On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures

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dc.creatorBoyer, Laurent
dc.creatorPoupet, Victor
dc.creatorTheyssier, Guillaume
dc.date2006-04-04
dc.date2006-10-02
dc.date.accessioned2026-07-07T07:09:18Z
dc.date.available2026-07-07T07:09:18Z
dc.descriptionWe study the notion of limit sets of cellular automata associated with probability measures (mu-limit sets). This notion was introduced by P. Kurka and A. Maass. It is a refinement of the classical notion of omega-limit sets dealing with the typical long term behavior of cellular automata. It focuses on the words whose probability of appearance does not tend to 0 as time tends to infinity (the persistent words). In this paper, we give a characterisation of the persistent language for non sensible cellular automata associated with Bernouilli measures. We also study the computational complexity of these languages. We show that the persistent language can be non-recursive. But our main result is that the set of quasi-nilpotent cellular automata (those with a single configuration in their mu-limit set) is neither recursively enumerable nor co-recursively enumerable.
dc.identifierhttps://arxiv.org/abs/cs/0604007
dc.identifierhttp://arxiv.org/abs/cs/0604007
dc.identifierMathematical Foundations of Computer Science 2006Springer (Ed.) (28/08/2006) 190-201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111013
dc.subjectDiscrete Mathematics
dc.subjectComputational Complexity
dc.subjectDynamical Systems
dc.titleOn the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
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