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Bibliography
Adamatzky A (1994) Identification of cellular automata. Taylor & Francis, London
Amoroso S, Patt YN (1972) Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J Comput Syst Sci 6:448–464
Baldwin JT (2002) Computation versus simulation. http://www.math.uic.edu/%7Ejbaldwin/pub/cafom.ps. Accessed May 2007
Baldwin JT, Shelah S (2000) On the classifiability of cellular automata. Theor Comput Sci 230(1–2):117–129
Baumslag G (2007) Magnus. http://caissny.org/. Accessed May 2007
Beal M-P, Perrin D (1997) Symbolic dynamics and finite automata. In: Rozenberg G, Salomaa A (eds) Handbook of formal languages. Springer, Berlin
Bennett CH (1973) Logical reversibility of computation. IBM J Res Dev 17:525–532
Börger E, Grädel E, Gurevich Y (2001) The classical decision problem. Springer, Berlin
Cook M (2004) Universality in elementary cellular automata. Complex Syst 15(1):1–40
Culik K (1987) On invertible cellular automata. Complex Syst 1(6):1035–1044
Culik K, Sheng Y (1988) Undecidability of CA classification schemes. Complex Syst 2(2):177–190
Davis M (1956) A note on universal Turing machines. In: Shannon CE, McCarthy J (eds) Automata studies. Annals of mathematics studies, vol 34. Princeton University Press, Princeton, pp 167–175
Davis M (1957) The definition of universal Turing machines. Proc Am Math Soc 8:1125–1126
Delorme M, Mazoyer J (1999) Cellular automata: a parallel model. Mathematics and its applications, vol 460. Kluwer, Dordrecht
Delvenne J-C, Kůrka P, Blondel V (2006) Decidability and universality in symbolic dynamical systems. Fundamenta Informaticae 74(4):463–490
Durand-Lose J (2001) Representing reversible cellular automata with reversible block automata. Disc Math Theor Comp Sci Proc AA:145–154
Elgaard J, Klarlund N, Møller A (1998) MONA 1.x: new techniques for WS1S and WS2S. In: Proceeding of the 10th international conference on computer-aided verification, CAV ’98. LNCS, vol 1427. Springer, Berlin, pp 516–520
Friedberg RM (1957) Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci U S A 43:236–238
Grädel E, Thomas W, Wilke T (eds) (2002) Automata, logics, and infinite games, LNCS, vol 2500. Springer, Berlin
Gutowitz H (1996a) Cellular automata and the sciences of complexity, part I. Complexity 1(5):16–22
Gutowitz H (1996b) Cellular automata and the sciences of complexity, part II. Complexity 1(6)
Harrington L, Shelah S (1982) The undecidability of the recursively enumerable degrees. Bull Am Math Soc 6:79–80
Head T (1989) Linear CA: injectivity from ambiguity. Complex Syst 3(4):343–348
Hedlund GA (1969) Endomorphisms and automorphisms of the shift dynamical system. Math Syst Theory 3:320–375
Hooper PK (1966) The undecidability of the Turing machine immortality problem. J Symb Log 31(2):219–234
Kari J (1990) Reversibility of 2D cellular automata is undecidable. Physica D 45:397–385
Kůrka P (1997) Languages, equicontinuity and attractors in cellular automata. Ergod Th Dyn Syst 17:417–433
Kůrka P (2003) Topological and symbolic dynamics, Cours Spécialisés, vol 11. Societe Mathematique de France, Paris
Langton CG (1990) Computation at the edge of chaos. Physica D 42:12–37
Lecerf Y (1963) Machine de Turing réversible. Insolubilité récursive en n ∈ N de l’équation u = θnu, où θ est un “isomorphisme de codes”. C R Acad Sci Paris 257:2597–2600
Lerman M (1983) Degrees of unsolvability. Perspectives in mathematical logic. Springer, Berlin
Li W, Packard N (1990) The structure of the elementary cellular automata rule space. Complex Syst 4(3):281–297
Li W, Packard N, Langton CG (1990) Transition phenomena in CA rule space. Physica D 45(1–3):77–94
Libkin L (2004) Elements of finite model theory. Springer, Berlin
Manzini G, Margara L (1999) A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm. Theor Comput Sci 221(1–2):157–177
Mazoyer J (1987) A six state minimal time solution to the firing squad synchronization problem. Theor Comput Sci 50:183–238
