Abstract
The Firing Squad Synchronization Problem (FSSP for short) has been intensively studied in the one-dimensional space. The problem consists in the synchronization of a segment of automata. We generalize this problem on Cayley graphs. We give minimal time solutions for (a) synchronizing all cells in all minimal paths between any pair of cells of a Cayley graph; (b) synchronizing all cells in all minimal paths starting at a given cell G (the “general”) and leading to all cells at a given distance from G in a Cayley graph. In solutions for (b), in some cases, all cells of a ball in a Cayley graph will be synchronized, in other cases this is not possible because of the existence of “culs-de-sac”.
This work was partially supported by the Esprit Basic Research Action “Algebraic and Syntactical Methods In Computer Science” and by a Grant of the French Government.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Balzer. A 8 state minimal time solution to the Firing Squad Synchronization Problem. Information and Control, 10:22–42, 1967.
C. Culik. Variation of the Firing Squad Synchronization Problem. Information Processing Letter, pages 152–157, 1989.
A. Machí and F. Mignosi. Garden of Eden configurations for cellular automata on Cayley graphs of groups. SIAM Journal on Discrete Mathematics, 6(1):44–56, 1993.
J. Mazoyer. A six states minimal time solution to the Firing Squad Synchronization Problem. Theoretical Computer Science, 50:183–238, 1987.
F.R. Moore and G.G. Langdon. A generalized firing squad problem. Information and Control, (12):212–220, 1968.
D.E. Müller and P.E. Schupp. Pushdown automata, ends, second-order logic and reachability problems. In 13th Annual ACM Symp. on the Theory of Computing, Milwaukee, 1981.
A. Holliger P. Rosenstiehl, J.R. Fiksel. Graph Theory and Computing, chapter Intelligent graphs: Networks of finite automata capable of solving graph problems. Lectures in Computer Science. R. C. Read, academic press edition, 1972.
Zs. Róka. Cellular automata on Cayley graphs. PhD thesis, Ecole Normale Supérieure de Lyon, France, July 1994.
Zs. Róka. The Firing Squad Synchronization Problem on Cayley graphs, preprint, 1995.
H. Szwerinsky. Time optimal solution for the Firing Squad Synchronization Problem for n-dimensional rectangles with the general at any position. Theoretical Computer Science, 19:305–320, 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Róka, Z. (1995). The firing squad synchronization problem on Cayley graphs. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_146
Download citation
DOI: https://doi.org/10.1007/3-540-60246-1_146
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60246-0
Online ISBN: 978-3-540-44768-9
eBook Packages: Springer Book Archive