Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear sequential dynamical systems, incidence algebras, and M\"{o}bius
  functions   A sequential dynamical system (SDS) consists of a graph, a set of local
functions and an update schedule. A linear sequential dynamical system is an
SDS whose local functions are linear. In this paper, we derive an explicit
closed formula for any linear SDS as a synchronous dynamical system. We also
show constructively, that any synchronous linear system can be expressed as a
linear SDS, i.e. it can be written as a product of linear local functions.
Furthermore, we study the connection between linear SDS and the incidence
algebras of partially ordered sets (posets). Specifically, we show that the
M\"{o}bius function of any poset can be computed via an SDS, whose graph is
induced by the Hasse diagram of the poset. Finally, we prove a cut theorem for
the M\"{o}bius functions of posets with respect to certain chain
decompositions.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat