5,124 research outputs found
A Max-Plus Model of Asynchronous Cellular Automata
This paper presents a new framework for asynchrony. This has its origins in
our attempts to better harness the internal decision making process of cellular
automata (CA). Thus, we show that a max-plus algebraic model of asynchrony
arises naturally from the CA requirement that a cell receives the state of each
neighbour before updating. The significant result is the existence of a
bijective mapping between the asynchronous system and the synchronous system
classically used to update cellular automata. Consequently, although the CA
outputs look qualitatively different, when surveyed on "contours" of real time,
the asynchronous CA replicates the synchronous CA. Moreover, this type of
asynchrony is simple - it is characterised by the underlying network structure
of the cells, and long-term behaviour is deterministic and periodic due to the
linearity of max-plus algebra. The findings lead us to proffer max-plus algebra
as: (i) a more accurate and efficient underlying timing mechanism for models of
patterns seen in nature, and (ii) a foundation for promising extensions and
applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23,
Issue 4, 201
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
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