Abstract
In this paper we study number-decreasing cellular automata. They form a super-class of standard number-conserving cellular automata. It is well-known that the property of being number-conserving is decidable in quasi-linear time. In this paper we prove that being number-decreasing is dimension sensitive i.e. it is decidable for one-dimensional cellular automata and undecidable for dimension 2 or greater. There are only few known examples of dimension sensitive properties for cellular automata and this denotes some rich panel of phenomena in this class.
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© 2004 Springer-Verlag Berlin Heidelberg
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Bernardi, V., Durand, B., Formenti, E., Kari, J. (2004). A New Dimension Sensitive Property for Cellular Automata. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_31
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DOI: https://doi.org/10.1007/978-3-540-28629-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22823-3
Online ISBN: 978-3-540-28629-5
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