A survey of cellular automata: types, dynamics, non-uniformity and applications (original) (raw)

• Acerbi L, Dennunzio A, Formenti E (2009) Conservation of some dynamical properties for operations on cellular automata. Theor Comput Sci 410(38–40):3685–3693
  Article MathSciNet MATH Google Scholar
• Adak S, Naskar N, Maji P, Das S (2016) On synthesis of non-uniform cellular automata having only point attractors. J Cell Autom 12(1–2):81–100
  MathSciNet MATH Google Scholar
• Adamatzky AI (1996) Computation of shortest path in cellular automata. Math Comput Model 23(4):105–113
  Article MathSciNet MATH Google Scholar
• Adami C (1995) Self-organized criticality in living systems. Phys Lett A 203(1):29–32
  Article Google Scholar
• Albert J, Culik K II (1987) A simple universal cellular automaton and its one-way and totalistic version. Complex Syst 1:1–16
  MathSciNet MATH Google Scholar
• Albicki A, Khare M (1987) Cellular automata used for test pattern generation. In: Proceedings of international conference of computer design, pp 56–59
• Alonso-Sanz R, Bull L (2009) Elementary cellular automata with minimal memory and random number generation. Complex Syst 18(2):195–213
  Article MathSciNet MATH Google Scholar
• Amoroso S, Cooper G (1970) The garden-of-eden theorem for finite configurations. Proc Am Math Soc 26(1):158–164
  Article MathSciNet MATH Google Scholar
• Amoroso S, Patt YN (1972) Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J Comput Syst Sci 6:448–464
  Article MATH Google Scholar
• Arbib MA (1966) Simple self-reproducing universal automata. Inf Control 9:177–189
  Article MATH Google Scholar
• Atrubin AJ (1965) A one-dimensional real-time iterative multiplier. IEEE Trans Electron Comput EC–14(3):394–399
  Article Google Scholar
• Banda P, Caughman J, Pospichal J (2015) Configuration symmetry and performance upper bound of one-dimensional cellular automata for the leader election problem. J Cell Autom 10(1–2):1–21
  MathSciNet MATH Google Scholar
• Banks ER (1970) Universality in cellular automata. In: Proceedings of IEEE conference record of 11th annual symposium on switching and automata theory, 1970. IEEE, pp 194–215
• Banks ER (1971) Information processing and transmission in cellular automata. Ph.D. thesis, MIT
• Bao F (2004) Cryptanalysis of a partially known cellular automata cryptosystem. IEEE Trans Comput 53(11):1493–1497
  Article Google Scholar
• Bardell PH (1990) Analysis of cellular automata used as pseudo-random pattern generators. In: Proceedings of international test conference, pp 762–768
• Beckers A, Worsch T (2001) A perimeter-time ca for the queen bee problem. Parallel Comput 27(5):555–569
  Article MathSciNet MATH Google Scholar
• Benjamin SC, Johnson NF (1997) A possible nanometer-scale computing device based on an adding cellular automaton. Appl Phys Lett 70(17):2321–2323
  Article Google Scholar
• Betel H, de Oliveira PPB, Flocchini P (2013) Solving the parity problem in one-dimensional cellular automata. Nat Comput 12(3):323–337
  Article MathSciNet MATH Google Scholar
• Bhattacharjee K, Das S (2016) Reversibility of \(d\)-state finite cellular automata. J Cell Autom 11(2–3):213–245
  MathSciNet MATH Google Scholar
• Bhattacharjee K, Paul D, Das S (2017) Pseudo-random number generation using a 3-state cellular automaton. Int J Mod Phys C 28(06):1750–078
  Article MathSciNet Google Scholar
• Bhattacharjee S, Bhattacharya J, Chaudhuri PP (1995) An efficient data compression hardware based on cellular automata. In: Proceedings of data compression conference (DCC95), p 472
• Blanchard F, Maass A (1997) Dynamical properties of expansive one-sided cellular automata. Israel J Math 99(1):149–174
  Article MathSciNet MATH Google Scholar
• Blok HJ, Bergersen B (1999) Synchronous versus asynchronous updating in the “game of life”. Phys Rev E 59:3876–3879
  Article Google Scholar
• Boccara N, Fukś H (1998) Cellular automaton rules conserving the number of active sites. J Phys A Math Gen 31:6007
  Article MathSciNet MATH Google Scholar
• Boccara N, Fukś H (2002) Number-conserving cellular automaton rules. Fundam Inf 52(1–3):1–13
  MathSciNet MATH Google Scholar
• Boccara N, Roger M (1994) Some properties of local and nonlocal site exchange deterministic cellular automata. Int J Modern Phys C 5(03):581–588
  Article Google Scholar
• Bohm D (1980) Wholeness and the implicate order, ISBN 0-203-99515-5. Routledge, Abingdon
  Google Scholar
• Bouré O, Fatès N, Chevrier V (2012) Probing robustness of cellular automata through variations of asynchronous updating. Nat Comput 11(4):553–564
  Article MathSciNet MATH Google Scholar
• Burks C, Farmer D (1984) Towards modeling DNA sequences as automata. Phys D Nonlinear Phenom 10(1–2):157–167
  Article MathSciNet MATH Google Scholar
• Capobianco S (2007) Surjectivity and surjunctivity of cellular automata in besicovitch topology. In: Proceedings of international workshop on cellular automata and discrete complex systems, AUTOMATA 2007
• Cattaneo G, Formenti E, Margara L, Mauri G (1999) On the dynamical behavior of chaotic cellular automata. Theor Comput Sci 217(1):31–51
  Article MathSciNet MATH Google Scholar
• Cattaneo G, Finelli M, Margara L (2000) Investigating topological chaos by elementary cellular automata dynamics. Theor Comput Sci 244(1–2):219–241
  Article MathSciNet MATH Google Scholar
• Cattaneo G, Dennunzio A, Margara L (2004) Solution of some conjectures about topological properties of linear cellular automata. Theor Comput Sci 325(2):249–271
  Article MathSciNet MATH Google Scholar
• Cattaneo G, Dennunzio A, Formenti E, Provillard J (2009) Non-uniform cellular automata. In: Proceedings of 3rd international conference language and automata theory and applications, LATA, pp 302–313
• Cattell K, Muzio JC (1996) Synthesis of one-dimensional linear hybrid cellular automata. IEEE Trans Comput Aided Design Integr Circuits Syst 15(3):325–335
  Article MATH Google Scholar
• Cattell K, Zhang S (1995) Minimal cost one-dimensional linear hybrid cellular automata of degree through 500. J Electron Test Theory Appl 6(2):255–258
  Article Google Scholar
• Ceccherini-Silberstein TG, Machi A, Scarabotti F (1999) Amenable groups and cellular automata. Annales de l’institut Fourier 49(2):673–685
  Article MathSciNet MATH Google Scholar
• Chakraborty R, Chowdhury DR (2009) A novel seed selection algorithm for test time reduction in BIST. In: Proceedings of the 18th Asian test symposium, ATS 2009, Taiwan, pp 15–20
• Chakraborty S, Chowdhury DR, Chaudhuri PP (1996) Theory and application of non-group cellular automata for synthesis of easily testable finite state machines. IEEE Trans Comput 45(7):769–781
