Computing with Probabilistic Cellular Automata

Abstract. We investigate the computational capabilities of probabilistic cellular automata by means of the density classification problem. We find that a specific probabilistic cellular automata rule is able to solve the density classification problem, i.e. classifies binary input strings according to the number of 1’s and 0’s in the string, and show that its computational abilities are related to critical behaviour at a phase transition. 1 Preliminaries Cellular automata (CA) models have been widely studied and applied in physics, biology and computer science. They are among the simplest mathematical systems which exhibit self-organisation, complex patterning and capability of universal (Turing) computation [1,2,3]. Various authors have suggested CA as the generic model for parallel, biologically inspired computing [1,4,5]. As such they are closely related to neural networks [5]. In this contribution we investigate claims regarding the computational abilities of elementary pr...

• Type: Conference
• Year: 2009
• Where: ICANN
• Authors: Martin Schüle, Thomas Ott, Ruedi Stoop
• Keywords: Cellular Automata Rule, Density Classification Problem, ICANN 2009, Probabilistic Cellular Automata