Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugacy in Baumslag's group, generic case complexity, and division in
  power circuits   The conjugacy problem belongs to algorithmic group theory. It is the
following question: given two words x, y over generators of a fixed group G,
decide whether x and y are conjugated, i.e., whether there exists some z such
that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word
problem, in general. We investigate the complexity of the conjugacy problem for
two prominent groups: the Baumslag-Solitar group BS(1,2) and the
Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is
TC^0-complete. To the best of our knowledge BS(1,2) is the first natural
infinite non-commutative group where such a precise and low complexity is
shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that
the conjugacy problem is decidable (which has been known before); but our
results go far beyond decidability. In particular, we are able to show that
conjugacy in G(1,2) can be solved in polynomial time in a strongly generic
setting. This means that essentially for all inputs conjugacy in G(1,2) can be
decided efficiently. In contrast, we show that under a plausible assumption the
average case complexity of the same problem is non-elementary. Moreover, we
provide a lower bound for the conjugacy problem in G(1,2) by reducing the
division problem in power circuits to the conjugacy problem in G(1,2). The
complexity of the division problem in power circuits is an open and interesting
problem in integer arithmetic.

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The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics