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Reversible Cellular Automata

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Primary Literature

  • Amoroso S, Cooper G (1970) The Garden of Eden theorem for finite configurations. Proc Am Math Soc 26:158–164

    Article  MathSciNet  MATH  Google Scholar 

  • Amoroso S, Patt Y-N (1972) Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures. J Comput Syst Sci 6:448–464

    Article  MathSciNet  MATH  Google Scholar 

  • Bennett C-H (1973) Logical reversibility of computation. IBM J Res Dev 17:525–532

    Article  MathSciNet  MATH  Google Scholar 

  • Bennett C-H (1982) The thermodynamics of computation – a review. Int J Theor Phys 21:905–940

    Article  Google Scholar 

  • Bennett C-H, Landauer R (1985) The fundamental physical limits of computation. Sci Am 253:38–46

    Article  ADS  Google Scholar 

  • Boykett T (2004) Efficient exhaustive listings of reversible one dimensional cellular automata. Theor Comput Sci 325:215–247

    Article  MathSciNet  MATH  Google Scholar 

  • Cocke J, Minsky M (1964) Universality of tag systems with P = 2. J ACM 11:15–20

    Article  MathSciNet  MATH  Google Scholar 

  • Cook M (2004) Universality in elementary cellular automata. Complex Syst 15:1–40

    MathSciNet  MATH  Google Scholar 

  • Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253

    Article  MathSciNet  MATH  Google Scholar 

  • Gruska J (1999) Quantum computing. McGraw-Hill, London

    MATH  Google Scholar 

  • Hedlund G-A (1969) Endomorphisms and automorphisms of the shift dynamical system. Math Syst Theory 3:320–375

    Article  MathSciNet  MATH  Google Scholar 

  • Imai K, Morita K (1996) Firing squad synchronization problem in reversible cellular automata. Theor Comput Sci 165:475–482

    Article  MathSciNet  MATH  Google Scholar 

  • Imai K, Morita K (2000) A computation-universal two-dimensional 8-state triangular reversible cellular automaton. Theor Comput Sci 231:181–191

    Article  MathSciNet  MATH  Google Scholar 

  • Imai K, Hori T, Morita K (2002) Self-reproduction in three-dimensional reversible cellular space. Artif Life 8:155–174

    Article  Google Scholar 

  • Kari J (1994) Reversibility and surjectivity problems of cellular automata. J Comput Syst Sci 48:149–182

    Article  MathSciNet  MATH  Google Scholar 

  • Kari J (1996) Representation of reversible cellular automata with block permutations. Math Syst Theory 29:47–61

    Article  MathSciNet  MATH  Google Scholar 

  • Landauer R (1961) Irreversibility and heat generation in the computing process. IBM J Res Dev 5:183–191

    Article  MathSciNet  MATH  Google Scholar 

  • Langton C-G (1984) Self-reproduction in cellular automata. Phys D 10:135–144

    Article  MATH  Google Scholar 

  • Margolus N (1984) Physics-like model of computation. Phys D 10:81–95

    Article  MathSciNet  MATH  Google Scholar 

  • Maruoka A, Kimura M (1976) Condition for injectivity of global maps for tessellation automata. Inf Control 32:158–162

    Article  MathSciNet  MATH  Google Scholar 

  • Maruoka A, Kimura M (1979) Injectivity and surjectivity of parallel maps for cellular automata. J Comput Syst Sci 18:47–64

    Article  MathSciNet  MATH  Google Scholar 

  • Minsky M-L (1967) Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Moore E-F (1962) Machine models of self-reproduction. Proc Symp Appl Math Am Math Soc 14:17–33

    Article  MATH  Google Scholar 

  • Mora JCST, Vergara SVC, Martinez GJ, McIntosh HV (2005) Procedures for calculating reversible one-dimensional cellular automata. Phys D 202:134–141

    Article  MathSciNet  MATH  Google Scholar 

  • Morita K (1990) A simple construction method of a reversible finite automaton out of Fredkin gates, and its related problem. Trans IEICE Jpn E73:978–984

    Google Scholar 

  • Morita K (1995) Reversible simulation of one-dimensional irreversible cellular automata. Theor Comput Sci 148:157–163

    Article  MathSciNet  MATH  Google Scholar 

  • Morita K (1996) Universality of a reversible two-counter machine. Theor Comput Sci 168:303–320

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Morita K (2007) Simple universal one-dimensional reversible cellular automata. J Cell Autom 2:159–166

