized as a circuit composed only of them. Such reversible circuits work in a very different fashion from conventional ones. We also discuss a simple reversible cellular automaton in which a rotary element can be implemented.
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
Bennett, C.H., Logical reversibility of computation, IBM J. Res. Dev., 17, 525–532 (1973).
Feynman, R.P., Feynman Lectures on Computation (eds., A.J.G. Hey and R.W. Allen), Perseus Books, Reading, Massachusetts (1996).
Fredkin, E. and Toffoli, T., Conservative logic, Int. J. Theoret. Phys., 21, 219–253 (1982).
Gruska, J., Quantum Computing, McGraw-Hill, London (1999).
Margolus, N., Physics-like model of computation, Physica, 10D, 81–95 (1984).
Morita, K., Shirasaki, A. and Gono, Y., A 1-tape 2-symbol reversible Turing machine, Trans. IEICE Japan, E-72, 223–228 (1989).
Morita, K., and Ueno, S., Computation-universal models of two-dimensional 16-state reversible cellular automata, IEICE Trans. Inf. &Syst., E75-D, 141–147 (1992).
Morita, K., Tojima, Y. and Imai, K.,A simple computer embedded in a reversible and number-conserving two-dimensional cellular space, Multiple-Valued Logic, (in press). Movie: http://www.ke.sys.hiroshima-u.ac.jp/”morita/p4/
Morita, K., A new universal logic element for reversible computing, Technical Report of IEICE Japan, COMP99-94 (2000).
Morita, K. and Ogiro T., Embedding a counter machine in a simple reversible 2-D cellular space, Proc. Int. Workshop on Cellular Automata, Osaka, 30–31 (2000). Movie: http://www.ke.sys.hiroshima-u.ac.jp/”morita/p3/
Păun, Gh., Rozenberg, G. and Salomaa, A., DNA Computing, Springer-Verlag, Berlin (1998).
Toffoli, T., Reversible computing, in Automata, Languages and Programming, Springer-Verlag, LNCS-85, 632–644 (1980).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Morita, K. (2001). A Simple Universal Logic Element and Cellular Automata for Reversible Computing. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_6
Download citation
DOI: https://doi.org/10.1007/3-540-45132-3_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42121-4
Online ISBN: 978-3-540-45132-7
eBook Packages: Springer Book Archive