  Article MathSciNet MATH Google Scholar
• Chattopadhyay P, Choudhury PP, Dihidar K (1999) Characterisation of a particular hybrid transformation of two-dimensional cellular automata. Comput Math Appl 38(5–6):207–216
  Article MathSciNet MATH Google Scholar
• Chattopadhyay S, Adhikari S, Sengupta S, Pal M (2000) Highly regular, modular, and cascadable design of cellular automata-based pattern classifier. IEEE Trans VLSI Syst 8(6):724–735
  Article Google Scholar
• Chaudhuri PP, Chowdhury DR, Nandi S, Chatterjee S (1997) Additive cellular automata–theory and applications, ISBN 0-8186-7717-1, vol 1. IEEE Computer Society Press, Los Alamitos
  Google Scholar
• Cheybani S, Kertész J, Schreckenberg M (2000) Stochastic boundary conditions in the deterministic nagel-schreckenberg traffic model. Phys Rev E 63(016):107
  MATH Google Scholar
• Chopard B, Droz M (1998) Cellular automata modeling of physical systems. Cambridge University Press, Cambridge
  Book MATH Google Scholar
• Chowdhury DR (1994) Theory and applications of additive cellular automata for reliable and testable VLSI circuit design. Ph.D. thesis, IIT, Kharagpur
• Chowdhury DR, Chakraborty S, Vamsi B, Chaudhuri PP (1993) Cellular automata based synthesis of easily and fully testable FSMs. In: Proceedings of international conference on computer aided design, ICCAD, pp 650–653
• Chowdhury DR, Basu S, Gupta IS, Chaudhuri PP (1994) Design of CAECC—cellular automata based error correcting code. IEEE Trans Comput 43(6):759–764
  Article MathSciNet MATH Google Scholar
• Cinkir Z, Akin H, Siap I (2011) Reversibilty of 1D cellular automata with periodic boundary over finite fields \( {{\mathbb{Z}}}_{p}\). J Stat Phys 143:807–823
  Article MathSciNet MATH Google Scholar
• Codd EF (1968) Cellular automata. Academic Press Inc, Cambridge
  MATH Google Scholar
• Codenotti B, Margara L (1996) Transitive cellular automata are sensitive. Am Math Mon 103(1):58–62
  Article MathSciNet MATH Google Scholar
• Cole SN (1969) Real time computation by n-dimensional iterative arrays of finite state machines. IEEE Trans Comput C–18:55–77
  MathSciNet Google Scholar
• Comer JM, Cerda JC, Martinez CD, Hoe DH (2012) Random number generators using cellular automata implemented on FPGAs. In: Proceedings of 44th southeastern symposium on system theory (SSST), 2012, pp 67–72
• Cook M (2004) Universality in elementary cellular automata. Complex Syst 15(1):1–40
  MathSciNet MATH Google Scholar
• Cori R, Metivier Y, Zielonka W (1993) Asynchronous mappings and asynchronous cellular automata. Inf Comput 106(2):159–202
  Article MathSciNet MATH Google Scholar
• Culik K (1987) On invertible cellular automata. Complex Syst 1(6):1035–1044
  MathSciNet MATH Google Scholar
• Culik K, Dube S (1991) An efficient solution to the firing mob problem. Theor Comput Sci 91:57–69
  Article MathSciNet MATH Google Scholar
• Culik K, Yu S (1988) Undecidability of cellular automata classification schemes. Complex Syst 2:177–190
  MATH Google Scholar
• Culik K, Hard LP, Yu S (1990) Computation theoretic aspects of cellular automata. Physica D 45(1–3):357–378
  Article MathSciNet MATH Google Scholar
• Darabos C, Giacobini M, Tomassini M (2007) Performance and robustness of cellular automata computation on irregular networks. Adv Complex Syst 10:85–110
  Article MATH Google Scholar
• Das AK (1990) Additive cellular automata: theory and application as a built-in self-test structure. Ph.D. thesis, IIT, Kharagpur
• Das AK, Chaudhuri PP (1989) An efficient on-chip deterministic test pattern generation scheme. Microprocess Microprogr 26:195–204
  Article Google Scholar
• Das AK, Chaudhuri PP (1993) Vector space theoretic analysis of additive cellular automata and its applications for pseudo-exhaustive test pattern generation. IEEE Trans Comput 42(3):340–352
  Article MathSciNet MATH Google Scholar
• Das AK, Ganguly A, Dasgupta A, Bhawmik S, Chaudhuri PP (1990a) Efficient characterisation of cellular automata. IEE Proc E Comput Digit Tech 137(1):81–87
  Article Google Scholar
• Das AK, Saha D, Chowdhury AR, Misra S, Chaudhuri PP (1990b) Signature analyzer based on additive cellular automata. In: Proceedings of 20th fault tolerant computing systems, pp 265–272
• Das AK, Sanyal A, Chaudhuri PP (1992) On characterization of cellular automata with matrix algebra. Inf Sci 61(3):251–277
  Article MathSciNet MATH Google Scholar
• Das S (2007) Theory and applications of nonlinear cellular automata in VLSI design. Ph.D. thesis, Bengal Engineering and Science University, Shibpur
• Das S (2011) Characterization of non-uniform number conserving cellular automata. In: Proceedings of international workshop on cellular automata and discrete complex systems, AUTOMATA 2011, Chile, pp 17–28
• Das S, Chowdhury DR (2011) Cryptographically suitable maximum length cellular automata. J Cell Autom 6(6):439–459
  MathSciNet MATH Google Scholar
• Das S, Chowdhury DR (2013) CAR30: a new scalable stream cipher with rule 30. Cryptogr Commun 5(2):137–162
  Article MathSciNet MATH Google Scholar
• Das S, Sikdar BK (2008) Characterization of non-reachable states in irreversible ca state space. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2008, Japan. Springer, Berlin, pp 160–167
• Das S, Sikdar BK (2009) Characterization of 1-D periodic boundary reversible ca. Electron Notes Theor Comput Sci 252:205–227
  Article MathSciNet MATH Google Scholar
• Das S, Sikdar BK (2010) A scalable test structure for multicore chip. IEEE Trans CAD Integr Circuits Syst 29(1):127–137
  Article Google Scholar
• Das S, Ganguly N, Sikdar BK, Chaudhuri PP (2003a) Design of a universal BIST (UBIST) structure. In: Proceedings of 16th international conference on VLSI design, pp 161–166
• Das S, Kundu A, Sen S, Sikdar BK, Chaudhuri PP (2003b) Non-linear celluar automata based PRPG design (without prohibited pattern set) in linear time complexity. In: Proceedings of Asian test symposium, pp 78–83
• Das S, Sikdar BK, Chaudhuri PP (2004) Characterization of reachable/nonreachable cellular automata states. In: Proceedings of internationl conference on cellular automata, research and industry, ACRI 2004, Netherlands. Springer, Berlin, pp 813–822
  Google Scholar
• Das S, Mukherjee S, Naskar N, Sikdar BK (2009) Characterization of single cycle ca and its application in pattern classification. Electron Notes Theor Comput Sci 252:181–203
  Article MathSciNet MATH Google Scholar
• Das S, Sarkar A, Sikdar BK (2012) Synthesis of reversible asynchronous cellular automata for pattern generation with specific hamming distance. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2012, Greece. Springer, Berlin, pp 643–652
  Google Scholar
