The set of minimal braids is Co-NP-complete
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The main result of this paper is that the set of minimal braids is co-NP-complete.About:
This article is published in Journal of Algorithms.The article was published on 1991-09-01 and is currently open access. It has received 63 citations till now. The article focuses on the topics: Braid theory & Braid.read more
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Book ChapterDOI
New Public-Key Cryptosystem Using Braid Groups
TL;DR: The aim of this article is to show that the braid groups can serve as a good source to enrich cryptography and to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in thebraid groups.
Journal ArticleDOI
A new approach to the word and conjugacy problems in the braid groups
TL;DR: In this paper, a new presentation of the n-string braid group B n is studied, which retains most of the desirable features of the Garside-Thurston solution and makes possible certain computational improvements.
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A new approach to the word and conjugacy problems in the braid groups
TL;DR: In this paper, a new presentation of the $n$-string braid group $B_n$ is studied, which retains most of the desirable features of the Garside-Thurston solution and at the same time makes possible certain computational improvements.
Journal ArticleDOI
Braid groups are linear
TL;DR: In this article, the authors considered a representation of the braid group p: Bn -- GLm(Z[ql1, t±l]) (m = n(n-1)/2), and proved it to be faithful for n = 4.
Book ChapterDOI
Braids: A Survey
Joan S. Birman,Tara E. Brendle +1 more
TL;DR: Artin's braid group, B n and its role in knot theory was discussed in this article. But the main focus of this paper is on the topological concept of a braid and of a group of braids via the notion of configuration space.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Combinatorial Group Theory
Roger C. Lyndon,Paul E. Schupp +1 more
TL;DR: In this article, the authors introduce the concept of Free Products with Amalgamation (FPAM) and Small Cancellation Theory over free products with amalgamation and HNN extensions.
Journal ArticleDOI
Theory of Braids
TL;DR: A theory of braids leading to a classification was given in my paper "Theorie der Zopfe" in vol.
Journal Article
The theory of braids.
TL;DR: The theory of braids as discussed by the authors shows the interplay of two disciplines of pure mathematics? topology, used in the definition of Braids, and the theory of groups used in their treatment.