论文信息 - The Constructibility of a Configuration in a Cellular automaton

The Constructibility of a Configuration in a Cellular automaton

A configuration is said to be with finite support if the states of all but fintely many cells in the array are quiescent. The results are as follows. It is recursively unsolvable when d>=2, for a configuration c with finite support in a d-dimensional cellular automaton, whether or not:o1.c is in the image of the parallel map for the cellular automaton. 2.c is in the image of the parallel map for the cellular automaton restricted to the set of configurations with finite support. Further properties of parallel maps are also considered.

Takeo Yaku | T. Yaku

[1] Serafino Amoroso,et al. Decision Procedures for Surjectivity and Injectivity of Parallel Maps for Tessellation Structures , 1972, J. Comput. Syst. Sci..

[2] S. Amoroso,et al. The Garden-of-Eden theorem for finite configurations , 1970 .

[3] E. F. Codd,et al. Cellular automata , 1968 .

[4] Alvy Ray Smith,et al. Simple Computation-Universal Cellular Spaces , 1971, JACM.

[5] G. Herman. Computing ability of a developmental model for filamentous organisms. , 1969, Journal of theoretical biology.

[6] Serafino Amoroso,et al. A Completeness Problem for Pattern Generation in Tessellation Automata , 1970, J. Comput. Syst. Sci..

[7] J. Myhill. The converse of Moore’s Garden-of-Eden theorem , 1963 .

[8] Hidenosuke Nishio,et al. Some regular state sets in the system of one-dimensional iterative automata , 1973, Inf. Sci..

[9] Serafino Amoroso,et al. Tessellation Structures for Reproduction of Arbitrary Patterns , 1971, J. Comput. Syst. Sci..

[10] Marvin Minsky,et al. Computation : finite and infinite machines , 2016 .

[11] E. F. Moore. Machine Models of Self-Reproduction , 1962 .

[12] Thomas J. Ostrand. Pattern Reproduction in Tessellation Automata of Arbitrary Dimension , 1971, J. Comput. Syst. Sci..

[13] John von Neumann,et al. Theory Of Self Reproducing Automata , 1967 .

[14] Serafino Amoroso,et al. Structural and Behavioral Equivalences of Tessellation Automata , 1971, Inf. Control..