The complete lists of 1D reversible number-conserving cellular automata with radius one of up to 7 states

This dataset contains complete lists of all one-dimensional reversible number-conserving k-ary cellular automata with radius one of up to 7 states, i.e. with state sets {0,1}, {0,1,2}, {0,1,2,3}, {0,1,2,3,4}, {0,1,2,3,4,5} and {0,1,2,3,4,5,6}. The detailed definitions and the method of enumerating are given in the paper: Barbara Wolnik, Maciej Dziemiańczuk, Adam Dzedzej, and Bernard De Baets “Reversibility of number-conserving 1D cellular automata: unlocking insights into the dynamics for larger state sets”. For a given number of states k, we use m=k-1 as the largest state. The list of all one-dimensional reversible number-conserving k-ary cellular automata with radius one with state set {0,1,...,m} is given in the look up table format, i.e.,each rule f is given as the string f(000) f(001) ... f(00m) f(010) ... f(01m) ... f(mm0) f(mm1) ... f(mmm) of k^3 integers from the set {0,1, ..., m}. The dataset contains a single file 1D-reversible-NCCAs-k-states.txt for each k in {5,6,7}. Each file contains a header line formatted as "The complete list of [number] 1D reversible number-conserving cellular automata with radius 1 and state set {0,...,m}". The header line is followed by [number] lines containing strings denoting the look up table of the listed automaton. The complete lists of rules for k=2, 3, 4, were already known. For example, they are given in the paperImai K., Martin B., Saito R. (2018) On Radius 1 Nontrivial Reversible and Number-Conserving Cellular Automata. In: Adamatzky A. (eds) Reversibility and Universality. Emergence, Complexity and Computation, vol 30. Springer, Cham. DOI: 10.1007/978-3-319-73216-9_12. We attach the known lists in the file 1D-reversible-NCCAs-2-3-4-states.txt in order to give researchers a possibility to have all results relevant to the subjects in one place.