On two-way communication in cellular automata with a fixed number of cells

Authors:
Andreas Malcher
Affiliations:
Institut für Informatik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany
Venue:
Theoretical Computer Science - Descriptional complexity of formal systems
Year:
2005

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Abstract

The effect of adding two-way communication to k cells one-way cellular automata (kC-OCAs) on their size of description is studied, kC-OCAs are a parallel model for the regular languages that consists of an array of k identical deterministic finite automata (DFAs), called cells, operating in parallel. Each cell gets information from its right neighbor only. In this paper, two models with different amounts of two-way communication are investigated. Both models always achieve quadratic savings when compared to DFAs. When compared to a one-way cellular model, the result is that minimum two-way communication can achieve at most quadratic savings whereas maximum two-way communication may provide savings bounded by a polynomial of degree k.