A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
Smaller solutions for the firing squad
Theoretical Computer Science
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
ACRI '01 Proceedings of the 5th International Conference on Cellular Automata for Research and Industry
Computation: finite and infinite machines
Computation: finite and infinite machines
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
A New Time-Optimum Synchronization Algorithm for Rectangle Arrays
Fundamenta Informaticae - Membrane Computing
A new time-optimum synchronization algorithm for two-dimensional cellular arrays
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
Two-dimensional cellular automata synchronizers
CI'10 Proceedings of the 4th WSEAS international conference on Computational intelligence
UC'10 Proceedings of the 9th international conference on Unconventional computation
A seven-state time-optimum square synchronizer
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Faster synchronization in P systems
Natural Computing: an international journal
A New Time-Optimum Synchronization Algorithm for Rectangle Arrays
Fundamenta Informaticae - Membrane Computing
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The firing squad synchronization problem has been studied extensively for more than 40 years [1-18]. The present authors are involved in research on firing squad synchronization algorithms on two-dimensional (2-D) rectangular cellular arrays. Several synchronization algorithms on 2-D arrays have been proposed, including Beyer [2], Grasselli [3], Kobayashi [4], Shinahr [10], Szwerinski [12] and Umeo et al. [13, 15]. To date, the smallest number of cell states for which an optimum-time synchronization algorithm has been developed is 14 for rectangular array, achieved by Umeo et al. [15]. In the present paper, we propose a new optimum-time synchronization algorithm that can synchronize any 2-D m × n rectangular arrays in m + n + max(m, n) –3 steps. We progressively reduce the number of internal states of each cellular automaton on rectangular arrays, achieving twelve states. This is the smallest number of states reported to date for synchronizing rectangular arrays in optimum-step.