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Learning theory allows for the study of the theoretical limits of the inductive inference of computable sets and functions. It is based on ´machines´ (or functions) called scientists, which receive as input a finite sequence of observations (either points of the graph of a function or elements in a set) and return conjectures about the object to which those observations belong (the respective function or set). We say that a scientist is successful in identifying the object if there is a point in which it stabilizes on a correct conjecture. In this work, we cover a brief introduction to learning theory, including a collection of existing results on different types of learning environments and different restrictions on the identificational power of scientists. We introduce some new methods to test the identifiability of a class: Markov scientists for memory-limited identification and limit sets for noncomputable identification, which were developed in collaboration with Professor José Félix Costa. Finally, we propose a concept for empirical identification so that these results may be applicable in practice under certain assumptions.

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Martim LobÆo was born in Lisbon in 1990. He enrolled at Técnico Lisboa in 2008 and proceeded to obtain a Master of Science degree in Mathematics of Computation. After working as a consultant at Accenture, he moved to Boston where he currently writes for an online technology publication. In his free time, he enjoys going cycling and rock climbing.

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