The complete lists of 1D reversible number-conserving cellular automata with radius one of up to 7 states - Open Research Data - Bridge of Knowledge

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

Description

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 paper
Imai 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.

Dataset file

1D-reversible-NCCAs-up-to-7-states.ZIP
52.5 kB, S3 ETag c413d78841a0557d8dd29ca56218e706-1, downloads: 79
The file hash is calculated from the formula
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.

Example script for calculation:
https://github.com/antespi/s3md5
download file 1D-reversible-NCCAs-up-to-7-states.ZIP

File details

License:
Creative Commons: by 4.0 open in new tab
CC BY
Attribution

Details

Year of publication:
2020
Verification date:
2020-12-18
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
  • computer and information sciences (Natural sciences)
  • physical sciences (Natural sciences)
DOI:
DOI ID 10.34808/b8pn-1523 open in new tab
Verified by:
Gdańsk University of Technology

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