Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Por circuits are data structures which support efficient algorithms#R##N#for highly compressed integers. Using this new data structure it has#R##N#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  provide new results for por circuits and  give new applications in algorithmic group theory: 1.  define a modified reduction procedure on por circuits which runs in quadratic time thereby improving the known cubic time complexity. 2.  improve the complexity of the Word Problem for the Baumslag group to cubic time thereby providing the first practical algorithm for that problem. (The algorithm has been implemented and is available in the CRAG library.) 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 Por Circuits.
['Volker Diekert', 'Jürn Laun', 'Alexander Ushakov']
I am writing a research paper on a idea Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P.
[{"from": "human", "value": "I am writing a research paper on a idea Efficient algorithms for highly compressed data: The Word Problem in Higman's group is in P."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Por circuits are data structures which support efficient algorithms#R##N#for highly compressed integers. Using this new data structure it has#R##N#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  provide new results for por circuits and  give new applications in algorithmic group theory: 1.  define a modified reduction procedure on por circuits which runs in quadratic time thereby improving the known cubic time complexity. 2.  improve the complexity of the Word Problem for the Baumslag group to cubic time thereby providing the first practical algorithm for that problem. (The algorithm has been implemented and is available in the CRAG library.) 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 Por Circuits."}]