On elementary cellular automata asymptotic (a)synchronism sensitivity and complexity
Latin American Symposium on Theoretical Informatics(2023)
摘要
Among the fundamental questions in computer science is that of the impact of
synchronism/asynchronism on computations, which has been addressed in various
fields of the discipline: in programming, in networking, in concurrence theory,
in artificial learning, etc. In this paper, we tackle this question from a
standpoint which mixes discrete dynamical system theory and computational
complexity, by highlighting that the chosen way of making local computations
can have a drastic influence on the performed global computation itself. To do
so, we study how distinct update schedules may fundamentally change the
asymptotic behaviors of finite dynamical systems, by analyzing in particular
their limit cycle maximal period. For the message itself to be general and
impacting enough, we choose to focus on a “simple” computational model which
prevents underlying systems from having too many intrinsic degrees of freedom,
namely elementary cellular automata. More precisely, for elementary cellular
automata rules which are neither too simple nor too complex (the problem should
be meaningless for both), we show that update schedule changes can lead to
significant computational complexity jumps (from constant to superpolynomial
ones) in terms of their temporal asymptotes.
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