WEBVTT

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This overview explains which variables can actually affect an output,
compared with the variables named by a surrounding interface.

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Irrelevant display variables can enlarge
a layout without adding distinct behavior.

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Use the rule A or B.

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To test whether A can influence the answer, hold B fixed at zero and compare A

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zero with A one.

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The answers change from zero to one.

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This pair is a witness that A belongs to the live support of the function.

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Now hold B at one instead.

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Changing A no longer changes the answer, because B already makes the or true.

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That local masking does not erase the earlier witness.

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Live support asks whether some fixed context exposes an influence,

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not whether every context does.

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A variable can also be written in the expression without influencing the function at all.

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In A exclusive-or A exclusive-or B, the two A terms cancel for both values of A.

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The result is always B.

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Textual occurrence and semantic support are different properties.

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Textual occurrence and semantic support are different properties.

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An input is in semantic support if changing it
can alter the output in at least one context.

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The ambient universe may name extra variables, and a written
variable list can overestimate support before simplification.

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The function takes the exclusive-or of two results: A AND B, and C OR D.

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Its ambient universe includes A through F,
although E and F never occur in the rule.

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Fix C to one.

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C OR D becomes one for either D, leaving NOT of A AND B.

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With B equal one, toggling A changes the output.

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With A equal one, toggling B changes it too.

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D cannot change the restricted output in any context.

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It is outside the remaining support.

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The four A-B assignments produce four distinct cases.

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Retaining D as a display axis repeats the outputs across eight cells.

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With B equal zero, toggling A happens to change nothing.

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The B-equals-one witness still establishes that A is in support.

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Return to the opening two-input rule F equals A or B.

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A and B are Boolean inputs.

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The intervening restricted four-input rule is a separate example.

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Here set A to zero and B to zero; then change only B to one.

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At zero zero the output is zero.

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Hold A at zero and change B to one; the output becomes one.

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This is a witness that B can influence the unrestricted function.

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The earlier context with A one masked that influence but did not invalidate this witness.

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This case establishes a specific contrast.

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Some fixed context exposes B.

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One masked context does not remove support.

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Keep the input, intermediate values, and conclusion together when comparing it with the previous case.

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The calculated answer belongs to this complete assignment under the stated rule.

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The calculated answer belongs to this complete assignment under the stated rule.

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A restriction fixes an input and produces the remaining function.

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With B fixed to zero, A or zero becomes A.

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We have not filled in an unknown answer by guessing.

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We have explicitly selected one slice of the original function.

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With B fixed to one, the remaining function is the constant one.

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A was live in the original function but is not live after this restriction.

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The support of a restricted function must be determined for that new function.

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Suppose we display the original function using an extra input C that does not occur in it.

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Every A B assignment now appears twice, once for each C value, with the same output.

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The larger ambient layout has more cells, but the rule has gained no dependence on C.

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Support means that some context can distinguish an input's values.

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Declare fixed inputs and display axes separately.