• Delorme M, Mazoyer J, Tougne L (1999) Discrete parabolas and circles on 2D cellular automata. Theor Comput Sci 218(2):347–417
  Article MATH Google Scholar
• Dennunzio A, Lena PD, Formenti E, Margara L (2009) On the directional dynamics of additive cellular automata. Theor Comput Sci 410(47):4823–4833
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Formenti E, Manzoni L (2012a) Computing issues of asynchronous CA. Fundam Inf 120(2):165–180
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Formenti E, Provillard J (2012b) Non-uniform cellular automata: classes, dynamics, and decidability. Inf Comput 215:32–46
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Di Lena P, Formenti E, Margara L (2013a) Periodic orbits and dynamical complexity in cellular automata. Fundam Inform 126(2–3):183–199
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Formenti E, Manzoni L, Mauri G (2013b) m-asynchronous cellular automata: from fairness to quasi-fairness. Nat Comput 12(4):561–572
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Formenti E, Provillard J (2013c) Local rule distributions, language complexity and non-uniform cellular automata. Theor Comput Sci 504:38–51
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Formenti E, Provillard J (2014a) Three research directions in non-uniform cellular automata. Theor Comput Sci 559:73–90
  Article MathSciNet MATH Google Scholar
• Dennunzio A, Formenti E, Weiss M (2014b) Multidimensional cellular automata: closing property, quasi-expansivity, and (un)decidability issues. Theor Comput Sci 516:40–59
  Article MathSciNet MATH Google Scholar
• de Oliveira GMB, Siqueira SRC (2006) Parameter characterization of two-dimensional cellular automata rule space. Physica D 217(1):1–6
  Article MathSciNet MATH Google Scholar
• de Oliveira PPB (2013) Conceptual connections around density determination in cellular automata. In: Proceedings of international workshop on cellular automata and discrete complex systems, AUTOMATA 2013, Germany, pp 1–14
• Devaney RL (1986) An introduction to chaotic dynamical systems. Addison Wesley, Boston
  MATH Google Scholar
• Di Gregorio S, Trautteur G (1975) On reversibility in cellular automata. J Comput Syst Sci 11(3):382–391
  Article MathSciNet MATH Google Scholar
• Domosi P, Nehaniv CL (2005) Algebraic theory of automata networks: an introduction. SIAM monographs on discrete mathematics and applications. Society for Industrial and Applied Mathematics, Philadelphia
  Book MATH Google Scholar
• Droste M, Gastin P, Kuske D (2000) Asynchronous cellular automata for pomsets. Theor Comput Sci 247(1–2):1–38
  Article MathSciNet MATH Google Scholar
• Dubacq JC (1995) How to simulate turing machines by invertible one-dimensional cellular automata. Int J Found Comput Sci 6(4):395–402
  Article MATH Google Scholar
• Durand B (1993) Global properties of 2d cellular automata: Some complexity results. In: Proceedings of 18th international symposium, MFCS’93, Poland. Springer, Berlin, pp 433–441
  Google Scholar
• Durand B, Formenti E, Róka Z (2003a) Number-conserving cellular automata i: decidability. Theor Comput Sci 299(1–3):523–535
  Article MathSciNet MATH Google Scholar
• Durand B, Formenti E, Varouchas G (2003b) On undecidability of equicontinuity classification for cellular automata. Discrete Math Theor Comput Sci 3:117–128
  MathSciNet MATH Google Scholar
• Durand-Lose JO (1998) About the universality of the billiard ball model. In: Proceedings international colloquium universal machines and computations, MCU’98, France, pp 118–132
• Dyer C (1980) One-way bounded cellular automata. Inf Control 44:261–281
  Article MathSciNet MATH Google Scholar
• Ermentrout GB, Edelstein-Keshet L (1993) Cellular automata approaches to biological modeling. J Theor Biol 160(1):97–133
  Article Google Scholar
• Fatès N (2013) Stochastic cellular automata solutions to the density classification problem—when randomness helps computing. Theory Comput Syst 53(2):223–242
  Article MathSciNet MATH Google Scholar
• Fatès N (2014) Guided tour of asynchronous cellular automata. J Cell Autom 9(5–6):387–416
  MathSciNet MATH Google Scholar
• Fatés N (2017) FiatLux: cellular automata and discrete complex systems simulator. http://fiatlux.loria.fr/. Accessed Aug 25, 2017
• Fatès N, Thierry E, Morvan M, Schabanel N (2006) Fully asynchronous behavior of double-quiescent elementary cellular automata. Theor Comput Sci 362(1–3):1–16
  Article MathSciNet MATH Google Scholar
• Finelli M, Manzini G, Margara L (1998) Lyapunov exponents versus expansivity and sensitivity in cellular automata. J Complex 14(2):210–233
  Article MathSciNet MATH Google Scholar
• Fischer PC (1965) Generation of primes by a one-dimensional real-time iterative array. J ACM 12:388–394
  Article MathSciNet MATH Google Scholar
• Formenti E, Grange A (2003) Number conserving cellular automata ii: dynamics. Theor Comput Sci 304:269–290
  Article MathSciNet MATH Google Scholar
• Formenti E, Imai K, Martin B, Yunès JB (2014) Advances on random sequence generation by uniform cellular automata. In: Calude CS, Freivalds R, Kazuo I (eds) Computing with new resources: essays dedicated to jozef gruska on the occasion of his 80th birthday. Springer, Cham, pp 56–70
  Chapter Google Scholar
• Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253
  Article MathSciNet MATH Google Scholar
• Frisch U, Hasslacher B, Pomeau Y (1986) Lattice gas automata for the Navier–Stokes equation. Phys Rev Lett 56(14):1505–1508
  Article Google Scholar
• Fukś H (1997) Solution of the density classification problem with two cellular automata rules. Phys Rev E 55:R2081–R2084
  Article Google Scholar
• Fukś H (2004) Probabilistic cellular automata with conserved quantities. Nonlinearity 17(1):159
  Article MathSciNet MATH Google Scholar
• Gandin CA, Rappaz M (1997) A 3D cellular automaton algorithm for the prediction of dendritic grain growth. Acta Mater 45(5):2187–2195
  Article Google Scholar
• Ganguly N, Halder D, Deb J, Sikdar BK, Chaudhuri PP (2000) Hashing through cellular automata. In: Proceedings of 8th international conference of advance computing and communication, pp 95–101
• Ganguly N, Maji P, Dhar S, Sikdar BK, Chaudhuri PP (2002a) Evolving cellular automata as pattern classifier. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2002, Switzerland. Springer, Berlin, pp 56–68
  Google Scholar
• Ganguly N, Maji P, Sikdar BK, Chaudhuri PP (2002b) Generalized multiple attractor cellular automata (GMACA) For associative memory. Int J of Pattern Recognit Artif Intell 16(7):781–795 (Special Issue: Computational Intelligence for Pattern Recognition)
  Article Google Scholar
