Fast one-way cellular automata

Authors:
Andreas Klein;Martin Kutrib
Affiliations:
Fachbereich Mathematik/Informatik, Universität Kassel, Heinrich Plett Straße 40, D-34132 Kassel, Germany;Institut für Informatik, Universität Giessen, Arndtstrasse 2, D-35392 Giessen, Germany
Venue:
Theoretical Computer Science - Mathematical foundations of computer science
Year:
2003

Citing 5
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Signals in one-dimensional cellular automata

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On Algebraic Structure of Neighborhoods of Cellular Automata: Horse Power Problem

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On Algebraic Structure of Neighborhoods of Cellular Automata: Horse Power Problem

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Abstract

Space-bounded one-way cellular language acceptors (OCA) are investigated. The only inclusion known to be strict in their time hierarchy from real-time to exponential-time is between real-time and linear-time! We show the surprising result that there exists an infinite hierarchy of properly included OCA-language families in that range. A generalization of a method in Terrier (Theoret. Comput. Sci. 156 (1-2) (1996) 281) is shown which provides a tool for proving that languages are not acceptable by OCAs with small time bounds. The hierarchies are established by such a language and a translation result. In addition, a notion of constructibility for CAs is introduced, along with some of its properties. We prove several closure properties of the families in the hierarchy.