A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
A linear speed-up theorem for cellular automata
Theoretical Computer Science - Special issue on logic and applications to computer science
Garden of Eden configurations for cellular automata on Cayley graphs of groups
SIAM Journal on Discrete Mathematics
A universal cellular automaton in quasi-linear time and its S—m—n form
Theoretical Computer Science
Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
Reversible simulation of one-dimensional irreversible cellular automata
Theoretical Computer Science
A simulation of cellular automata on hexagons by cellular automata on rings
Theoretical Computer Science
The Firing Squad Synchronization Problem on Cayley Graphs
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
One-way Cellular Automata on Cayley Graphs
FCT '93 Proceedings of the 9th International Symposium on Fundamentals of Computation Theory
Simple 8-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
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We consider cellular automata on Cayley graphs and we simulate the behavior of a torus of nxm automata (nodes) by a ring of n.m automata (cells). Our simulation technique requires the neighborhood of the nodes to be preserved. We achieve this constraint by copying the contents of nodes on the cells. We consider the problem of minimizing the number of the copies. We prove that it is possible to simulate the behavior of a torus on a ring with a single copy on each cell if and only if n and m satisfy a given condition. In that case we propose a time-optimal algorithm. We thus improve a previous work done by Martin where two copies were requested. When the condition on n and m is not fulfilled one can use the previous algorithm.