ABSTRACT
With the introduction of computers, automata have been playing a continuously increasing role in the natural sciences. This chapter focuses on special automata called learning systems. A learning system has a learning procedure by which it can develop methods that cannot be deduced trivially from its learning procedure. The learning system tries out hypotheses (methods) and selects the better ones. Artificial learning systems need huge processing capabilities. New physical concepts of information processing have to be developed to meet these requirements. In science, a central task is to develop and compare models to account for data. Two levels of inference are involved in the task of data-driven modelling. At the first level of inference, one assumes that one of the models that was invented is true. The second level of inference is the task of model comparison. Computational complexity is a characterization of the time or space requirements for solving a problem by a particular algorithm.
