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The Bounded and Precise Word Problems for Presentations of Groups (Paperback)
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The Bounded and Precise Word Problems for Presentations of Groups (Paperback)
Series: Memoirs of the American Mathematical Society
Expected to ship within 12 - 17 working days
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The author introduces and studies the bounded word problem and the
precise word problem for groups given by means of generators and
defining relations. For example, for every finitely presented
group, the bounded word problem is in NP, i.e., it can be solved in
nondeterministic polynomial time, and the precise word problem is
in PSPACE, i.e., it can be solved in polynomial space. The main
technical result of the paper states that, for certain finite
presentations of groups, which include the Baumslag-Solitar
one-relator groups and free products of cyclic groups, the bounded
word problem and the precise word problem can be solved in
polylogarithmic space. As consequences of developed techniques that
can be described as calculus of brackets, the author obtains
polylogarithmic space bounds for the computational complexity of
the diagram problem for free groups, for the width problem for
elements of free groups, and for computation of the area defined by
polygonal singular closed curves in the plane. The author also
obtains polynomial time bounds for these problems.
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