Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Bounded Tree Depth Homomorphisms   We prove that graphs G, G' satisfy the same sentences of first-order logic
with counting of quantifier rank at most k if and only if they are
homomorphism-indistinguishable over the class of all graphs of tree depth at
most k. Here G, G' are homomorphism-indistinguishable over a class C of graphs
if for each graph F in C, the number of homomorphisms from F to G equals the
number of homomorphisms from F to G'.

37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys