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|All Authors / Contributors:||
B Curtis Eaves; Uriel G Rothblum
|Description:||83 pages : illustrations ; 28 cm.|
|Series Title:||DIMACS technical report, 92-42.|
|Responsibility:||by B. Curtis Eaves and Uriel G. Rothblum.|
We describe a single, one, method, to which we refer as the Univeral Linear Machine, which can be used to solve any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates an ordered field algorithm for the problem. Then, given an instance of the linear problem, in the second phase the ordered field algorithm solves the particular instance of the linear problem. The ordered field algorithm is finite, deterministic, loopless and executes only the five ordered field operations -- additions, multiplications, subtractions, divisions and comparisons.
Conversely, we show that for each ordered field algorithm there is a linear problem which the ordered field algorithm solves uniquely. Finally, it is shown that with an ordered field algorithm for a linear problem, one can solve certain parametric instances of the linear problem."