Abstract
Cellular automata (CA) comprise a simple and well-formalized model of massively parallel computation, which is known to be capable of universal computation. Because of their parallel behavior, CA have rich abilities of information processing; however, it is not easy to define their power limitations. A convenient approach to characterizing the computation capacity of CA is to investigate their complexity classes. This chapter discusses the CA complexity classes and their relationships with other models of computations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Beyer WT (1969) Recognition of topological invariants by iterative arrays. Technical Report AITR-229, MIT Artificial Intelligence Laboratory, October 1, 1969
Bucher W, Čulik K II (1984) On real time and linear time cellular automata. RAIRO Theor Inf Appl 81:307–325
Buchholz T, Kutrib M (1998) On time computability of functions in one-way cellular automata. Acta Inf 35(4):329–352
Buchholz T, Klein A, Kutrib M (2000) Iterative arrays with small time bounds. In: Nielsen M, Rovan B (eds) MFCS, Lecture notes in computer science, vol 1893. Springer, Berlin, Heidelberg, pp 243–252
Cervelle J, Formenti E (2009) Algorithmic complexity and cellular automata. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, New York
Chang JH, Ibarra OH, Palis MA (1987) Parallel parsing on a one-way array of finite state machines. IEEE Trans Comput C-36(1):64–75
Chang JH, Ibarra OH, Vergis A (1988) On the power of one-way communication. J ACM 35(3):697–726
Chang JH, Ibarra OH, Palis MA (1989) Efficient simulations of simple models of parallel computation by time-bounded ATMs and space-bounded TMs. Theor Comput Sci 68(1):19–36
Choffrut C, Culik K II (1984) On real-time cellular automata and trellis automata. Acta Inf 21(4):393–407
Cole SN (1969) Real-time computation by n-dimensional iterative arrays of finite-state machine. IEEE Trans Comput 18:349–365
Culik K II (1989) Variations of the firing squad problem and applications. Inf Process Lett 30(3):153–157
Culik K II, Gruska J, Salomaa A (1984) Systolic trellis automata. I. Int J Comput Math 15(3–4):195–212
Delacourt M, Poupet V (2007) Real time language recognition on 2D cellular automata: Dealing with non-convex neighborhoods. In: Kucera L, Kucera A (eds) Mathematical foundations of computer science 2007, vol 4708 of Lecture Notes in Computer Science, pp 298–309
Delorme M, Mazoyer J (1994) Reconnaisance de langages sur automates cellulaires. Research Report 94–46, LIP, ENS Lyon, France
Delorme M, Mazoyer J (2002) Reconnaissance parallèle des langages rationnels sur automates cellulaires plans. [Parallel recognition of rational languages on plane cellular automata] Selected papers in honour of Maurice Nivat. Theor Comput Sci 281(1–2):251–289
Delorme M, Mazoyer J (2004) Real-time recognition of languages on an two-dimensional Archimedean thread. Theor Comput Sci 322(2):335–354
Dyer CR (1980) One-way bounded cellular automata. Inf Control 44(3):261–281
Fischer PC (1965) Generation of primes by one-dimensional real-time iterative array. J ACM 12:388–394
Giammarresi D, Restivo A (1997) Two-dimensional languages. In: Rozenberg G, Salomaa A (eds) Handbook of Formal Languages, vol 3. Springer, New York, pp 215–267
Goldschlager LM (1982) A universal interconnection pattern for parallel computers. J ACM 29(4):1073–1086
Hartmanis J, Stearns RE (1965) On the computational complexity of algorithms. Trans Am Math Soc (AMS) 117:285–306
Ibarra OH, Jiang T (1987) On one-way cellular arrays. SIAM J Comput 16(6):1135–1154
Ibarra OH, Jiang T (1988) Relating the power of cellular arrays to their closure properties. Theor Comput Sci 57(2–3):225–238
Ibarra OH, Kim SM (1984) Characterizations and computational complexity of systolic trellis automata. Theor Comput Sci 29(1–2):123–153
Ibarra OH, Palis MA (1987) On efficient simulations of systolic arrays of random-access machines. SIAM J Comput 16(2):367–377
Ibarra OH, Palis MA (1988) Two-dimensional iterative arrays: characterizations and applications. Theor Comput Sci 57(1):47–86
Ibarra OH, Kim SM, Moran S (1985a) Sequential machine characterizations of trellis and cellular automata and applications. SIAM J Comput 14(2):426–447
Ibarra OH, Palis MA, Kim SM (1985b) Some results concerning linear iterative (systolic) arrays. J Parallel Distrib Comput 2(2):182–218
Ito A, Inoue K, Takanami I (1989) Deterministic two-dimensional on-line tessellation acceptors are equivalent to two-way two-dimensional alternating finite automata through 180∘ rotation. Theor Comput Sci 66(3):273–287
Kobuchi Y (1987) A note on symmetrical cellular spaces. Inf Process Lett 25(6):413–415
Kosaraju SR (1979) Fast parallel processing array algorithms for some graph problems (preliminary version). In ACM conference record of the eleventh annual ACM symposium on theory of computing: papers presented at the symposium, Atlanta, Georgia, ACM Press, New York, 30 April–2 May 1979, pp 231–236
Klein A, Kutrib M (2003) Fast one-way cellular automata. Theor Comput Sci 295(1–3):233–250
Kutrib M (2001) Automata arrays and context-free languages. In Where mathematics, computer science, linguistics and biology meet, Kluwer, Dordrecht, The Netherlands, pp 139–148
Levialdi S (1972) On shrinking binary picture patterns. Commun ACM 15(1):7–10
Mazoyer J, Reimen N (1992) A linear speed-up theorem for cellular automata. Theor Comput Sci 101(1):59–98
Okhotin A (2002) Automaton representation of linear conjunctive languages. In International conference on developments in language theory (DLT), LNCS, vol 6. Kyoto, Japan
Poupet V (2005) Cellular automata: real-time equivalence between one-dimensional neighborhoods. In Diekert V, Durand B (eds) STACS 2005, 22nd annual symposium on theoretical aspects of computer science, Stuttgart, Germany, February 24–26, 2005, Proceedings, vol 3404 of Lecture Notes in Computer Science. Springer, pp 133–144
Poupet V (2007) A padding technique on cellular automata to transfer inclusions of complexity classes. In Diekert V, Volkov MV, Voronkov A (eds) Second international symposium on computer science in Russia, vol 4649 of Lecture Notes in Computer Science. Springer, pp 337–348
Rosenberg AL (1967) Real-time definable languages. J ACM 14(4):645–662
Savage C (1988) Recognizing majority on a one-way mesh. Inf Process Lett 27(5):221–225
Smith AR III (1971) Simple computation-universal cellular spaces. J ACM 18(3):339–353
Smith AR III (1972) Real-time language recognition by one-dimensional cellular automata. J Comput Syst Sci 6:233–253
Szwerinski H (1985) Symmetrical one-dimensional cellular spaces. Inf Control 67(1–3):163–172
Terrier V (1995) On real time one-way cellular array. Theor Comput Sci 141(1–2):331–335
Terrier V (1996) Language not recognizable in real time by one-way cellular automata. Theor Comput Sci 156(1–2):281–285
Terrier V (1999) Two-dimensional cellular automata recognizer. Theor Comput Sci 218(2):325–346
Terrier V (2003a) Characterization of real time iterative array by alternating device. Theor Comput Sci 290(3):2075–2084
Terrier V (2003b) Two-dimensional cellular automata and deterministic on-line tessalation automata. Theor Comput Sci 301(1–3):167–186
Terrier V (2004) Two-dimensional cellular automata and their neighborhoods. Theor Comput Sci 312(2–3): 203–222
Terrier V (2006a) Closure properties of cellular automata. Theor Comput Sci 352(1–3):97–107
Terrier V (2006b) Low complexity classes of multidimensional cellular automata. Theor Comput Sci 369(1–3):142–156
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Terrier, V. (2012). Language Recognition by Cellular Automata. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-92910-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92909-3
Online ISBN: 978-3-540-92910-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering