Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automata Learning: An Algebraic Approach   We propose a generic categorical framework for learning unknown formal
languages of various types (e.g. finite or infinite words, weighted and nominal
languages). Our approach is parametric in a monad T that represents the given
type of languages and their recognizing algebraic structures. Using the concept
of anautomata presentation of T-algebras, we demonstrate that the task of
learning a T-recognizable language can be reduced to learning an abstract form
of algebraic automaton whose transitions are modeled by a functor. For the
important case of adjoint automata, we devise a learning algorithm generalizing
Angluin's L*. The algorithm is phrased in terms of categorically described
extension steps; we provide for a termination and complexity analysis based on
a dedicated notion of finiteness. Our framework applies to structures like
omega-regular languages that were not within the scope of existing categorical
accounts of automata learning. In addition, it yields new learning algorithms
for several types of languages for which no such algorithms were previously
known at all, including sorted languages, nominal languages with name binding,
and cost functions.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom