Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dehn Functions, the Word Problem, and the Bounded Word Problem For
  Decidable Group Presentations   We construct examples of finitely generated decidable group presentations
that satisfy certain combinations of solvability for the word problem,
solvability for the bounded word problem, and computablity for the Dehn
function. We prove that no finitely generated decidable presentations exist
satisfying the combinations for which we do not provide examples. The
presentations we construct are also minimal. These constructions answer an open
question asked by R.I. Grigorchuk and S.V. Ivanov. Our approach uses machinery
developed by Birget, Ol'shanskii, Rips, and Sapir for constructing finite group
presentations that simulate Turing machines. We generalize this machinery to
construct finitely generated decidable group presentations that simulate
computing objects similar to oracle Turing machines.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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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: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: stat