Abstract
We consider asynchronous one-dimensional cellular automata (CA). It is shown that there is one with von Neumann neighborhood of radius 1 which can simulate each asynchronous one-dimensional cellular automaton. Analogous constructions are described for α-asynchronous CA (where each cell independently enters a new state with probability α, and for “neighborhood independent” asynchronous CA (where never two cells are updated simultaneously if one is in the neighborhood of the other). This also gives rise to a construction for so-called fully asynchronous CA (where in each step exactly one cell is updated).
Similar content being viewed by others
References
Arrighi P, Schabanel N, Theyssier G (2012) Intrinsic simulations between stochastic cellular automata. In: Proceedings automata/JAC 2012, pp 208–224
Bandini S, Bonomi A, Vizzari G (2010) What do we mean by asynchronous CA? A reflection on types and effects of asynchronicity. In: Bandini S, Manzoni S, Umeo H, Vizzari G (eds) Proceedings ACRI 2010. LNCS, vol 6350. Springer, Heidelberg, pp 385–394
Bouré O, Fatès N, Chevrier V (2012) Probing robustness of cellular automata through variations of asynchronous updating. Nat Comput 11(4):553–564
Delorme M, Mazoyer J, Ollinger N, Theyssier G (2011) Bulking II: classifications of cellular automata. Theor Comput Sci 412(30):3881–3905
Dennunzio A, Formenti E, Manzoni L, Mauri G (2012) m-asynchronous cellular automata. In: Proceedings ACRI 2012. LNCS, vol 7495. Springer, Heidelberg, pp 653–662
Durand-Lose JO (2000) Reversible space–time simulation of cellular automata. Theor Comput Sci 246(1–2):117–129
Fatès N, Gerin L (2008) Examples of fast and slow convergence of 2D asynchronous cellular systems. In: Umeo H et al (eds) Proceedings ACRI 2008. Springer, Heidelberg, pp 184–191
Golze U (1978) (A-)synchronous (non-)deterministic cell spaces simulating each other. J Comput Syst Sci 17(2):176–193
Lee J, Adachi S, Peper F, Morita K (2004) Asynchronous game of life. Physica D 194(3–4):369–384
Nakamura K (1974) Asynchronous cellular automata and their computational ability. Syst Comput Control 5(5):58–66
Ollinger N (2008) Universalities in cellular automata: a (short) survey. In: Durand B (ed) Proceedings JAC 2008, Uze, France, pp 102–118
Regnault D, Schabanel N, Thierry E (2009) Progresses in the analysis of stochastic 2D cellular automata: a study of asynchronous 2D minority. Theor Comput Sci 410(47–49):4844–4855
Schuhmacher A (2012) Simulationsbegriffe bei asynchronen Zellularautomaten. Report for a student seminar
Worsch T (2010) A note on (intrinsically?) universal asynchronous cellular automata. In: Fatès N, Kari J, Worsch T (eds) Proceedings Automata 2010, Nancy, France, pp 339–350
Worsch T (2012a) (Intrinsically?) universal asynchronous cellular automata. In: Sirakoulis G, Bandini S (eds) Proceedings ACRI 2012. LNCS, vol 7495. Springer, Heidelberg, pp 689–698
Worsch T (2012b) (Intrinsically?) universal asynchronous cellular automata II. In: Formenti E (ed) exploratory papers proceedings ACRI 2012. LNCS. Springer, Heidelberg, pp 38–51
Worsch T, Nishio H (2009) Achieving universality of CA by changing the neighborhood. J Cell Autom 4(3):237–246
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Worsch, T. Towards intrinsically universal asynchronous CA. Nat Comput 12, 539–550 (2013). https://doi.org/10.1007/s11047-013-9388-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-013-9388-3