Formal language recognition by stochastic cellular automata

Authors:
Daniel Merkle;Thomas Worsch
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
Venue:
Fundamenta Informaticae - Special issue on cellular automata
Year:
2002

Citing 3
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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).