Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Complexity of Reachability Problems for Flat Counter Machines with
  Periodic Loops   This paper proves the NP-completeness of the reachability problem for the
class of flat counter machines with difference bounds and, more generally,
octagonal relations, labeling the transitions on the loops. The proof is based
on the fact that the sequence of powers $\{R^i\}_{i=1}^\infty$ of such
relations can be encoded as a periodic sequence of matrices, and that both the
prefix and the period of this sequence are $2^{\mathcal{O}(\bin{R})}$ in the
size of the binary encoding $\bin{R}$ of a relation $R$. This result allows to
characterize the complexity of the reachability problem for one of the most
studied class of counter machines \cite{cav10,comon-jurski98}, and has a
potential impact for other problems in program verification.

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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin