Complexity through the Observation of Simple Systems

TL;DR

This paper surveys the paradigm of 'computing by observing,' showing how simple systems can exhibit complex behavior when observed appropriately, with applications to grammars and sticker systems, and suggests future research directions.

Contribution

It introduces the concept of observing simple systems to achieve computational complexity, including new applications to grammars and sticker systems.

Findings

Observed simple systems can be computationally complete.

Regular observers enable complex behavior in simple systems.

Applications to grammars and sticker systems demonstrate the paradigm.

Abstract

We survey work on the paradigm called "computing by observing." Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this end an observer records this behavior. It has turned out that the observed behavior of computationally simple systems can be very complex, when an appropriate observer is used. For example, a restricted version of context-free grammars with regular observers suffices to obtain computational completeness. As a second instantiation presented here, we apply an observer to sticker systems. Finally, some directions for further research are proposed.