Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recurrent Neural Networks as Weighted Language Recognizers   We investigate the computational complexity of various problems for simple
recurrent neural networks (RNNs) as formal models for recognizing weighted
languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs
with softmax, which are commonly used in natural language processing
applications. We show that most problems for such RNNs are undecidable,
including consistency, equivalence, minimization, and the determination of the
highest-weighted string. However, for consistent RNNs the last problem becomes
decidable, although the solution length can surpass all computable bounds. If
additionally the string is limited to polynomial length, the problem becomes
NP-complete and APX-hard. In summary, this shows that approximations and
heuristic algorithms are necessary in practical applications of those RNNs.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th