Abstract
This chapter is dedicated to classic tools and methods involved in cellular transformations and constructions of signals and of functions by means of signals, which will be used in subsequent chapters. The term “signal” is widely used in the field of cellular automata (CA). But, as it arises from different levels of understanding, a general definition is difficult to formalize. This chapter deals with a particular notion of signal, which is a basic and efficient tool in cellular algorithmics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Balzer R (1966) Studies concerning minimal time solutions to the firing squad synchronization problem. Ph.D. thesis, Carnegie Institute of Technology
Balzer R (1967) An 8-states minimal time solution to the firing squad synchronization problem. Inform Control 10:22–42
Čulik K (1989) Variations of the firing squad synchronization problem. Inform Process Lett 30:153–157
Čulik K, Dube S (1993) L-systems and mutually recursive function systems. Acta Inform 30:279–302
Čulik K, Karhumäki J (1983) On the Ehrenfeucht conjecture for DOL languages. ITA 17(3):205–230
Delorme M, Mazoyer J (1996) Languages recognition and cellular automata. In: Almeida J, Gomez GMS, Silva PV (eds) World Scientific, Singapore, pp 85–100
Delorme M, Mazoyer J (2002a) Reconnaissance parallèle des languages rationnels sur automates cellulaires plans. Theor Comput Sci 281:251–289
Delorme M, Mazoyer J (2002b) Signals on cellular automata. In: Adamatzky A (ed) Springer, London, pp 231–274
Delorme M, Mazoyer J (2004) Real-time recognition of languages on a two-dimensional archimedean thread. Theor Comput Sci 322(2):335–354
Delorme M, Mazoyer J, Tougne L (1999) Discrete parabolas and circles on 2D cellular automata. Theor Comput Sci 218(2):347–417
Fisher PC (1965) Generation of primes by a one dimensional real time iterative array. J ACM 12:388–394
Gruska J, Salvatore L, Torre M, Parente N (2006) Different time solutions for the firing squad synchronization problem. Theor Inform Appl 40(2):177–206
Heen O (1996) Economie de ressources sur automates cellulaires. Ph.D. thesis, Université Paris Diderot. In French
Kari J (1994) Rice's theorem for limit sets of cellular automata. Theor Comp Sci 127(2):227–254
Mazoyer J (1987) A six states minimal time solution to the firing squad synchronization problem. Theor Comput Sci 50:183–238
Mazoyer J (1989a) An overview on the firing squad synchronization problem. In: Choffrut C (ed) Automata networks, Lecture notes in computer science. Springer, Heidelberg
Mazoyer J (1989b) Solutions au problème de la synchronisation d'une ligne de fusiliers. Habilitation à diriger des recherches (1989). In French
Mazoyer J (1992) Entrées et sorties sur lignes d'automates. In: Cosnard MNM, Robert Y (eds) Algorithmique parallèle, Masson, Paris, pp 47–64. In French
Mazoyer J (1999) Computations on cellular automata. In: Delorme M, Mazoyer J (eds) Springer-Verlag, London, pp 77–118
Mazoyer J, Reimen N (1992) A linear speed-up theorem for cellular automata. Theor Comput Sci 101:59–98
Mazoyer J, Terrier V (1999) Signals in one-dimensional cellular automata. Theor Comput Sci 217(1):53–80
Ollinger N (2002) Automates cellulaires: structures. Ph.D. thesis, Ecole Normale Supérieure de Lyon. In French
Rapaport I (1998) Ordre induit sur les automates cellulaires par l'opération de regroupement. Ph.D. thesis, Ecole Normale Supérieure de Lyon
Richard G (2008) Systèmes de particules et collisions discrètes dans les automates cellulaires. Ph.D. thesis, Aix-Marseille Université. In French
Romani F (1976) Cellular automata synchronization. Inform Sci 10:299–318
Sutner K (1997) Linear cellular automata and Fisher automaton. Parallel Comput 23(11):1613–1634
Szwerinski H (1982) Time optimal solution of the firing squad synchronization problem for n-dimensional rectangles with the general at any position. Theor Comput Sci 19:305–320
Terrier V (1991) Temps réel sur automates cellulaires. Ph.D. thesis, Université Lyon 1. In French
Terrier V (2006) Closure properties of cellular automata. Theor Comput Sci 352(1):97–107
Theyssier G (2005) Automates cellulaires: un modèle de complexité. Ph.D. thesis, Ecole Normale Supérieure de Lyon. In French
Ulam S (1957) The Scottish book: a collection of problems. Los Alamos
Vaskhavsky VI, Marakhovsky VB, Peschansky VA (1969) Synchronization of interacting automata. Math Syst Theory 14:212–230
von Neumann J (1966) Theory of self-reproducing. University of Illinois Press, Urbana, IL
Waksman A (1996) An optimum solution to the firing squad synchronization problem. Inform Control 9:66–78
Yunès JB (2008) Goto's construction and Pascal's triangle: new insights in cellular automata. In: Proceeding of JAC08. Uzès, France, pp 195–202
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Delorme, M., Mazoyer, J. (2012). Algorithmic Tools on 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-92910-9_3
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