Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A coalgebraic take on regular and $\omega$-regular behaviours   We present a general coalgebraic setting in which we define finite and
infinite behaviour with B\"uchi acceptance condition for systems whose type is
a monad. The first part of the paper is devoted to presenting a construction of
a monad suitable for modelling (in)finite behaviour. The second part of the
paper focuses on presenting the concepts of a (coalgebraic) automaton and its
($\omega$-) behaviour. We end the paper with coalgebraic Kleene-type theorems
for ($\omega$-) regular input. The framework is instantiated on
non-deterministic (B\"uchi) automata, tree automata and probabilistic automata.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org