Abstract
As explained in Chapter 2, conventional computing requires encoding of information into strings of symbols over a given alphabet. Classical computation thus deals with recognition and generation problems of formal languages consisting of words (strings of symbols). Classical computational theories originated in attempts to understand calculation as performed by humans. All the resultant models (Turing machines, Church’s A-calculus, Chomsky grammars, Markov algorithms, etc.) are based on the seemingly sequential nature of conscioushuman calculation. They are inherently sequential.
One picture is worth a thousand words.
Old folk saying
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Balzer: An 8-state minimal solution to the firing-squad synchronization problem. Inform, and Control 10(1967) 22–42
M. Blum and C. Hewitt: Automata on a 2-dimensional tape. Proc. 6th IEEE Annual Symp. on Switching and Automata theory (now FOCS) (1967) 179–190
S.N. Cole: Real computation by n-dimensional iterative arrays. IEEE Trans, on Computers C-18 (1969) 349–365
K. Culik: Variations on the firing squad problem and applications. Inf. Proc. Letters 30 (1989) 153–157
C. Dyer: One-way bounded cellular automata. Inf. and Control 44 (1980) 261–281
P.C. Fisher: Generation of primes by a one-dimensional iterative array. J. Assoc. Comput. Mach. 12 (1965) 388–394
M. Garzon: Cyclic Automata. Theoret. Computer Sci. 53 (1987) 307–317
M. Garzon: Cayley Automata Theoret. Computer Sci. A 108 (1993) 83–102
M. Garzon: Graphical Words and Languages. In: Proc. Int. Conf. on Words, Languages and Combinatorics, Kyoto, 1990. M. Ito, ed., World Scientific Publishing, Singapore, pp. 160–178
M. Garzon, Y. Zalcstein: The complexity of Grigorchuk groups with application to cryptography. Theoret. Computer Sci. 88:1 (1991) 83–98
D. Giammarresi, A. Restivo: Recognizable picture languages. Int. J. of Pattern Recognition and Artif. Intel. 6:2/3 (1992)
R. Grigorchuk: Degrees of growth of finitely generated groups and the theory of invariant means. Math. USSR Izv. 25 (1985) 259–300
M. Gromov: Groups of polynomial growth and expanding maps. Inst. Hautes Etudes Scientifiques Publ. Math. 53 (1981) 53–78
H. Gutowitz (editor): Cellular automata: theory and applications. Proc. 3rd. Int. Conf. Cellular Automata, Los Alamos, 1991. Physica D 45 (1990) 431–440. Also issued as a separate book by MIT Press, 1992
H.A. Gutowitz: Statistical Properties of Cellular Automata in the Context of Learning and Recognition, Part I: Introduction. In: Learning and Recognition - A Modern Approach, K.H. Zhao, (ed.) World Scientific Publishing, Singapore (1989), pp. 233–255
H.A. Gutowitz: Statistical Properties of Cellular Automata in the Context of Learning and Recognition, Part II: Inverting Local Structure Theory Equations to Find Cellular Automata With Specified Properties. In: Learning and Recognition - A Modern Approach, K.H. Zhao, (ed.) World Scientific Publishing, Singapore (1989), pp. 256–280
F.C. Hennie: Iterative arrays of logical circuits. MIT Press, Cambridge MA, 1961
K. Inoue, I. Takanami, A. Nakamura: A note on two-dimensional finite automata. Inf. Process. Lett. 7 (1978) 49–52
K. Inoue, I. Takanami: A survey of two-dimensional finite automata. In: Proc. 5th Int. Meeting of Young Computer Scientists, J. Dassow and J. Kelemen (eds.). Lecture Notes in Computer Science, Vol. 381. Springer-Verlag, Berlin, 1989, pp. 72–91
T. Jiang: The synchronization of nonuniform networks of finite automata. Proc. IEEE Symp. on Foundations of Computer Science FOCS 30 (1989) 376–381
K. Kobayashi: The firing squad synchronization problem for two-dimensional arrays. Inf. and Control 34 (1977) 177–197
