Synchronization of Growing Cellular Arrays

A generalized version of the firing squad synchronization problem is investigated. The generalization consists of allowing the linear array of automata to grow (by division of automata into two or more) while it is trying to synchronize itself. A solution is presented for the case in which the growth takes place at the ends of the array, with possibly different rates.

[1]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[2]  C H Waddington,et al.  Computer simulation of a mulluscan pigmentation pattern. , 1969, Journal of theoretical biology.

[3]  Abraham Waksman,et al.  An Optimum Solution to the Firing Squad Synchronization Problem , 1966, Inf. Control..

[4]  J. Wanscher.  The effect of genic time-factors upon growth and differentiation as observed in certain snail shells, bivalves and plants. , 2009, Hereditas.

[5]  Gabor T. Herman,et al.  The daughter of Celia, the French flag, and the firing squad , 1973 .

[6]  J. A. Marsh,et al.  Cone shells of the world , 1964 .

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

[8]  Grzegorz Rozenberg,et al.  Developmental systems and languages , 1972, STOC.

[9]  G. T. Herman,et al.  The daughter of CELIA, the french flag and the firing squad , 1973, WSC '73.

[10]  Gabor T. Herman,et al.  Simulation of organisms using a developmental model part 1: Basic description , 1972 .

[11]  Alvy Ray Smith,et al.  Two-Dimensional Formal Languages and Pattern Recognition by Cellular Automata , 1971, SWAT.

[12]  G. Herman.  I. General description and the problem of universal computing ability , 1971 .

[13]  G. Herman.  Role of environment in developmental models. , 1970, Journal of theoretical biology.

[14]  Robert Balzer,et al.  An 8-state Minimal Time Solution to the Firing Squad Synchronization Problem , 1967, Inf. Control..

[15]  A. Lindenmayer.  Mathematical models for cellular interactions in development. II. Simple and branching filaments with two-sided inputs. , 1968, Journal of theoretical biology.

[16]  Gabor T. Herman,et al.  Models for cellular interactions in development without polarity of individual cells II. Problems of synchronization and regulation , 1972 .

[17]  E. F. Moore.  Sequential Machines: Selected Papers , 1964 .