Mitchell M, Crutchfield JP, Hraber PT (1994) Evolving cellular automata to perform computations: mechanisms and impediments. Physica D (75):361–369
Morita K (1994) Reversible cellular automata. J Inf Process Soc Japan 35:315–321
Morita K (1995) Reversible simulation of one-dimensional irreversible cellular automata. Theor Comput Sci 148:157–163
Morita K, Harao M (1989) Computation universality of 1 dimensional reversible (injective) cellular automata. Trans Inst Electron, Inf Commun Eng E 72:758–762
Muchnik AA (1956) On the unsolvability of the problem of reducibility in the theory of algorithms. Dokl Acad Nauk SSSR 108:194–197
Neary R, Woods D (2006a) On the time complexity of 2-tag systems and small universal turing machines. In: FOCS. IEEE Comput Soc, Berkeley, pp 439–448
Neary R, Woods D (2006b) Small fast universal turing machines. Theor Comput Sci 362(1–3):171–195
Oliveira G, Oliveira P, Omar N (2001) Definition and application of a five-parameter characterization of one-dimensional cellular automata rule space. Artif Life 7(3):277–301
Ollinger N (2003) The intrinisic universality problem of one-dimensional cellular automata. In: Alt H, Habib M (eds) Proceeings STACS. LNCS, vol 2607. Springer, Berlin, pp 632–641
Packard NH (1988) Adaptation towards the edge of chaos. In: Dynamic patterns in complex systems. World Scientific, Singapore, pp 29–301
Rogers H (1967) Theory of recursive functions and effective computability. McGraw Hill, New York
Rozenberg G, Salomaa A (1997) Handbook of formal languages. Springer, Berlin
Shepherdson JC (1965) Machine configuration and word problems of given degree of unsolvability. Z Math Logik Grundl Math 11:149–175
Shoenfield JR (1967) Mathematical logic. Addison Wesley, Reading
Soare RI (1972) The Friedberg-Muchnik theorem re-examined. Can J Math 24:1070–1078
Soare RI (1987) Recursively enumerable sets and degrees. Perspectives in mathematical logic. Springer, Berlin
Sutner K (1989) A note on Culik-Yu classes. Complex Syst 3(1):107–115
Sutner K (1990) Classifying circular cellular automata. Physica D 45(1–3):386–395
Sutner K (1991) De Bruijn graphs and linear cellular automata. Complex Syst 5(1):19–30
Sutner K (1995) The complexity of finite cellular automata. J Comput Syst Sci 50(1):87–97
Sutner K (2002) Cellular automata and intermediate reachability problems. Fundamentae Informaticae 52(1–3):249–256
Sutner K (2003a) Almost periodic configurations on linear cellular automata. Fundamentae Informaticae 58(3,4):223–240
Sutner K (2003b) Cellular automata and intermediate degrees. Theor Comput Sci 296:365–375
Sutner K (2004) The complexity of reversible cellular automata. Theor Comput Sci 325(2):317–328
Taati S (2007) Cellular automata reversible over limit set. J Cell Autom 2(2):167–177
Toffoli T, Margolus N (1990) Invertible cellular automata: a review. Physica D 45:229–253
Turing AM (1936) On computable numbers, with an application to the Entscheidungsproblem. P Lond Math Soc 42:230–265
Vorhees B (1996) Computational analysis of one-dimensional cellular automata. World Scientific, Singapore
Wang H (1993) Popular lectures on mathematical logic. Dover Publications, Dover/New York
Weihrauch K (2000) Computable analysis. EATCS monographs. Springer, Berlin
Wolfram S (1984a) Computation theory of cellular automata. Commun Math Phys 96(1):15–57
Wolfram S (1984b) Universality and complexity in cellular automata. Physica D 10:1–35
Wolfram S (1985) Twenty problems in the theory of cellular automata. Phys Scr T9:170–183
Wolfram S (2002a) The mathematica book. Cambridge University Press, Cambridge
Wolfram S (2002b) A new kind of science. Wolfram Media, Champaign
Wuensche A (1999) Classifying cellular automata automatically. Complexity 4(3):47–66
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Sutner, K. (2009). Classification of Cellular Automata. In: Adamatzky, A. (eds) Cellular Automata. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8700-9_50
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