Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Synchronizing Probability Function and the Triple Rendezvous Time
  for Synchronizing Automata   Cerny's conjecture is a longstanding open problem in automata theory. We
study two different concepts, which allow to approach it from a new angle. The
first one is the triple rendezvous time, i.e., the length of the shortest word
mapping three states onto a single one. The second one is the synchronizing
probability function of an automaton, a recently introduced tool which
reinterprets the synchronizing phenomenon as a two-player game, and allows to
obtain optimal strategies through a Linear Program.
  Our contribution is twofold. First, by coupling two different novel
approaches based on the synchronizing probability function and properties of
linear programming, we obtain a new upper bound on the triple rendezvous time.
Second, by exhibiting a family of counterexamples, we disprove a conjecture on
the growth of the synchronizing probability function. We then suggest natural
follow-ups towards Cernys conjecture.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an