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Volumn 91, Issue 5-6, 1998, Pages 909-951

Complexity of two-dimensional patterns

Author keywords

Cellular automata; Computational complexity; Entropy; Formal language; Patterns; Statistical mechanics

Indexed keywords


EID: 0032093264     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023027932419     Document Type: Article
Times cited : (89)

References (62)
  • 3
    • 84974546743 scopus 로고
    • The expressive power of transitive closure and 2-way multihead automata
    • Springer-Verlag
    • Y. Bargury and J. Makowsky, The expressive power of transitive closure and 2-way multihead automata, in Lecture Notes in Computer Science, Vol. 626 (Springer-Verlag, 1992), pp. 1-14.
    • (1992) Lecture Notes in Computer Science , vol.626 , pp. 1-14
    • Bargury, Y.1    Makowsky, J.2
  • 5
    • 0003359740 scopus 로고
    • The undecidability of the domino problem
    • R. Berger, The undecidability of the domino problem, Memoirs Amer. Math. Soc. 66:1-72 (1966).
    • (1966) Memoirs Amer. Math. Soc. , vol.66 , pp. 1-72
    • Berger, R.1
  • 7
    • 0003157917 scopus 로고
    • Linear time simulation of deterministic two-way pushdown automata
    • S. A. Cook, Linear time simulation of deterministic two-way pushdown automata, Proc. 1971 IFIP Congress, pp. 75-80.
    • (1971) Proc. 1971 IFIP Congress , pp. 75-80
    • Cook, S.A.1
  • 8
    • 84936795840 scopus 로고
    • Automata in labyrinths
    • Springer-Verlag
    • W. Coy, Automata in labyrinths, in Lecture Notes in Computer Science, Vol. 56 (Springer-Verlag, 1977), pp. 65-71.
    • (1977) Lecture Notes in Computer Science , vol.56 , pp. 65-71
    • Coy, W.1
  • 10
    • 0012875522 scopus 로고
    • Unreconstructible at any radius
    • J. P. Crutchfield, Unreconstructible at any radius, Physics Letters A 171:52-60 (1992).
    • (1992) Physics Letters A , vol.171 , pp. 52-60
    • Crutchfield, J.P.1
  • 14
    • 0003023825 scopus 로고    scopus 로고
    • Monadic second order logic over rectangular pictures and recognizability by tiling systems
    • D. Giammarresi, A. Restivo, S. Seibert, and W. Thomas, Monadic second order logic over rectangular pictures and recognizability by tiling systems, Information and Computation 125(1):32-45 (1996).
    • (1996) Information and Computation , vol.125 , Issue.1 , pp. 32-45
    • Giammarresi, D.1    Restivo, A.2    Seibert, S.3    Thomas, W.4
  • 15
    • 0011975194 scopus 로고    scopus 로고
    • Two-dimensional languages
    • G. Rosenberg and A. Salomaa, eds. Springer-Verlag
    • D. Giammarresi and A. Restivo, Two-dimensional languages. To appear in Handbook of Formal Languages, G. Rosenberg and A. Salomaa, eds. (Springer-Verlag, 1996).
    • (1996) Handbook of Formal Languages
    • Giammarresi, D.1    Restivo, A.2
  • 22
    • 0001072208 scopus 로고
    • Endomorphisms and automorphisms of the shift dynamical system
    • G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system. Mathematical Systems Theory 3:320-375 (1969).
    • (1969) Mathematical Systems Theory , vol.3 , pp. 320-375
    • Hedlund, G.A.1
  • 24
    • 0039592483 scopus 로고
    • Formal language characterization of cellular automaton limit sets
    • L. P. Hurd, Formal language characterization of cellular automaton limit sets, Complex Systems 1:69-80 (1987).
    • (1987) Complex Systems , vol.1 , pp. 69-80
    • Hurd, L.P.1
  • 25
    • 0001657151 scopus 로고
    • Recursive cellular automata invariant sets
    • L. P. Hurd, Recursive cellular automata invariant sets, Complex Systems 4:119-129 (1990).
    • (1990) Complex Systems , vol.4 , pp. 119-129
    • Hurd, L.P.1
  • 26
    • 0017731929 scopus 로고
    • Some properties of two-dimensional on-line tesselation acceptors
    • K. Inoue and A. Nakamura, Some properties of two-dimensional on-line tesselation acceptors, Information Sciences 13:95-121 (1977).
    • (1977) Information Sciences , vol.13 , pp. 95-121
    • Inoue, K.1    Nakamura, A.2
  • 28
    • 0018737170 scopus 로고
    • Two-dimensional finite automata and unacceptable functions
    • K. Inoue and A. Nakamura, Two-dimensional finite automata and unacceptable functions, Int. J. Comput. Math. A 7:207-213 (1979).
    • (1979) Int. J. Comput. Math. A , vol.7 , pp. 207-213
    • Inoue, K.1    Nakamura, A.2
  • 29
    • 0026177621 scopus 로고
    • A survey of two-dimensional automata theory
    • K. Inoue and I. Takanami, A survey of two-dimensional automata theory, Information Sciences 55:99-121 (1991).
    • (1991) Information Sciences , vol.55 , pp. 99-121
    • Inoue, K.1    Takanami, I.2
  • 30
    • 0039592487 scopus 로고
    • Global properties of cellular automata
    • E. Jen, Global properties of cellular automata, Journal of Statistical Physics 43:219-242 (1986).
    • (1986) Journal of Statistical Physics , vol.43 , pp. 219-242
    • Jen, E.1
  • 31
    • 33646825939 scopus 로고
    • Periodic points, decidability, and Markov subgroups
    • Springer-Verlag
    • B. Kitchens and K. Schmidt, Periodic points, decidability, and Markov subgroups, in Lecture Notes in Mathematics, Vol. 1042, pp. 440-454 (Springer-Verlag, 1988).
    • (1988) Lecture Notes in Mathematics , vol.1042 , pp. 440-454
    • Kitchens, B.1    Schmidt, K.2
  • 33
    • 0015024264 scopus 로고
    • Developmental systems without cellular interaction, their languages and grammars
    • A. Lindenmayer, Developmental systems without cellular interaction, their languages and grammars. Journal of Theoretical Biology 30:455-484 (1971).
    • (1971) Journal of Theoretical Biology , vol.30 , pp. 455-484
    • Lindenmayer, A.1
  • 34
    • 0006409105 scopus 로고
    • Correlations and random information in cellular automata
    • K. Lindgren, Correlations and random information in cellular automata, Complex Systems 1:529-543 (1987).
    • (1987) Complex Systems , vol.1 , pp. 529-543
    • Lindgren, K.1
  • 35
    • 0001223260 scopus 로고
    • Universal computation in simple one-dimensional cellular automata
    • K. Lindgren and M. G. Nordahl, Universal computation in simple one-dimensional cellular automata, Complex Systems 4:299-318 (1990).
    • (1990) Complex Systems , vol.4 , pp. 299-318
    • Lindgren, K.1    Nordahl, M.G.2
  • 37
    • 0038999730 scopus 로고
    • A positive pumping condition for regular sets
    • A. de Luca and S. Varrichio, A positive pumping condition for regular sets. Bulletin of the ETACS 39:171-175 (1989).
    • (1989) Bulletin of the ETACS , vol.39 , pp. 171-175
    • De Luca, A.1    Varrichio, S.2
  • 38
    • 21144469824 scopus 로고
    • The global minimum of energy is not always a sum of local minima - A note on frustration
    • J. Mikiesz, The global minimum of energy is not always a sum of local minima - a note on frustration, Journal of Statistical Physics 71:425-434 (1993).
    • (1993) Journal of Statistical Physics , vol.71 , pp. 425-434
    • Mikiesz, J.1
  • 39
    • 0039592485 scopus 로고
    • A region crossing problem for array-bounded automata
    • D. L. Milgram, A region crossing problem for array-bounded automata, Information and Control 31:147-152 (1976).
    • (1976) Information and Control , vol.31 , pp. 147-152
    • Milgram, D.L.1
  • 40
    • 4243368165 scopus 로고
    • Towards finding exact residual entropies of the Ising antiferromagnets
    • S. Milošević, B. Stošić, and T. Stošić, Towards finding exact residual entropies of the Ising antiferromagnets, Physica A 157:899-906 (1989).
    • (1989) Physica A , vol.157 , pp. 899-906
    • Milošević, S.1    Stošić, B.2    Stošić, T.3
  • 42
    • 0016872357 scopus 로고
    • Transformational methods and their application to complexity problems
    • B. Monien, Transformational methods and their application to complexity problems, Acta Informatica 6:95-108 (1976); and Corrigenda, 8:383-384 (1977).
    • (1976) Acta Informatica , vol.6 , pp. 95-108
    • Monien, B.1
  • 43
    • 0016872357 scopus 로고
    • B. Monien, Transformational methods and their application to complexity problems, Acta Informatica 6:95-108 (1976); and Corrigenda, 8:383-384 (1977).
    • (1977) Corrigenda , vol.8 , pp. 383-384
  • 44
    • 0001102743 scopus 로고
    • Unpredictability and undecidability in dynamical systems
    • C. Moore, Unpredictability and undecidability in dynamical systems, Phys. Rev. Lett. 64:2354-2357 (1990); and Nonlinearity 4:199-230 (1991).
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 2354-2357
    • Moore, C.1
  • 45
    • 30244452047 scopus 로고
    • C. Moore, Unpredictability and undecidability in dynamical systems, Phys. Rev. Lett. 64:2354-2357 (1990); and Nonlinearity 4:199-230 (1991).
    • (1991) Nonlinearity , vol.4 , pp. 199-230
  • 46
    • 0039592486 scopus 로고
    • Formal languages and finite cellular automata
    • M. G. Nordahl, Formal languages and finite cellular automata, Complex Systems 3:63-78 (1989).
    • (1989) Complex Systems , vol.3 , pp. 63-78
    • Nordahl, M.G.1
  • 47
    • 38249009114 scopus 로고
    • Three-dimensional connected pictures are not recognizable by finite-state acceptors
    • A. Nakamura, Three-dimensional connected pictures are not recognizable by finite-state acceptors, Information Sciences 66:225-234 (1992).
    • (1992) Information Sciences , vol.66 , pp. 225-234
    • Nakamura, A.1
  • 51
    • 0000457926 scopus 로고
    • On context-free languages
    • R. J. Parikh, On context-free languages, Journal of the ACM 4:570-581 (1966).
    • (1966) Journal of the ACM , vol.4 , pp. 570-581
    • Parikh, R.J.1
  • 52
    • 0000536874 scopus 로고
    • Undecidability and nonperiodicity of tilings of the plane
    • R. M. Robinson, Undecidability and nonperiodicity of tilings of the plane, Inventiones Math. 12:177 (1971).
    • (1971) Inventiones Math. , vol.12 , pp. 177
    • Robinson, R.M.1
  • 55
    • 33744712534 scopus 로고
    • Tiling problems and undecidability in the cluster variation method
    • A. G. Schlijper, Tiling problems and undecidability in the cluster variation method, Journal of Statistical Physics 50:689-714 (1988).
    • (1988) Journal of Statistical Physics , vol.50 , pp. 689-714
    • Schlijper, A.G.1
  • 56
    • 0000765417 scopus 로고
    • Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions
    • J. D. Shore, M. Holzer, and J. P. Sethna, Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions, Physical Review B 46:376-404 (1992).
    • (1992) Physical Review B , vol.46 , pp. 376-404
    • Shore, J.D.1    Holzer, M.2    Sethna, J.P.3
  • 57
    • 0013229185 scopus 로고
    • Halting space-bounded computations
    • M. Sipser, Halting space-bounded computations, Theoretical Computer Science 10:335-338 (1980).
    • (1980) Theoretical Computer Science , vol.10 , pp. 335-338
    • Sipser, M.1
  • 58
    • 38249010000 scopus 로고
    • Two-dimensional on-line tesselation acceptors are not closed under complement
    • A. Szepietowski, Two-dimensional on-line tesselation acceptors are not closed under complement, Information Sciences 64:115-120 (1992).
    • (1992) Information Sciences , vol.64 , pp. 115-120
    • Szepietowski, A.1
  • 59
    • 84944488797 scopus 로고
    • Proving theorems by pattern recognition II
    • H. Wang, Proving theorems by pattern recognition II, Bell System Tech. J. 40:1-42 (1961).
    • (1961) Bell System Tech. J. , vol.40 , pp. 1-42
    • Wang, H.1
  • 60
    • 33845991986 scopus 로고
    • Subshifts of finite type and sofic systems
    • B. Weiss, Subshifts of finite type and sofic systems, Monatsh. Math. 77:462 (1973).
    • (1973) Monatsh. Math. , vol.77 , pp. 462
    • Weiss, B.1
  • 61
    • 0040183705 scopus 로고
    • On the ergodic theory of cellular automata
    • S. Willson, On the ergodic theory of cellular automata, Mathematical Systems Theory 9:132-141 (1975).
    • (1975) Mathematical Systems Theory , vol.9 , pp. 132-141
    • Willson, S.1


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