Reversible computing and cellular automata - A survey

Reversible computing is a paradigm where computing models are defined so that they reflect physical reversibility, one of the fundamental microscopic physical property of Nature. In this survey/tutorial paper, we discuss how computation can be carried out in a reversible system, how a universal reversible computer can be constructed by reversible logic elements, and how such logic elements are related to reversible physical phenomena. We shall see that, in reversible systems, computation can often be carried out in a very different manner from conventional (i.e., irreversible) computing systems, and even very simple reversible systems or logic elements have computation- or logical-universality. We discuss these problems based on reversible logic elements/circuits, reversible Turing machines, reversible cellular automata, and some other related models of reversible computing.

[1]  Claudio Baiocchi,et al.  Three Small Universal Turing Machines , 2001, MCU.

[2]  Manfred Kudlek,et al.  A Universal Turing Machine with 3 States and 9 Symbols , 2001, Developments in Language Theory.

[3]  Arthur W. Burks,et al.  Essays on cellular automata , 1970 .

[4]  Kenichi Morita,et al.  A New Universal Logic Element for Reversible Computing , 2003, Grammars and Automata for String Processing.

[5]  Turlough Neary,et al.  Small Semi-Weakly Universal Turing Machines , 2007, Fundam. Informaticae.

[6]  Katsunobu Imai,et al.  Firing Squad Synchronization Problem in Reversible Cellular Automata , 1996, Theor. Comput. Sci..

[7]  C. Petri.  Grundsätzliches zur Beschreibung Diskreter Prozesse , 1967 .

[8]  Matthew Cook,et al.  Universality in Elementary Cellular Automata , 2004, Complex Syst..

[9]  Kenichi Morita,et al.  A Universal Reversible Turing Machine , 2007, MCU.

[10]  Tommaso Toffoli,et al.  Computation and Construction Universality of Reversible Cellular Automata , 1977, J. Comput. Syst. Sci..

[11]  N. Margolus,et al.  Invertible cellular automata: a review , 1991 .

[12]  Turlough Neary,et al.  Four Small Universal Turing Machines , 2007, Fundam. Informaticae.

[13]  Kenichi Morita,et al.  Classification and Universality of Reversible Logic Elements with One-Bit Memory , 2004, MCU.

[14]  K. Morita,et al.  Computation universality of one-dimensional reversible (injective) cellular automata , 1989 .

[15]  Masayuki Kimura,et al.  Condition for Injectivity of Global Maps for Tessellation Automata , 1976, Inf. Control..

[16]  Tim Boykett,et al.  Efficient exhaustive listings of reversible one dimensional cellular automata , 2004, Theor. Comput. Sci..

[17]  Jarkko Kari,et al.  Reversibility and Surjectivity Problems of Cellular Automata , 1994, J. Comput. Syst. Sci..

[18]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[19]  Jarkko Kari,et al.  Theory of cellular automata: A survey , 2005, Theor. Comput. Sci..

[20]  J. Myhill.  The converse of Moore’s Garden-of-Eden theorem , 1963 .

[21]  D. Richardson,et al.  Tessellations with Local Transformations , 1972, J. Comput. Syst. Sci..

[22]  Charles H. Bennett.  Notes on the history of reversible computation , 2000, IBM J. Res. Dev..

[23]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[24]  G. A. Hedlund.  Endomorphisms and automorphisms of the shift dynamical system , 1969, Mathematical systems theory.

[25]  Lei Qian,et al.  Thermodynamics of Computation , 2009, Encyclopedia of Complexity and Systems Science.

[26]  Kenichi Morita,et al.  Computation-Universal Models of Two-Dimensional 16-State Reversible Cellular Automata , 1992 .

[27]  Katsunobu Imai,et al.  Universal Computing in Reversible and Number-Conserving Two-Dimensional Cellular Spaces , 2002, Collision-Based Computing.

[28]  Anthony J. G. Hey,et al.  Feynman Lectures on Computation , 1996 .

[29]  Tommaso Toffoli,et al.  Bicontinuous extensions of invertible combinatorial functions , 1981, Mathematical systems theory.

[30]  Katsunobu Imai,et al.  Self-Reproduction in a Reversible Cellular Space , 1996, Theor. Comput. Sci..

[31]  Kenichi Morita,et al.  Universality of a Reversible Two-Counter Machine , 1996, Theor. Comput. Sci..

[32]  Charles H. Bennett.  Time/Space Trade-Offs for Reversible Computation , 1989, SIAM J. Comput..

[33]  S. Amoroso,et al.  The Garden-of-Eden theorem for finite configurations , 1970 .

[34]  Kenichi Morita,et al.  A 1-Tape 2-Symbol Reversible Turing Machine , 1989 .

[35]  Andrew Adamatzky.  Collision-Based Computing , 2002, Springer London.

[36]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[37]  Katsunobu Imai,et al.  Self-Reproduction in Three-Dimensional Reversible Cellular Space , 2002, Artificial Life.

[38]  Masayuki Kimura,et al.  Injectivity and Surjectivity of Parallel Maps for Cellular Automata , 1979, J. Comput. Syst. Sci..

[39]  Yurii Rogozhin,et al.  Small Universal Turing Machines , 1996, Theor. Comput. Sci..

[40]  Tommaso Toffoli,et al.  Reversible Computing , 1980, ICALP.

[41]  Kenichi Morita,et al.  Simple Universal One-Dimensional Reversible Cellular Automata , 2007, J. Cell. Autom..

[42]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[43]  E. F. Moore.  Machine Models of Self-Reproduction , 1962 .

[44]  Juan Carlos Seck Tuoh Mora,et al.  Procedures for calculating reversible one-dimensional cellular automata , 2005 .

[45]  Kenichi Morita,et al.  A Simple Universal Logic Element and Cellular Automata for Reversible Computing , 2001, MCU.

[46]  Kenichi Morita,et al.  A Simple Construction Method of a Reversible Finite Automaton out of Fredkin Gates, and Its Related Problem , 1990 .

[47]  Maurice Margenstern,et al.  Surprising Areas in the Quest for Small Universal Devices , 2006, MFCSIT.

[48]  U. S. Army.  Decision Procedures for Surjectivity and Injectivity of Parallel Maps for Tessellation Structures , 2007 .

[49]  Katsunobu Imai,et al.  A computation-universal two-dimensional 8-state triangular reversible cellular automaton , 2000, Theor. Comput. Sci..