Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete Characterization of Structure of Rule 54   The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are
a discrete analog of a space-time dynamics of excitations in nonlinear active
medium with mutual inhibition. A cell switches its state 0 to state 1 if one of
its two neighbors is in state 1 (propagation of a perturbation) and a cell
remains in state 1 only if its two neighbors are in state 0. A lateral
inhibition is because a 1-state neighbor causes a 1-state cell to switch to
state 0. The rule produces a rich spectrum of space-time dynamics, including
gliders and glider guns just from four primitive gliders. We construct a
catalogue of gliders and describe them by tiles. We calculate a subset of
regular expressions $\Psi_{R54}$ to encode gliders. The regular expressions are
derived from de Bruijn diagrams, tile-based representation of gliders, and
cycle diagrams sometimes. We construct an abstract machine that recognizes
regular expressions of gliders in rule 54 and validate $\Psi_{R54}$. We also
propose a way to code initial configurations of gliders to depict any type of
collision between the gliders and explore self-organization of gliders,
formation of larger tiles, and soliton-like interactions of gliders and
computable devices.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci