Compressed word problems in HNN-extensions and amalgamated products
Niko Haubold, Markus Lohrey
TL;DR
This paper demonstrates that the compressed word problem for certain complex group constructions like HNN-extensions and amalgamated free products can be efficiently reduced to the problem for their base groups, simplifying computational analysis.
Contribution
It establishes polynomial time reductions of the compressed word problem from HNN-extensions and amalgamated free products to their base groups, advancing computational group theory.
Findings
Polynomial time Turing-reducibility for HNN-extensions
Polynomial time Turing-reducibility for amalgamated free products
Simplification of the compressed word problem in complex groups
Abstract
It is shown that the compressed word problem for an HNN-extension with base group H and finite associated subgroups is polynomial time Turing-reducible to the compressed word problem for H. An analogous result for amalgamated free products is shown as well.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · Cellular Automata and Applications