Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Total Variation Distance of Labelled Markov Chains   Labelled Markov chains (LMCs) are widely used in probabilistic verification,
speech recognition, computational biology, and many other fields. Checking two
LMCs for equivalence is a classical problem subject to extensive studies, while
the total variation distance provides a natural measure for the "inequivalence"
of two LMCs: it is the maximum difference between probabilities that the LMCs
assign to the same event.
  In this paper we develop a theory of the total variation distance between two
LMCs, with emphasis on the algorithmic aspects: (1) we provide a
polynomial-time algorithm for determining whether two LMCs have distance 1,
i.e., whether they can almost always be distinguished; (2) we provide an
algorithm for approximating the distance with arbitrary precision; and (3) we
show that the threshold problem, i.e., whether the distance exceeds a given
threshold, is NP-hard and hard for the square-root-sum problem. We also make a
connection between the total variation distance and Bernoulli convolutions.

24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin