An Effective Approach for Solving the Density Classification Task by Cellular Automata

Evolution of Hybrid Cellular Automata for Density Classification Problem

“…Instead of operating over a complete solution space (as presented, for instance, in the references [7,8,12,16,19,37]), the method presented here focuses on a limited set of CA evolution rules (specifically nine rules, in Table 2 and Figure 9) and only six combinations thereof (refer to Figure 9), where optimal solutions are located. Consequently, this streamlines the design process, making it more straightforward and more efficient.…”

“…The large number of candidate rules (the high cardinality of the rule space) makes this approach unsuitable for intricate tasks; heuristic search-a workable alternative which involves the use of search and optimization algorithms, notably emphasizing evolutionary computation techniques [7][8][9][10][11]. These approaches were the key to the discovery of a significant number of solutions, especially with the introduction of the symmetry property [12][13][14], with the introduction of the conserving property [15,16], asynchronous updating methods [17], and even firing-squad synchronization that aims to establish an evolution rule whereby all cells within a given region enter into a special state after an identical number of steps [18] (p. 1035). Another interesting approach is presented in [19], where symmetry and conserving properties are achieved using CA with neighborhood dimension r = 4.…”