Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logic Meets Algebra: the Case of Regular Languages   The study of finite automata and regular languages is a privileged meeting
point of algebra and logic. Since the work of Buchi, regular languages have
been classified according to their descriptive complexity, i.e. the type of
logical formalism required to define them. The algebraic point of view on
automata is an essential complement of this classification: by providing
alternative, algebraic characterizations for the classes, it often yields the
only opportunity for the design of algorithms that decide expressibility in
some logical fragment.
  We survey the existing results relating the expressibility of regular
languages in logical fragments of MSO[S] with algebraic properties of their
minimal automata. In particular, we show that many of the best known results in
this area share the same underlying mechanics and rely on a very strong
relation between logical substitutions and block-products of pseudovarieties of
monoid. We also explain the impact of these connections on circuit complexity
theory.

5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph