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So for English each character can convey log 2 (26) = 4.7 bits of information. However the average amount of actual information carried per character in meaningful English text is only about 1.5 bits per character. So the plain text redundancy is D = 4.7 − 1.5 = 3.2. [1] Basically the bigger the unicity distance the better.
The quantity is called the relative redundancy and gives the maximum possible data compression ratio, when expressed as the percentage by which a file size can be decreased. (When expressed as a ratio of original file size to compressed file size, the quantity R : r {\displaystyle R:r} gives the maximum compression ratio that can be achieved.)
The second pattern of potentially globally redundant proofs appearing in global redundancy definition is related to the well-known [further explanation needed] notion of regularity [further explanation needed]. Informally, a proof is irregular if there is a path from a node to the root of the proof such that a literal is used more than once as ...
There are many names for interaction information, including amount of information, [1] information correlation, [2] co-information, [3] and simply mutual information. [4] Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, beyond that which is present in any subset of those variables.
Theorems are those logical formulas where is the conclusion of a valid proof, [4] while the equivalent semantic consequence indicates a tautology. The tautology rule may be expressed as a sequent :
Theorem — If ⌈ ((+)) ⌉ then the following is true for every encoding and decoding function : {,} {,} and : {,} {,} respectively: [(() +)]. The intuition behind the proof is however showing the number of errors to grow rapidly as the rate grows beyond the channel capacity.
In Boolean algebra, the consensus theorem or rule of consensus [1] is the identity: ¯ = ¯ The consensus or resolvent of the terms and ¯ is . It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.
Theorem — (sufficiency) If there exists a solution to the primal problem, a solution (,) to the dual problem, such that together they satisfy the KKT conditions, then the problem pair has strong duality, and , (,) is a solution pair to the primal and dual problems.