Finitely Presented Group Whose Word Problem Has the Same Degree as That of an Arbitrarily given Thue System (an Application of Methods of Britton).
نویسنده
چکیده
work done with P. C. Gilmore on knapsack problems strongly suggested the results of this paper. Finally, we note that the following steps, (i) solve P1 obtaining the opitmal B, (ii) put M(I)/M(B) into standard form and identify the a,, (iii) solve (4) obtaining y, (iv) compute XB = B-1(b Ny), will yield an optimal solution (XB, Y) if XB 2 0. It is not necessary for b to be in KB(l(D 1)) to apply the procedure. The problems for which the procedure provides a solution are those for which those inequalities binding the solution of P1 alone determine the solution to P2.
منابع مشابه
Turing Degrees and the Word and Conjugacy Problems for Finitely Presented Groups
The unsolvability of the conjugacy problem for finitely presented groups was first shown by Novikov [26]. Shortly thereafter the corresponding result for the word problem was proved by Novikov [27] and Boone [6] (see also Boone [7], Higman [20] and Britton [9]). Friedberg [19] and Mucnik [25] revitalised the theory of recursively enumerable (r.e.) Turing degrees by showing that there are degree...
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عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 53 2 شماره
صفحات -
تاریخ انتشار 1965