Formal language recognition by stochastic cellular automata

Issue title: Cellular Automata

Article type: Research Article

Authors: Merkle, Daniel | Worsch, Thomas

Affiliations: Institut für Angewandte Informatik und Formale Beschreibungsverfahren (AIFB), Universität Karlsruhe (TH), Kollegiengebäude am Ehrenhof Englerstrasse, 11 D-76131 Karlsruhe, Germany | IAKS, Vollmar Department of Informatics, University Karlsruhe, Am Fasanengarten 5, 76128 Karlsruhe, Germany

Abstract: We present two generalizations of cellular automata where transitions from one configuration to the next are no longer deterministic but depend on some element of randomization. The main topic is a model which not only takes into account the probabilities of cells being in certain states but also their dependencies. It formalizes the approach of ``randomized simulations'' often used for the modeling of real phenomena. In this paper the power of stochastic CA as language recognizers is investigated. Generalizations of well-known tools (stochastic signals and product automata) are used to prove that stochastic CA are strictly more powerful than deterministic CA and stochastic finite automata (which are known to recognize uncountably many languages).

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Journal: Fundamenta Informaticae, vol. 52, no. 1-3, pp. 183-201, 2002