Abstract
A reversible logic element with memory (RLEM) is a primitive by which reversible computing systems can be constructed. Different from a reversible logic gate, it has a finite memory, and thus is defined as a kind of reversible sequential machine (RSM). It is known that any reversible Turing machine (RTM) can be built in a simple way using a rotary element (RE), a typical 2-state RLEM (i.e., having 1-bit memory) with four input/output lines. In this paper, we show another compact realization of an RTM using a 2-state RLEM No. 4-31 with four input/output lines. Since RLEM 4-31 can be simulated by a circuit composed of only two copies of 2-state RLEM 3-7, we also obtain another compact realization by an RLEM with three input/output lines.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)
Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theoret. Phys. 21, 219–253 (1982)
Lee, J., Peper, F., Adachi, S., Morita, K.: 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.) ACRI 2008. LNCS, vol. 5191, pp. 67–76. Springer, Heidelberg (2008)
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)
Morita, K.: A new universal logic element for reversible computing. In: Martin-Vide, C., Mitrana, V. (eds.) Grammars and Automata for String Processing, pp. 285–294. Taylor & Francis, London (2003)
Morita, K.: Reversible computing and cellular automata — A survey. Theoret. Comput. Sci. 395, 101–131 (2008)
Morita, K.: Constructing a reversible Turing machine by a rotary element, a reversible logic element with memory. Hiroshima University Institutional Repository (2010), http://ir.lib.hiroshima-u.ac.jp/00029224
Morita, K.: Reversible Computing. Kindai Kagaku-sha Co., Ltd., Tokyo (2012) (in Japanese) ISBN 978-4-7649-0422-4
Morita, K., Ogiro, T., Alhazov, A., Tanizawa, T.: Non-degenerate 2-state reversible logic elements with three or more symbols are all universal. J. Multiple-Valued Logic and Soft Computing 18, 37–54 (2012)
Morita, K., Ogiro, T., Tanaka, K., Kato, H.: Classification and universality of reversible logic elements with one-bit memory. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 245–256. Springer, Heidelberg (2005)
Mukai, Y., Morita, K.: Realizing reversible logic elements with memory in the billiard ball model. Int. J. of Unconventional Computing 8(1), 47–59 (2012)
Mukai, Y., Ogiro, T., Morita, K.: Universality problems on reversible logic elements with 1-bit memory. Int. J. Unconventional Computing (to appear)
Toffoli, T.: Reversible computing. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 632–644. Springer, Heidelberg (1980)
Toffoli, T.: Bicontinuous extensions of invertible combinatorial functions. Math. Syst. Theory 14, 12–23 (1981)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Morita, K., Suyama, R. (2014). Compact Realization of Reversible Turing Machines by 2-State Reversible Logic Elements. In: Ibarra, O., Kari, L., Kopecki, S. (eds) Unconventional Computation and Natural Computation. UCNC 2014. Lecture Notes in Computer Science(), vol 8553. Springer, Cham. https://doi.org/10.1007/978-3-319-08123-6_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-08123-6_23
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08122-9
Online ISBN: 978-3-319-08123-6
eBook Packages: Computer ScienceComputer Science (R0)