• Ganguly N, Sikdar BK, Chaudhuri PP (2002c) Design of an on-chip test pattern generator without prohibitited pattern set (PPS). In: Proceedings of ASP-DAC/VLSI design 2002, India, pp 689–694
• Ganguly N, Sikdar BK, Chaudhuri PP (2008) Exploring cycle structures of additive cellular automata. Fundam Inf 87(2):137–154
  MathSciNet MATH Google Scholar
• Gardner M (1971) On cellular automata self-reproduction, the garden of eden and the game of ‘Life’. Sci Am 224(2):112–118
  Article Google Scholar
• Ghosh S, Laskar N, Mahapatra S, Chaudhuri PP (2007) Probabilistic cellular automata model for identification of cpg island in DNA string. In: Proceedings of Indian international conference on artificial intelligence (IICAI), pp 1490–1509
• Ghosh S, Bachhar T, Maiti NS, Mitra I, Chaudhuri PP (2010) Theory and application of equal length cycle cellular automata (ELCCA) for enzyme classification. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2010, Italy, pp 46–57
• Ghosh S, Maiti NS, Chaudhuri PP, Sikdar BK (2011) On invertible three neighborhood null-boundary uniform cellular automata. Complex Syst 20:47–65
  Article MathSciNet MATH Google Scholar
• Ghosh S, Maiti NS, Chaudhuri PP (2012) Theory and application of restricted five neighborhood cellular automata (r5nca) for protein structure prediction. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2012, Greece. Springer, Berlin, pp 360–369
  Google Scholar
• Ghosh S, Maiti NS, Chaudhuri PP (2014) Cellular automata model for protein structure synthesis (PSS). In: Proceedings of international conference on cellular automata, research and industry, ACRI 2014, Poland, pp 268–277
• Goles E, Moreira A, Rapaport I (2011) Communication complexity in number-conserving and monotone cellular automata. Theor Comput Sci 412(29):3616–3628
  Article MathSciNet MATH Google Scholar
• Golze U (1978) (a-)synchronous (non-)deterministic cell spaces simulating each other. J Comput Syst Sci 17(2):176–193
  Article MathSciNet MATH Google Scholar
• Golze U, Priese L (1982) Petri net implementations by a universal cell space. Inf Control 53(1–2):121–138
  Article MathSciNet MATH Google Scholar
• Grinstein G, Jayaprakash C, He Y (1985) Statistical mechanics of probabilistic cellular automata. Phys Rev Lett 55:2527–2530
  Article MathSciNet Google Scholar
• Guan S, Tan SK (2004) Pseudorandom number generation with self-programmable cellular automata. IEEE Trans CAD 23(7):1095–1101
  Article Google Scholar
• Guan S, Zhang S (2003) An evolutionary approach to the design of controllable cellular automata structure for random number generation. IEEE Trans CAD 7(1):23–36
  Google Scholar
• Hattori T, Takesue S (1991) Additive conserved quantities in discrete-time lattice dynamical systems. Physica D 49(3):295–322
  Article MathSciNet MATH Google Scholar
• Hazari R, Das S (2014) Number conservation property of elementary cellular automata under asynchronous update. Complex Syst 23:177–195
  Article MathSciNet MATH Google Scholar
• Hedlund GA (1969) Endomorphisms and automorphisms of the shift dynamical system. Mathe Syst Theory 3:320–375
  Article MathSciNet MATH Google Scholar
• Hemmerling A (1982) On the computational equivalence of synchronous and asynchronous cellular spaces. Elektronische Informationsverarbeitung und Kybernetik 18(7/8):423–434
  MathSciNet MATH Google Scholar
• Herman GT, Liu WH (1973) The daughter of celia, the french flag, and the firing squad. SIMULATION 21(2):33–41
  Article Google Scholar
• Hortensius PD, McLeod RD, Card HC (1989a) Parallel random number generation for VLSI systems using cellular automata. IEEE Trans Comput C–38(10):1466–1473
  Article Google Scholar
• Hortensius PD, McLeod RD, Pries W, Miller DM, Card HC (1989b) Cellular automata-based pseudorandom number generators for built-in self-test. IEEE Trans Comput Aided Design Integr Circuits Syst 8(8):842–859
  Article Google Scholar
• Hortensius PD, McLeod RD, Card HC (1990) Cellular automata based signature analysis for built-in self-test. IEEE Trans Comput C–39(10):1273–1283
  Article Google Scholar
• Imai K, Morita K (2000) A computation-universal two-dimensional 8-state triangular reversible cellular automaton. Theor Comput Sci 231(2):181–191
  Article MathSciNet MATH Google Scholar
• Ingerson TE, Buvel RL (1984) Structure in asynchronous cellular automata. Physica D 10(1–2):59–68
  Article MathSciNet Google Scholar
• Itô M, Ôsato N, Nasu M (1983) Linear cellular automata over \({{\mathbb{Z}}}_m\). J Comput Syst Sci 27(1):125–140
  Article MATH Google Scholar
• Jen E (1986) Invariant strings and pattern-recognizing properties of one-dimensional cellular automata. J Stat Phys 43(1):243–265
  Article MathSciNet Google Scholar
• Jin J, Wu ZH (2012) A secret image sharing based on neighborhood configurations of 2-D cellular automata. Optics Laser Technol 44(3):538–548
  Article Google Scholar
• Jump JR, Kirtane JS (1974) On the interconnection structure of cellular automata networks. Inf Control 24:74–91
  Article MATH Google Scholar
• Kari J (1990) Reversibility of 2D cellular automata is undecidable. Physica D 45:386–395
  Article MathSciNet MATH Google Scholar
• Kari J (1992) The nilpotency problem of one-dimensional cellular automata. SIAM J Comput 21(3):571–586
  Article MathSciNet MATH Google Scholar
• Kari J (1994) Reversibility and surjectivity problems of cellular automata. J Comput Syst Sci 48(1):149–182
  Article MathSciNet MATH Google Scholar
• Kari J (2005a) Reversible cellular automata. Springer, Berlin, pp 57–68
  MATH Google Scholar
• Kari J (2005b) Theory of cellular automata: a survey. Theor Comput Sci 334(1–3):3–33
  Article MathSciNet MATH Google Scholar
• Kari J, Le Gloannec B (2012) Modified traffic cellular automaton for the density classification task. Fundam Inf 116(1–4):141–156
  Article MathSciNet MATH Google Scholar
• Kayama Y (2012) Network view of binary cellular automata. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2012, Greece. Springer, Berlin, pp 224–233
  Google Scholar
• Kayama Y, Imamura Y (2011) Network representation of the game of life. J Artif Intell Soft Comput Res 1(3):233–240
  Google Scholar
• Kazar O, Slatnia S (2011) Evolutionary cellular automata for image segmentation and noise filtering using genetic algorithms. J Appl Comput Sci Math 5(10):33–40
  Google Scholar
• Kerner BS (2004) Three-phase traffic theory and highway capacity. Physica A 333(C):379–440
  Article MathSciNet Google Scholar
• Khan AR (1998) Replacement of some graphics routines with the help of 2D cellular automata algorithms for faster graphics operations. Ph.D. thesis, University of Kashmir
• Kohyama T (1989) Cellular automata with particle conservation. Progress Theoret Phys 81(1):47–59
  Article MathSciNet Google Scholar
• Kohyama T (1991) Cluster growth in particle-conserving cellular automata. J Stat Phys 63(3–4):637–651
  Article MathSciNet Google Scholar
• Kurka P (1997) Languages, equicontinuity and attractors in cellular automata. Ergod Theory Dyn Syst 17(02):417–433
  Article MathSciNet MATH Google Scholar
• Kurka P (2003) Cellular automata with vanishing particles. Fundam Inf 58(2003):203–221
  MathSciNet MATH Google Scholar
• Lafe O (1997) Data compression and encryption using cellular automata transforms. Eng Appl Artif Intell 10(6):581–591
  Article Google Scholar
• Lafe OE (2002) Method and apparatus for video compression using sequential frame cellular automata transforms. US Patent 6,456,744
• Land M, Belew RK (1995) No perfect two-state cellular automata for density classification exists. Phys Rev Lett 74:5148–5150
  Article Google Scholar
• Langton CG (1990) Computation at the edge of chaos. Physica D 42:12–37
  Article MathSciNet Google Scholar
• Le Caër G (1989) Comparison between simultaneous and sequential updating in \(2^{n+1}-1\) cellular automata. Physica A 157(2):669–687
  Article MathSciNet MATH Google Scholar
• Legendi T, Katona E (1981) A 5 state solution of the early bird problem in a one dimensional cellular space. Acta Cybern 5(2):173–179
  MathSciNet MATH Google Scholar
• Legendi T, Katona E (1986) A solution of the early bird problem in an n-dimensional cellular space. Acta Cybern 7(1):81–87
  MathSciNet MATH Google Scholar
• Leporati A, Mariot L (2014) Cryptographic properties of bipermutive cellular automata rules. J Cell Autom 9:437–475
  MathSciNet MATH Google Scholar
• Li J, Demaine E, Gymrek M (2010) Es.268 the mathematics in toys and games, spring 2010. (massachusetts institute of technology: Mit opencourseware). http://ocw.mit.edu. Accessed
• Li W, Packard NH, Langton CG (1990) Transition phenomena in cellular automata rule space. Physica D 45:77–94
  Article MathSciNet MATH Google Scholar
• Lindgren K, Nordahl MG (1990) Universal computation in simple one-dimensional cellular automata. Complex Syst 4(3):299–318
  MathSciNet MATH Google Scholar
• Machì A, Mignosi F (1993) Garden of eden configurations for cellular automata on cayley graphs of groups. SIAM J Discrete Math 6(1):44–56
  Article MathSciNet MATH Google Scholar
• Maiti NS, Munshi S, Chaudhuri PP (2006) An analytical formulation for cellular automata (CA) based solution of density classification task (DCT). In: Proceedings of international conference on cellular automata, research and industry, ACRI 2006. Springer, pp 147–156
• Maiti NS, Ghosh S, Munshi S, Chaudhuri PP (2010) Linear time algorithm for identifying the invertibility of null-boundary three neighborhood cellular automata. Complex Syst 19(1):89–113
  Article MathSciNet MATH Google Scholar
• Maji P (2005) Cellular automata evolution for pattern recognition. Ph.D. thesis, Jadavpur University, Kolkata
• Maji P, Chaudhuri PP (2004) Fmaca: A fuzzy cellular automata based pattern classifier. In: Proceedings of 9th international conference on database systems for advanced applications, DASFAA 2004. Springer, Berlin, pp 494–505
  Chapter Google Scholar
• Maji P, Chaudhuri PP (2005) Fuzzy cellular automata for modeling pattern classifier. IEICE Trans Inf Syst E88–D(4):691–702
  Article Google Scholar
• Maji P, Ganguly N, Chaudhuri PP (2003a) Error correcting capability of cellular automata based associative memory. IEEE Trans Syst Man Cybern A 33(4):466–480
  Article Google Scholar
• Maji P, Shaw C, Ganguly N, Sikdar BK, Chaudhuri PP (2003b) Theory and application of cellular automata for pattern classification. Fundam Inf Cell Autom 58(3):321–354 (special issue)
  MathSciNet MATH Google Scholar
• Manning FB (1977) An approach to highly integrated, computer-maintained cellular arrays. IEEE Trans Comput C–26:536–552
  Article Google Scholar
• Manzoni L (2012) Asynchronous cellular automata and dynamical properties. Nat Comput 11(2):269–276
  Article MathSciNet MATH Google Scholar
• Manzoni L, Umeo H (2014) The firing squad synchronization problem on ca with multiple updating cycles. Theor Comput Sci 559:108–117 (non-uniform Cellular Automata)
  Article MathSciNet MATH Google Scholar
• Margenstern M (2009) About the garden of eden theorems for cellular automata in the hyperbolic plane. Electron Notes Theor Comput Sci 252:93–102
  Article MathSciNet MATH Google Scholar
• Margenstern M, Morita K (1999) A polynomial solution for 3-sat in the space of cellular automata in the hyperbolic plane. J Univ Comput Sci 5(9):563–573
  MathSciNet MATH Google Scholar
• Margenstern M, Morita K (2001) Np problems are tractable in the space of cellular automata in the hyperbolic plane. Theor Comput Sci 259(1–2):99–128
  Article MathSciNet MATH Google Scholar
• Margolus N (1984) Physics-like models of computation. Physica D 10(1–2):81–95
  Article MathSciNet MATH Google Scholar
• Mariot L (2016) Asynchrony immune cellular automata. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2016, Morocco. Springer, Cham, pp 176–181
  Google Scholar
• Mariot L, Leporati A, Dennunzio A, Formenti E (2017) Computing the periods of preimages in surjective cellular automata. Nat Comput 16(3):367–381
  Article MathSciNet Google Scholar
• Marr C, Hütt MT (2009) Outer-totalistic cellular automata on graphs. Phys Lett A 373(5):546–549
  Article MATH Google Scholar
• Martin B (1994) A universal cellular automata in quasi-linear time and its s-m-n form. Theor Comput Sci 123(2):199–237
  Article MATH Google Scholar
• Martin O, Odlyzko AM, Wolfram S (1984) Algebraic properties of cellular automata. Commun Math Phys 93:219–258
  Article MathSciNet MATH Google Scholar
• Martinez GJ, McIntosh HV, Mora JCST, Vergara SVC (2008) Determining a regular language by glider-based structures called phases \(f_{i}\_1\) in rule 110. J Cell Autom 3(3):231–270 (special issues)
  MathSciNet MATH Google Scholar
• Maruoka A, Kimura M (1976) Condition for injectivity of global maps for tessellation automata. Inf Control 32(2):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(1):47–64
  Article MathSciNet MATH Google Scholar
• Matsukidaira J, Nishinari K (2003) Euler–Lagrange correspondence of cellular automaton for traffic-flow models. Phys Rev Lett 90:088,701(1–4)
  Article Google Scholar
• Mazoyer J, Nichitiu C, Rémila E (1999) Compass permits leader election. In: Proceedings of the 10th annual ACM-SIAM symposium on discrete algorithms, society for industrial and applied mathematics, SODA’99, pp 947–948
• McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115–133
  Article MathSciNet MATH Google Scholar
• Miller DB, Fredkin E (2005) Two-state, reversible, universal cellular automata in three dimensions. In: Proceedings of the 2nd conference on computing frontiers. ACM, pp 45–51
• Misra S, Mitra B, Chaudhuri PP (1992) Synthesis of self-testable sequential logic using programmable cellular automata. In: Proceedings of international conference on VLSI design, pp 193–198
• Mitchell M, Hraber PT, Crutchfield JP (1993) Revisiting the edge of chaos: evolving cellular automata to perform computations. Complex Syst 7:89–130
  MATH Google Scholar
• Mitra B, Panda PR, Chaudhuri PP (1991) A flexible scheme for state assignment based on characteristics of the FSM. In: Proceedings of international conference on computer aided design, ICCAD, California, pp 226–229
• Mitra S, Das S, Chaudhuri PP, Nandi S (1996) Architecture of a VLSI chip for modeling amino acid sequence in proteins. In: Proceedings of 9th international conference on VLSI design, 1996, pp 316–317
• Mo Y, Ren B, Yang W, Shuai J (2014) The 3-dimensional cellular automata for hiv infection. Physica A 399:31–39
  Article MathSciNet MATH Google Scholar
• Moore EF (1962) Machine models of self-reproduction. Proc Symp Appl Math 14:17–33
  Article MATH Google Scholar
• Mora JCST, Martínez GJ, McIntosh HV (2006) The inverse behavior of a reversible one-dimensional cellular automaton obtained by a single welch diagram. J Cell Autom 1(1):25–39
  MathSciNet MATH Google Scholar
• Mora JCST, Hernandez MG, Vergara SVC (2008) Pair diagram and cyclic properties characterizing the inverse of reversible automata. J Cell Autom 3(3):205–218 (special Issue)
  MathSciNet MATH Google Scholar
• Moraal H (2000) Graph-theoretical characterization of invertible cellular automata. Physica D 141(1):1–18
  Article MathSciNet MATH Google Scholar
• Morales FJ, Crutchfield JP, Mitchell M (2001) Evolving two-dimensional cellular automata to perform density classification: a report on work in progress. Parallel Comput 27:571–585
  Article MATH Google Scholar
• Moreira A (2003) Universality and decidability of number-conserving cellular automata. Theor Comput Sci 292(3):711–721
  Article MathSciNet MATH Google Scholar
• Moreira J, Deutsch A (2002) Cellular automaton models of tumor development: a critical review. Adv Complex Syst 05(02n03):247–267
  Article MathSciNet MATH Google Scholar
• Moreno JL, Whitin ES, Jennings HH (1932) Application of the group method to classification. National Committee on Prisons and Prison Labor, New York (reprinted in The first book on group pyschotherapy, 3d edn, 1957, pp. 3–103)
  Google Scholar
• Morita K (1995) Reversible simulation of one-dimensional irreversible cellular automata. Theor Comput Sci 148(1):157–163
  Article MathSciNet MATH Google Scholar
• Morita K (2008) Reversible computing and cellular automata–a survey. Theor Comput Sci 395(1):101–131
  Article MathSciNet MATH Google Scholar
• Morita K (2016) Universality of 8-state reversible and conservative triangular partitioned cellular automata. In: International conference on cellular automata. Springer, pp 45–54
• Morita K, Harao M (1989) Computation universality of one dimensional reversible injective cellular automata. IEICE Trans E 72:758–762
  Google Scholar
• Morita K, Imai K (1998) Number-conserving reversible cellular automata and their computation-universality. In: Proceedings of satellite workshop on cellular automata MFCS’98, pp 51–68
• Morita K, Margenstern M, Imai K (1999) Universality of reversible hexagonal cellular automata. RAIRO Theor Inf Appl 33(6):535–550
  Article MathSciNet MATH Google Scholar
• Morita K, Tojima Y, Imai K (1999) A simple computer embedded in a reversible and number conserving two-dimensional cellular space. In: Proceedings of LA Symposium’99, Hakone
• Myhill J (1963) The converse of moore’s garden of eden theorem. Proc Am Math Soc 14:685–686
  MathSciNet MATH Google Scholar
• Nagel K (1996) Particle hopping models and traffic flow theory. Phys Rev E 53:4655–4672
  Article Google Scholar
• Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J Phys I 2(12):2221–2229
  Google Scholar
• Nakamura K (1974) Asynchronous cellular automata and their computational ability. Syst Comput Controls 5(5):58–66
  MathSciNet Google Scholar
• Nakamura K (1981) Synchronous to asynchronous transformation of polyautomata. J Comput Syst Sci 23(1):22–37
  Article MathSciNet MATH Google Scholar
• Nandi S, Chaudhuri PP (1996) Analysis of periodic and intermediate boundary 90/150 cellular automata. IEEE Trans Comput 45(1):1–12
  Article MathSciNet MATH Google Scholar
• Nandi S, Kar BK, Chaudhuri PP (1994) Theory and application of cellular automata in cryptography. IEEE Trans Comput 43(12):346–357
  Article MathSciNet Google Scholar
• Naskar N (2015) Characterization and synthesis of non-uniform cellular automata with point state attractors. Ph.D. thesis, Indian Institute of Engineering Science and Technology, Shibpur
• Neumann JV (1966) Theory of self-reproducing automata. University of Illinois Press, Champaign
  Google Scholar
• Newman MEJ, Watts DJ (1999) Scaling and percolation in the small-world network model. Phys Rev E 60(6):7332–7342
  Article Google Scholar
• Nishio H (1981) Real time sorting of binary numbers by one-dimensional cellular automata. Technical report, Kyoto University
• Nishio H, Kobuchi Y (1975) Fault tolerant cellular space. J Comput Syst Sci 11:150–170
  Article MathSciNet MATH Google Scholar
• Noguchi K (2004) Simple 8-state minimal time solution to the firing squad synchronization problem. Theor Comput Sci 314(3):303–334
  Article MathSciNet MATH Google Scholar
• Ollinger N (2002) The quest for small universal cellular automata. In: Proceedings of 29th international colloquium automata, languages and programming, ICALP 2002, Spain. Springer, Berlin, pp 318–329
  Chapter MATH Google Scholar
• Ollinger N (2003) The intrinsic universality problem of one-dimensional cellular automata. In: Proceedings of international symposium on theoretical aspects of computer science, STACS 2003. Springer, pp 632–641
• Ollinger N, Richard G (2011) Four states are enough. Theor Comput Sci 412:22–32
  Article MathSciNet MATH Google Scholar
• Packard NH, Wolfram S (1985) Two-dimensional cellular automata. J Stat Phys 38(5/6):901–946
  Article MathSciNet MATH Google Scholar
• Paul K, Chowdhury DR (2000) Application of GF(2\(^p\)) CA in burst error correcting codes. In: Proceedings of international conference of VLSI design, pp 562–567
• Paul K, Chowdhury DR, Chaudhuri PP (1999) Cellular automata based transform coding for image compression. In: Proceedings of international conference on high performance computing (HiPC), pp 269–273
  Google Scholar
