Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P

Volker Diekert, Jürn Laun & Alexander Ushakov
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 was non-elementary. In the present paper we provide new results for power circuits and we give new applications in algorithmic group theory: 1. We define a modified reduction...