Shrinking one-way cellular automata

Abstract

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata (OCA) with the additional property that during a computation any cell of the OCA has the ability to dissolve itself and we call this model shrinking one-way cellular automata (SOCA). It turns out that real-time SOCA are more powerful than real-time OCA, since they can accept certain linear-time OCA languages. Additionally, a construction is provided that enables real-time SOCA to accept the reversal of real-time iterative array languages. Finally, restricted real-time SOCA are investigated which are allowed to dissolve only a number of cells that is bounded by some function. In this case, an infinite strict hierarchy of language classes is obtained.

Complexity-Theoretic Aspects of Expanding Cellular Automata

“…When shrinking, the automaton's structure and dimension are preserved by "gluing" the severed parts and reconnecting their delimiting cells as neighbors. When employed as language recognizers, shrinking CAs (SCAs) can be more efficient than standard CAs [18,10].…”