C.G. Langton: Computation at the edge of chaos: phase transitions and emergent computation. Physica D 42 (1990) 12–37
J. Lipton, Y. Zalcstein: Word problems solvable in logspace. J. Assoc. for Comput. Mach. 24 (1977) 522–526
J. Mazoyer: A six-state minimal time solution to the firing squad synchronization problem. Theoret. Comput. Sci. 50(1987) 183–238
J. Mazoyer: A minimal time solution to the firing squad synchronization problem with only one bit of information exchanged. Rapport de Recherche 89–03, LIP-Ecole Normale de Lyon, Prance
J. Mazoyer, V. Terrier: Signals in one dimensional cellular automata. Rapport de recherche, LIP École Normale Supérieure de Lyon, Prance, 1993
J. Milnor: Advanced Problem 3603, Amer. Math. Monthly 75 (1968) 685–686
M. Minsky: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs NJ, 1967
E. Moore: Sequential machines, selected papers. Addison-Wesley, Reading MA, 1964
F.R. Moore, G.G. Langdon: A generalized firing squad problem. Inf. And Control 12 (1968) 212–220
K. Morita, Y. Yamamoto, K. Sugata: Two-dimensional three-way array grammars and their acceptors. Int. J. of Pattern Recognition and Artificial Intelligence. 3:3/4 (1989) 353–376
K. Morita, S. Ueno: Parallel generation and parsing of array languages using reversible cellular automata. Preprint
J. Mycielski, D. Niwinski: Cellular automata on trees, a models for parallel computation. Fund. Informaticae XV (1991) 139–144
M. Nivat, A. Saudi, V.R. Dare: Parallel generation of finite images. Int. J. of Pattern Recognition and Artif. Intel. 3:3/4 (1989) 279–294
Z. Roka: One-way cellular automata on Cayley graphs. Preprint. LIP, École Normale Supérieure de Lyon, 1993
A. Rosenfeld: Picture languages (formal models for picture recognition). Academic press NY, 1979
P. Rujàn, Cellular Automata and Statistical Mechanical models. J. Statistical Physics 49 (1987) 139–232
M. Saoudi, K. Rangarajan, V.R. Dare: Finite images generated by GL- systems. Int. J. of Pattern Recognition and Artif. Intel. 3 (1989) 459–467
S.M. Selkow: One-pass complexity of digital picture properties. J. Assoc. Comput. Mach, 19 (1972) 283–295
H. Siegelman and E. Sontag: On the computational power of neural nets. Proc. 5th Comput. Learning Theory Conf. COLT (1992) 440–449
A.R. Smith III: Cellular automata and formal languages. Proc. 11th IEEE Symp. on Switching and Automata Theory (now FOCS) (1970) 216–224
A.R. Smith III: Two-dimensional formal languages and pattern recognition by cellular automata. Proc. 12th IEEE Annual Symp. on Switching and Automata Theory (now FOCS) (1971) 144–152
A.R. Smith III: Cellular automata complexity tradeoffs. Inform, and Control 18 (1971) 466–482
A.R. Smith III: Real-time language recognition by one-dimensional cellular automata. J. Assoc. Comput. Mach. 6 (1972) 233–253
J. Tits: Free subgroups in linear groups. J. of Algebra 20 (1972) 250–270
Y. Yamamoto, K. Morita, K. Sugata: Context-sensitivity of two-dimensional regular array grammars. Int. J. of Pattern Recognition and Artificial Intelligence. 3:3/4 (1989) 259–319
A. Waksman: An optimal solution to the firing squad synchronization problem. Information and Control 8(1966) 66–78
S. Wolfram: Theory and Applications of Cellular Automata. World Scientific, Singapore, 1986
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
folk, O. (1991). Some Inverse Problems. In: Models of Massive Parallelism. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77905-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-77905-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-77907-7
Online ISBN: 978-3-642-77905-3
eBook Packages: Springer Book Archive