Mathematics – Group Theory
Scientific paper
2011-03-07
Mathematics
Group Theory
Scientific paper
Power circuits are data structures which support efficient algorithms for highly compressed integers. 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. Before that the best known upper bound has been non-elementary. In the present paper we provide new results for power circuits and we give new applications in algorithmic algebra and algorithmic group theory: 1. We define a modified reduction procedure on power circuits which runs in quadratic time thereby improving the known cubic time complexity. The improvement is crucial for our other results. 2. We improve the complexity of the Word Problem for the Baumslag group to cubic time thereby providing the first practical algorithm for that problem. 3. The main result is that the Word Problem of Higman's group is decidable in polynomial time. The situation for Higman's group is more complicated than for the Baumslag group and forced us to advance the theory of power circuits.
Diekert Volker
Laun Jürn
Ushakov Alexander
No associations
LandOfFree
Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-606948