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Compressed word problems in HNN-extensions and amalgamated products
[article]
2008
arXiv
pre-print
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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. ...
In this paper, we prove a transfer theorem for the compressed word problem of HNN-extensions [7] . ...
arXiv:0811.3303v1
fatcat:ph4em5tysnfm3mqqqjm253gtjy
Compressed Word Problems in HNN-extensions and Amalgamated Products
2010
Theory of Computing Systems
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It is not hard to see that the word problem for an HNN-extension (1) with A finite can be reduced in polynomial time to the word problem of the base group H. ...
In this paper, we restrict to HNN-extensions (resp. amalgamated products) with finite associated (resp. amalgamated) subgroups, which is an important subcase. ...
From the close relationship of HNN-extensions with amalgamated free products, a polynomial time reduction from the compressed problem for an amalgamated free product H 1 * H 2 | a = ϕ(a) (a ∈ A 1 ) (with ...
doi:10.1007/s00224-010-9295-2
fatcat:bvn4l2vyvfdnblg3bdsedthnsy
Compressed Word Problems in HNN-Extensions and Amalgamated Products
[chapter]
2009
Lecture Notes in Computer Science
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It is not hard to see that the word problem for an HNN-extension (1) with A finite can be reduced in polynomial time to the word problem of the base group H. ...
In this paper, we restrict to HNN-extensions (resp. amalgamated products) with finite associated (resp. amalgamated) subgroups, which is an important subcase. ...
From the close relationship of HNN-extensions with amalgamated free products, a polynomial time reduction from the compressed problem for an amalgamated free product H 1 * H 2 | a = ϕ(a) (a ∈ A 1 ) (with ...
doi:10.1007/978-3-642-03351-3_23
fatcat:cdorifk36fdhfcbilz47rc3loa
Complexity of word problems for HNN-extensions
[article]
2021
arXiv
pre-print
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It is shown that the word problem for an ascending HNN-extension of a group H is logspace reducible to the so-called compressed word problem for H. ...
The computational complexity of the word problem in HNN-extension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. ...
The compressed word problem turns out to be useful for the solution of the word problem for an ascending HNN-extension: (3) in G. ...
arXiv:2107.01630v1
fatcat:dgv33bxrvjggpilmg2at7y3uhe
Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products
2016
Symposium on Theoretical Aspects of Computer Science
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We also prove general transfer results: NP-membership of the knapsack problem is passed on to finite extensions, HNN-extensions over finite associated subgroups, and amalgamated products with finite identified ...
This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. ...
HNN-extensions and amalgamated products. ...
doi:10.4230/lipics.stacs.2016.50
dblp:conf/stacs/LohreyZ16
fatcat:izbsudjb6fbkhg67szrcefx4ee
A relationship between HNN extensions and amalgamated free products in operator algebras
[article]
2008
arXiv
pre-print
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With a minor change made in the previous construction we observe that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product in both the von Neumann algebra ...
We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann algebras and also those of simplicity and K-theory of (reduced or universal) HNN extensions ...
Firstly, with a minor change of the previous construction in [19] we see that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product. ...
arXiv:math/0601706v4
fatcat:ttc27f42rnfrhnbniydbhlrdri
Editorial
2011
Theory of Computing Systems
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Niko Haubold and Markus Lohrey determine the complexity levels of the compressed word problem for HNN-extensions and amalgamated free products. ...
Artur Jeż and Alexander Okhotin find complexity levels for some algorithmic problems in conjunctive grammars over unary alphabet. ...
doi:10.1007/s00224-011-9328-5
fatcat:ihis5erdrzhw5hil74raavtrpi
Hilbert space compression for free products and HNN-extensions
2011
Journal of Functional Analysis
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We also investigate the case of HNN-extensions of a group relative to a subgroup which is finite or of finite index. ...
Given the (equivariant or non-equivariant) Hilbert space compression of two groups, we find bounds on the compression of their free product. ...
Acknowledgments I thank Alain Valette for reading previous versions of the article, for interesting conversations and for pointing out some open problems related to Hilbert space compression. ...
doi:10.1016/j.jfa.2011.08.012
fatcat:ibems3rosjeutg4z3je5a6am4q
Hilbert space compression for free products and HNN-extensions
[article]
2010
arXiv
pre-print
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We also investigate the Hilbert space compression of an HNN-extension of a group relative to a finite normal subgroup or a finite index subgroup. ...
Given the Hilbert space compression of two groups, we find bounds on the Hilbert space compression of their free product. ...
Acknowledgements I thank Alain Valette for reading previous versions of the article, for interesting conversations and for pointing out some open problems related to Hilbert space compression. ...
arXiv:1002.3879v3
fatcat:lhhr6hqvpffhdaarf2j7pav3ja
Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P
[article]
2011
arXiv
pre-print
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Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag group is in P. ...
The main result is that the Word Problem of Higman's group is decidable in polynomial time. ...
If this is the case, Π is not a power circuit and we stop with the output "no". From now on we assume ε(Q) ≥ 1. ...
arXiv:1103.1232v1
fatcat:rhrffduubnflppyu5dcjmkxovu
EFFICIENT ALGORITHMS FOR HIGHLY COMPRESSED DATA: THE WORD PROBLEM IN HIGMAN'S GROUP IS IN P
2012
International journal of algebra and computation
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Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag group is is decidable in polynomial time. ...
The Word Problem of Higman's group is decidable in polynomial time. It is due to the last result that we were forced to advance the theory of power circuits. Thanks. ...
The situation for G (2, 3) is open and related to questions in number theory. Baumslag and Higman groups are built via HNN extensions and amalgamated products. ...
doi:10.1142/s0218196712400085
fatcat:eau27rtkf5fwvmvsrhpcuusasi
Knapsack in graph groups, HNN-extensions and amalgamated products
[article]
2015
arXiv
pre-print
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We also prove general transfer results: NP-membership of the knapsack problem is passed on to finite extensions, HNN-extensions over finite associated subgroups, and amalgamated products with finite identified ...
This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. ...
This shows that the subset sum problem and the knapsack problem are NP-hard for the group F (Σ) × F (Σ), where for knapsack we allow integer exponents. ...
arXiv:1509.05957v1
fatcat:6232c63sdrhjxpfiunol2icshy
The Word Problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable
2011
Journal of Algebra
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We prove that the Word Problem in the Baumslag group G (1,2) = a, b; a a b = a 2 which has a non-elementary Dehn function is decidable in polynomial time. ...
The compressed form of the Magnus breakdown algorithm We mentioned in Section 2.2 that the Magnus breakdown algorithm for the Word Problem in G (1, 2) represents the group G (1, 2) as the HNN extension ...
This enables us to perform some variations of the standard algorithms in HNN extensions (or similar groups) keeping the actual rewriting in the compressed form. ...
doi:10.1016/j.jalgebra.2011.07.024
fatcat:zgerymcldrft7o5rre3uznfjpi
The Word Problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable
[article]
2011
arXiv
pre-print
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We prove that the Word problem in the Baumslag group G(1,2) which has a non-elementary Dehn function is decidable in polynomial time. ...
This enables us to perform some variations of the standard algorithms in HNN extensions (or similar groups) keeping the actual rewriting in the compressed form. ...
In section 2 we discuss algorithmic properties of elements of G (1, 2) as an HNN extension of the Baumslag-Solitar group, set up the notation, and outline the difficulty of solvig the Word problem using ...
arXiv:1102.2481v1
fatcat:4nhvsl47qjhypagvwv4ovpdxwe
Closure properties of knapsack semilinear groups
[article]
2019
arXiv
pre-print
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, ..., x_k take values in the natural numbers): graph products, amalgamated free products with finite amalgamated subgroups, HNN-extensions with finite associated subgroups, and finite extensions. ...
We show that the following group constructions preserve the semilinearity of the solution sets for knapsack equations (equations of the form g_1^x_1... g_k^x_k = g in a group G, where the variables x_1 ...
The first and second author were supported by the DFG research project LO 748/12-1. ...
arXiv:1911.12857v1
fatcat:graxo2mwuzhp7ja6latfxqufvi
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