On Learning and Testing Dynamic Environments by Oded Goldreich and Dana Ron (ECCC). Given a dynamic environment that is evolving according to a local rule, the goal is to query some of the states in the system at some point of time and determine if the system is evolving according to some fixed rule or is far from it. A harder problem is to learn the evolution of the environment. They give some upper and some lower bounds for various versions of these problems. In particular they show that using sub-linear queries a lot can be achieved even in this setting. This is the first of its kind result and possibly many more results in this area will follow soon.
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