Network structure and the firing squad synchronization problem
Journal of Computer and System Sciences
A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
An overview of the firing squad synchronization problem
Proceedings on LITP spring school on Theoretical Computer Science on Automata networks
Smaller solutions for the firing squad
Theoretical Computer Science
Proceedings of the Fourth International Conference on Cellular Automata for Research and Industry: Theoretical and Practical Issues on Cellular Automata
Bounding the firing synchronization problem on a ring
Theoretical Computer Science
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
State-Efficient One-Bit Communication Solutions for Some Classical Cellular Automata Problems
Fundamenta Informaticae - Special issue on DLT'04
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A simple and state-efficient mapping scheme is proposed for embedding any one-dimensional (1-D) firing squad synchronization algorithm onto two-dimensional (2-D) arrays, and some new 2-D synchronization algorithms based on the mapping scheme are presented. The proposed mapping scheme can be readily applied to the design of 2-D synchronization algorithms with fault tolerance, algorithms operating on multi-dimensional cellular arrays, and for the generalized case where the general is located at an arbitrary position on the 2-D array. First a six-state algorithm is developed that can synchronize any m×n rectangular array in 2(m+n)−4 steps. Then, a fourteen-state generalized algorithm is also developed that can synchronize any m×n rectangular array with the general at an arbitrary initial position (r,s) in m+n+max(r+s,m+n−r−s+2)−4 steps. The latter algorithm is interesting in that it includes a new optimum-time synchronization algorithm as a special case where the general is located at one corner. We progressively reduce the number of internal states of each cellular automaton on rectangular arrays, achieving six states and fourteen states for a rectangular array in non-optimum and optimum-time complexities, respectively. These are the smallest number of states reported to date for synchronizing rectangular arrays.