    MathSciNet  MATH  Google Scholar 

  • Morita K (2008) Reversible computing and cellular automata – a survey. Theor Comput Sci 395:101–131

    Article  MathSciNet  MATH  Google Scholar 

  • Morita K (2011) Simulating reversible Turing machines and cyclic tag systems by one-dimensional reversible cellular automata. Theor Comput Sci 412:3856–3865

    Article  MathSciNet  MATH  Google Scholar 

  • Morita K (2016a) An 8-state simple reversible triangular cellular automaton that exhibits complex behavior. In: Cook M, Neary T (eds) AUTOMATA 2016. LNCS 9664, Springer, Cham, pp 170–184. Slides with movies of computer simulation: Hiroshima University Institutional Repository. http://ir.lib.hiroshima-u.ac.jp/00039321

  • Morita K (2016b) Universality of 8-state reversible and conservative triangular partitioned cellular automaton. In: El Yacoubi S et al (eds) ACRI 2016. LNCS 9863, Springer, Cham, pp 45–54. Slides with movies of computer simulation: Hiroshima University Institutional Repository. http://ir.lib.hiroshima-u.ac.jp/00039997

  • Morita K (2017a) Two small universal reversible Turing machines. In: Adamatzky A (ed) Advances in unconventional computing. Vol. 1: Theory. Springer, Cham, pp 221–237

    Google Scholar 

  • Morita K, Harao M (1989) Computation universality of one-dimensional reversible (injective) cellular automata. Trans IEICE Jpn E72:758–762

    Google Scholar 

  • Morita K, Imai K (1996) Self-reproduction in a reversible cellular space. Theor Comput Sci 168:337–366

    Article  MathSciNet  MATH  Google Scholar 

  • Morita K, Ueno S (1992) Computation-universal models of two-dimensional 16-state reversible cellular automata. IEICE Trans Inf Syst E75-D:141–147

    Google Scholar 

  • Morita K, Shirasaki A, Gono Y (1989) A 1-tape 2-symbol reversible Turing machine. Trans IEICE Jpn E72:223–228

    Google Scholar 

  • Morita K, Tojima Y, Imai K, Ogiro T (2002) Universal computing in reversible and number-conserving two-dimensional cellular spaces. In: Adamatzky A (ed) Collision-based computing. Springer, London, pp 161–199

    Google Scholar 

  • Myhill J (1963) The converse of Moore’s Garden-of-Eden theorem. Proc Am Math Soc 14:658–686

    Article  MathSciNet  MATH  Google Scholar 

  • von Neumann J (1966) In: Burks AW (ed) Theory of self-reproducing automata. Urbana, The University of Illinois Press

    Google Scholar 

  • Richardson D (1972) Tessellations with local transformations. J Comput Syst Sci 6:373–388

    Article  MathSciNet  MATH  Google Scholar 

  • Sutner K (2004) The complexity of reversible cellular automata. Theor Comput Sci 325:317–328

    Article  MathSciNet  MATH  Google Scholar 

  • Toffoli T (1977) Computation and construction universality of reversible cellular automata. J Comput Syst Sci 15:213–231

    Article  MathSciNet  MATH  Google Scholar 

  • Toffoli T (1980) Reversible computing. In: de Bakker JW, van Leeuwen J (eds) Automata, languages and programming. LNCS 85, Springer, Berlin, Heiderberg, pp 632–644

    Google Scholar 

  • Toffoli T, Margolus N (1990) Invertible cellular automata: a review. Phys D 45:229–253

    Article  MathSciNet  MATH  Google Scholar 

  • Toffoli T, Capobianco S, Mentrasti P (2004) How to turn a second-order cellular automaton into a lattice gas: a new inversion scheme. Theor Comput Sci 325:329–344

    Article  MathSciNet  MATH  Google Scholar 

  • Watrous J (1995) On one-dimensional quantum cellular automata. In: Proceedings of the FOCS, IEEE Computer Society Press, pp 528–537

    Google Scholar 

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Correspondence to Kenichi Morita .

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Morita, K. (2018). Reversible Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_455-7

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_455-7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

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Chapter history

  1. Latest

    Reversible Cellular Automata
    Published:
    31 January 2018

    DOI: https://doi.org/10.1007/978-3-642-27737-5_455-7

  2. Reversible Cellular Automata
    Published:
    26 September 2017

    DOI: https://doi.org/10.1007/978-3-642-27737-5_455-6

  3. Original

    Reversible Cellular Automata
    Published:
    05 November 2015

    DOI: https://doi.org/10.1007/978-3-642-27737-5_455-5