A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
On optimal solutions to the firing squad synchronization problem
Theoretical Computer Science - Special issue on universal machines and computations
ACRI '01 Proceedings of the 5th International Conference on Cellular Automata for Research and Industry
Proceedings of the Fourth International Conference on Cellular Automata for Research and Industry: Theoretical and Practical Issues on Cellular Automata
Computation: finite and infinite machines
Computation: finite and infinite machines
Simulation of generalized synchronization processes on one-dimensional cellular automata
SMO'09 Proceedings of the 9th WSEAS international conference on Simulation, modelling and optimization
Two-dimensional cellular automata synchronizers
CI'10 Proceedings of the 4th WSEAS international conference on Computational intelligence
UC'05 Proceedings of the 4th international conference on Unconventional Computation
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
State-Efficient One-Bit Communication Solutions for Some Classical Cellular Automata Problems
Fundamenta Informaticae - Special issue on DLT'04
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In this paper, we study a generalized synchronization problem for large scale cellular automata (CA) on one- and two- dimensional arrays. Some new generalized synchronization algorithms will be designed both on O(1)-bit and 1-bit inter-cell communication models of cellular automata. We give a 9-state and 13-state CA that can solve the generalized synchronization problem in optimum- and linear-time on O(1)-bit 1-D and 2-D CA, respectively. The number of internal states of the CA implemented is the smallest one known at present. In addition, it is shown that there exists a 1-bit inter-cell communication CA that can synchronize 1-D n cells with the general on the kth cell in n+max(k, n - k + 1) steps, which is two steps larger than the optimum time. We show that there still exist several new generalized synchronization algorithms, although more than 40 years have passed since the development of the problem.