• Paul K, Chowdhury DR, Chaudhuri PP (2000) Scalable pipelined micro-architecture for wavelet transform. In: Proceedings of international conference on VLSI design, pp 144–147
• Pighizzini G (1994) Asynchronous automata versus asynchronous cellular automata. Theor Comput Sci 132(1–2):179–207
  Article MathSciNet MATH Google Scholar
• Pivato M (2002) Conservation laws in cellular automata. Nonlinearity 15(6):1781
  Article MathSciNet MATH Google Scholar
• Pries W, Thanailakis A, Card HC (1986) Group properties of cellular automata and VLSI applications. IEEE Trans Comput C–35(12):1013–1024
  Article MATH Google Scholar
• Provillard J, Formenti E, Dennunzio A (2011) Non-uniform cellular automata and distributions of rules. arXiv preprint arXiv:11081419
• Raghavan R (1993) Cellular automata in pattern recognition. Inf Sci 70:145–177
  Article Google Scholar
• Martın del Rey A, Rodrıguez Sınchez G (2011) Reversibility of linear cellular automata. Appl Math Comput 217(21):8360–8366
  MathSciNet MATH Google Scholar
• Richardson D (1972) Tessellations with local transformations. J Comput Syst Sci 6:373–388
  Article MathSciNet MATH Google Scholar
• Roncken M, Stevens K, Pendurkar R, Rotem S, Chaudhuri PP (2000) Ca-bist for asynchronous circuits: a case study on the rappid asynchronous instruction length decoder. In: Proceedings of advanced research in asynchronous circuits and systems (ASYNC 2000), pp 62–72
• Rosenstiehl P, Fiksel JR, Holliger A (1972) Intelligent graphs: networks of finite automata capable of solving graph problems. In: Read RC (ed) Graph theory and computing. Academic press, New York, pp 219–265
  Chapter MATH Google Scholar
• Rosin PL (2006) Training cellular automata for image processing. Trans Imge Process 15(7):2076–2087
  Article Google Scholar
• Rosin PL (2010) Image processing using 3-state cellular automata. Comput Vis Image Underst 114(7):790–802
  Article Google Scholar
• Roy S, Das S (2017) Distributed mutual exclusion problem in cellular automata. J Cell Autom 12(6):493–512
  MathSciNet MATH Google Scholar
• Ruxton G, Saravia LA (1998) The need for biological realism in the updating of cellular automata models. Ecol Model 107(2–3):105–112
  Article Google Scholar
• Sadeghi S, Rezvanian A, Kamrani E (2012) An efficient method for impulse noise reduction from images using fuzzy cellular automata. AEU Int J Electron Commun 66(9):772–779
  Article Google Scholar
• Salo V (2014) Realization problems for nonuniform cellular automata. Theor Comput Sci 559:91–107
  Article MathSciNet MATH Google Scholar
• Santos J, Villot P, Diéguez M (2013) Protein folding with cellular automata in the 3d hp model. In: Proceedings of the 15th annual conference companion on genetic and evolutionary computation, GECCO’13, pp 1595–1602
• dos Santos RMZ, Coutinho S (2001) Dynamics of HIV approach: a cellular automata approach. Phys Rev Lett 87:168,102
  Article Google Scholar
• Saraniti M, Goodnick SM (2000) Hybrid fullband cellular automaton/monte carlo approach for fast simulation of charge transport in semiconductors. IEEE Trans Electron Devices 47(10):1909–1916
  Article Google Scholar
• Sarkar A, Mukherjee A, Das S (2012) Reversibility in asynchronous cellular automata. Complex Syst 21(1):71
  Article MathSciNet Google Scholar
• Sarkar P (2000) A brief history of cellular automata. ACM Comput Surv 32(1):80–107
  Article Google Scholar
• Sarkar P, Barua R (1998) Multi-dimensional \(\sigma \)-automata, \(\pi \)-polynomial and generalized \(s\)-matrices. Theor Comput Sci 197(1–2):111–138
  Article MATH Google Scholar
• Sato T, Honda N (1977) Certain relations between properties of maps of tessellation automata. J Comput Syst Sci 15(2):121–145
  Article MathSciNet MATH Google Scholar
• Seredynski F, Bouvry P, Zomaya AY (2004) Cellular automata computations and secret key cryptography. Parallel Comput 30(5–6):753–766
  Article MathSciNet MATH Google Scholar
• Seredynski M, Bouvry P (2005) Block cipher based on reversible cellular automata. New Gener Comput 23(3):245–258
  Article MATH Google Scholar
• Serra M, Slater T, Muzio JC, Miller DM (1990) The analysis of one-dimensional linear cellular automata and their aliasing properties. IEEE Trans CAD 9(7):767–778
  Article Google Scholar
• Sethi B, Das S (2015) Convergence of asynchronous cellular automata (under null boundary condition) and their application in pattern classification. In: Recent advances in natural computing: selected results from the IWNC 7 symposium, Springer Japan, pp 35–55
• Sethi B, Das S (2016) On the use of asynchronous cellular automata in symmetric-key cryptography. In: Mueller P, Thampi SM, Alam Bhuiyan MZ, Ko R, Doss R, Alcaraz Calero JM (eds) Security in computing and communications: 4th international symposium, SSCC 2016, Jaipur, India, Sept 21–24, 2016, Proceedings. Springer, Singapore, pp 30–41
  Chapter Google Scholar
• Sethi B, Fatès N, Das S (2014) Reversibility of elementary cellular automata under fully asynchronous update. In: Proceedings of 11th annual conference theory and applications of models of computation, TAMC 2014, India. Springer, pp 39–49
• Sethi B, Roy S, Das S (2016) Asynchronous cellular automata and pattern classification. Complexity 21(S1):370–386
  Article MathSciNet Google Scholar
• Shaw C, Chatterji D, Maji P, Sen S, Roy BN, Chaudhuri PP (2003) A pipeline architecture for encompression (encryption + compression) technology. In: Proceedings of VLSI design, pp 277–282
• Shaw C, Maji P, Saha S, Sikdar BK, Roy S, Chaudhuri PP (2004a) Cellular automata based encompression technology for voice data. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2004, Netherlands, pp 258–267
• Shaw C, Sikdar BK, Maiti NC (2004b) CA based document compression technology. In: Proceedings of 11th international conference on neural information processing, ICONIP, pp 679–685
• Shaw C, Das S, Sikdar BK (2006) Cellular automata based encoding technique for wavelet transformed data targeting still image compression. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2006, France, pp 141–146
• Shereshevsky MA (1992) Lyapunov exponent for one-dimensional cellular automata. J Nonlinear Sci 2:1–8
  Article MathSciNet MATH Google Scholar
• Siap I, Akin H, Uğuz S (2011) Structure and reversibility of 2d hexagonal cellular automata. Comput Math Appl 62(11):4161–4169
  Article MathSciNet MATH Google Scholar
• Sikdar BK, Paul K, Biswas GP, Boppana V, Yang C, Mukherjee S, Chaudhuri PP (2000) Theory and application of gf(\(2^p\)) cellular automata as on-chip test pattern generator. In: Proceedings of 13th international conference on VLSI design, 2000, pp 556–561
