%0 Conference Proceedings
%T Exact discretization of 3-speed rational signal machines
%+ Laboratoire d'Informatique Fondamentale d'Orléans (LIFO)
%A Besson, Tom
%A Durand-Lose, Jérôme
%Z Part 2: Regular Papers
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA)
%C Zurich, Switzerland
%Y Matthew Cook
%Y Turlough Neary
%I Springer
%3 Cellular Automata and Discrete Complex Systems
%V LNCS-9664
%P 63-76
%8 2016-06-15
%D 2016
%R 10.1007/978-3-319-39300-1_6
%K abstract geometrical computation
%K signal machines
%K cellular automata
%K automatic discretization
%Z Computer Science [cs]Conference papers
%X Cellular Automata (CA) operate in discrete time and space whereas Signal Machines (SM) have been developed as a continuous idealization of CA capturing the key concept of signals/particles and collisions. Inside a Euclidean space, dimensionless signals move freely; collisions are instantaneous. Today's issue is the automatic generation of a CA <i>mimicking</i> a given SM. On the one hand, many ad hoc manual conversions exist. On the other hand, some irrational or 4+-speed SM exhibit Zeno-like behaviors/space-time compression or rely on information being locally unbounded, both being incompatible with CA. This article provides a solution to automatically generate an exactly <i>mimicking</i> CA for a restricted class of SM: the ones that uses only three rational speeds, and rational initial positions. In these SM, signals are always contained inside a regular mesh. The discretization brings forth the corresponding discrete mesh. The simulation is valid on any infinite run and preserves the relative position of collisions.
%G English
%Z TC 1
%Z WG 1.5
%2 https://hal.science/hal-01298378/document
%2 https://hal.science/hal-01298378/file/395687_1_En_6_Chapter.pdf
%L hal-01298378
%U https://hal.science/hal-01298378
%~ UNIV-ORLEANS
%~ MSL
%~ MSL-THESE
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-LNCS-9664
%~ IFIP-WG1-5
%~ IFIP-AUTOMATA