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|All Authors / Contributors:||
Charles H Bennett
|Description:||15 pages ; 29 cm.|
|Series Title:||Report (Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands). Computer Science/Dept. of Algorithmics and Architecture, CS-R9341.|
|Responsibility:||C.H. Bennett [and others].|
A third information distance, based on the idea that one should aim for dissipationless computations, and hence for reversible ones, is given by the length [formula] of the shortest reversible program that transforms x into y and y into x on a universal reversible computer. It is shown that also E₂ = E₁, up to a logarithmic additive term. It is remarkable that three so differently motivated definitions turn out to define one and the same notion.
Another information distance, E₃, is obtained by minimizing the total amount of information flowing in and out during a reversible computation in which the program is not retained, in other words the number of extra bits (apart from x) that must be irreversibly supplied at the beginning, plus the number of garbage bits (apart from y) that must be irreversibly erased at the end of the computation to obtain a 'clean' y. This distance is within a logarithmic additive term of the sum of the conditional complexities, [formula]. Finally, using the physical theory of reversible computation, the simple difference K(x) - K(y) is shown to be an appropriate (universal, antisymmetric, and transitive) measure of the amount of thermodynamic work required to transform string x into string y by the most efficient process."