• Sikdar BK, Ganguly N, Karmakar A, Chowdhury S, Chaudhuri PP (2001) Multiple attractor cellular automata for hierarchical diagnosis of VLSI circuits. In: Proceedings of 10th Asian test symposium, Japan, pp 385–390
• Sikdar BK, Ganguly N, Chaudhuri PP (2002) Design of hierarchical cellular automata for on-chip test pattern generator. IEEE Trans Comput Aided Design Integr Circuits Syst 21(12):1530–1539
  Article Google Scholar
• Sipper M, Tomassini M (1996) Generating parallel random number generators by cellular programming. Int J Modern Phys 7(2):180–190
  Article Google Scholar
• Smith AR III (1971a) Cellular automata complexity trade-offs. Inf Control 18:466–482
  Article MathSciNet MATH Google Scholar
• Smith AR III (1971b) Simple computation-universal cellular spaces. J ACM 18(3):339–353
  Article MathSciNet MATH Google Scholar
• Smith AR III (1976) Introduction to and survey of polyautomata theory. In: Automata languages development, pp 405–422
• Soto JMG (2008) Computation of explicit preimages in one-dimensional cellular automata applying the de bruijn diagram. J Cell Autom 3(3):219–230 (Special Issues)
  MathSciNet MATH Google Scholar
• Stratmann M, Worsch T (2002) Leader election in d-dimensional ca in time diam log(diam). Future Gener Comput Syst 18(7):939–950
  Article MATH Google Scholar
• Sutner K (1991) De bruijin graphs and linear cellular automata. Complex Syst 5(1):19–30
  MathSciNet MATH Google Scholar
• Suzudo T (2004) Spatial pattern formation in asynchronous cellular automata with mass conservation. Physica A 343:185–200
  Article MathSciNet Google Scholar
• Takesue S (1995) Staggered invariants in cellular automata. Complex Syst 9(2):149–168
  MathSciNet MATH Google Scholar
• Terrier V (2004) Two-dimensional cellular automata and their neighborhoods. Theor Comput Sci 312(2):203–222
  Article MathSciNet MATH Google Scholar
• Thatcher JW (1964) Universality in the von neumann cellular model. Technical report, DTIC Document
• 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, Margolus N (1987) Cellular automata machines: a new environment for modeling. MIT Press, Cambridge
  Book MATH Google Scholar
• Toffoli T, Margolus NH (1990) Invertible cellular automata: a review. Physica D 45(1):229–253
  Article MathSciNet MATH Google Scholar
• Tomassini M (2006) Generalized automata networks. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2006, France. Springer, Berlin, pp 14–28
  Google Scholar
• Tomassini M, Venzi M (2002) Artificially evolved asynchronous cellular automata for the density task. In: Proceedings of international conference on cellular automata, research and industry, ACRI 2002, Switzerland. Springer, Berlin, pp 44–55
  Google Scholar
• Tomassini M, Sipper M, Perrenoud M (2000) On the generation of high-quality random numbers by two-dimensional cellular automata. IEEE Trans Comput 49(10):1146–1151
  Article MATH Google Scholar
• Tomassini M, Giacobini M, Darabos C (2005) Evolution and dynamics of small-world cellular automata. Complex Syst 15:261–284
  MathSciNet MATH Google Scholar
• Tsalides P (1990) Cellular automata based built-in self-test structures for VLSI systems. Electron Lett 26(17):1350–1352
  Article Google Scholar
• Tsalides P, York TA, Thanailakis A (1991) Pseudo-random number generators for VLSI systems based on linear cellular automata. IEEE Proc E Comput Digit Tech 138(4):241–249
  Article Google Scholar
• Uğuz S, Akin H, Siap I (2013) Reversibility algorithms for 3-state hexagonal cellular automata with periodic boundaries. Int J Bifurc Chaos 23(06):1350101
  Article MathSciNet MATH Google Scholar
• Uğuz S, Sahin U, Akin H, Siap I (2014) Self-replicating patterns in 2D linear cellular automata. Int J Bifurc Chaos 24(1):1430,002
  Article MathSciNet MATH Google Scholar
• Umeo H, Hisaoka M, Sogabe T (2005) A survey on optimum-time firing squad synchronization algorithms for one-dimensional cellular automata. Intl J Unconv Comput 1(4):403–426
  MATH Google Scholar
• Vichniac GY (1984) Simulating physics with cellular automata. Physica D 10(1):96–116
  Article MathSciNet MATH Google Scholar
• Vollmar R (1977) On two modified problems of synchronization in cellular automata. Acta Cybern 3(4):293–300
  MathSciNet MATH Google Scholar
• Voorhees B (1997) Some parameters characterizing cellular automata rules. Complex Syst 11(5):373–386
  MathSciNet MATH Google Scholar
• Voorhees B (2008) Remarks on applications of de bruijn diagrams and their fragments. J Cell Autom 3(3):187–204
  MathSciNet MATH Google Scholar
• Wang Q, Yu S, Ding W, Leng M (2008) Generating high-quality random numbers by cellular automata with pso. In: Proceedings of 4th international conference on natural computation, ICNC’08, pp 430–433
• Ward T (1994) Automorphisms of \({{\mathbb{Z}}}^d\)-subshifts of finite type. Indag Math 5(4):495–504
  Article MathSciNet MATH Google Scholar
• Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440–442
  Article MATH Google Scholar
• Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55(3):601–644
  Article MathSciNet MATH Google Scholar
• Wolfram S (1984) Universality and complexity in cellular automata. Physica 10:1–35
  MathSciNet MATH Google Scholar
• Wolfram S (1985) Origins of randomness in physical systems. Phys Rev Lett 55:449–452
  Article MathSciNet Google Scholar
• Wolfram S (1986a) Cryptography with cellular automata. In: Advances in cryptology—Crypto’85, vol 218. Springer, pp 429–432
• Wolfram S (1986b) Random sequence generation by cellular automata. Adv Appl Math 7(2):123–169
  Article MathSciNet MATH Google Scholar
• Wolfram S (1994) Cellular automata and complexity–collected papers. Westview Press
• Wolfram S (2002) A new kind of science. Wolfram-Media, Champaign
  MATH Google Scholar
• Wongthanavasu S, Sadananda R (2003) A ca-based edge operator and its performance evaluation. J Vis Commun Image Represent 14(2):83–96
  Article Google Scholar
• Wuensche A (1994) Complexity in one-D cellular automata: gliders, basins of attraction and the z parameter. Working papers 94-04-025, Santa Fe Institute
• Wuensche A (1998) Classifying cellular automata automatically. Santa Fe Institute Working Paper 98-02-018
• Wuensche A (2017) Discrete dynamics lab. http://www.ddlab.com/. Accessed Aug 25, 2017
• Xiao X, Shao S, Huang Z, Chou K (2006) Using pseudo amino acid composition to predict protein structural classes: approached with complexity measure factor. J Comput Chem 27(4):478–482
  Article Google Scholar
• Yang XS, Yang YZ (2007) Cellular automata networks. In: Proceedings of unconventional computing. Luniver Press, pp 280–302
• Ye R, Li H (2008) A novel image scrambling and watermarking scheme based on cellular automata. In: Proceedings of international symposium on electronic commerce and security, pp 938–941