Paper Info
Title
Abstract geometrical computation 11: Slanted firing squad synchronisation on signal machines
Abstract
Firing Squad Synchronisation on Cellular Automata is the dynamical synchronisation of finitely many cells without any prior knowledge of their range. This can be conceived as a signal with an infinite speed. Most of the proposed constructions naturally translate to the continuous setting of signal machines and generate fractal figures with an accumulation on a horizontal line, i.e. synchronously, in the space-time diagram. Signal machines are studied in a series of articles named Abstract Geometrical Computation. In the present article, we design a signal machine that is able to synchronise/accumulate on any non-infinite slope. The slope is encoded in the initial configuration. This is done by constructing an infinite tree such that each node computes the way the tree expands. The interest of Abstract Geometrical computation is to do away with the constraint of discrete space, while tackling new difficulties from continuous space. The interest of this paper in particular is to provide basic tools for further study of computable accumulation lines in the signal machine model. (C) 2021 Elsevier B.V. All rights reserved.
Year
DOI
Venue
2021
10.1016/j.tcs.2021.06.009
THEORETICAL COMPUTER SCIENCE
Keywords
DocType
Volume
Abstract geometrical computation, Cellular automata, Divide and conquer, Firing squad synchronisation, Fractal, Signal machines
Journal
894
ISSN
Citations 
PageRank 
0304-3975
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Jérôme Durand-Lose112714.93
Aurélien Emmanuel200.34