WEBVTT

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This overview explains why one evaluated bit,

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a witness, a truth vector, and a reusable program are different deliverables.

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Comparing methods that return different artifacts
can produce a misleading performance claim.

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Take the rule A or B and input zero one.

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A point query asks for one output bit, which is one.

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It does not request the answer for zero zero or for any other assignment.

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A full-vector request asks for all four bits.

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A witness request can ask for just one satisfying assignment, such as zero one.

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A full satisfying-assignment enumeration asks for all three witnesses.

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These outputs answer different questions even though they start from the same formula.

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Now project the witnesses onto A alone.

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The three full witnesses produce selected values zero, one, and one.

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Removing duplicates leaves two distinct selected answers.

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A full-model count of three is not the projected count of two.

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Choose the output before choosing the method.

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Choose the output before choosing the method.

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The same rule can be asked for one evaluated bit, one satisfying
assignment, every truth output, or a reusable program.

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These are different deliverables.

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F is the exclusive-or of two results: A AND B, and C OR D.

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At assignment 1011, F evaluates to one.

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It is also a satisfying witness.

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A full AB-by-CD matrix contains all 16 outputs,

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in ascending binary order: the selected bit occupies row two, column three.

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A program graph instead stores operations and
dependencies; it can be used to produce answers later.

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A witness does not contain every truth output.

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A graph is not the already-filled matrix.

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Asking how many distinct selected-variable
assignments satisfy a rule is yet another contract;

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count each projection once even when it has several witnesses.

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

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This is separate from the intervening four-input example.

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Set A and B to zero.

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We will answer this one point while keeping the other assignments in mind.

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For the supplied point zero zero, or returns zero.

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That is a correct completed point answer.

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It does not mean the formula is unsatisfiable, because zero one, one zero, and one one still make it true.

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Point evaluation and existence of a satisfying assignment ask different questions.

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This case establishes a specific contrast.

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Correct point answer: 0.

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The complete function is still satisfiable.

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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 compiled representation can describe how to evaluate the rule.

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It may be compact and reusable.

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That does not imply it already contains every full assignment, every selected answer, or

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the complete truth vector.

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Specify the artifact the caller actually needs before comparing methods.

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A fast witness is not a substitute for every truth-table output.

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A full table may be unnecessary when the caller only needs one decision.

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The example establishes a contract distinction.

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It does not rank all representations by speed.

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Any performance comparison must make both methods deliver the same required artifact and

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include the preparation and delivery costs relevant to that request.

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Name the required output before choosing a method.

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Name the required output before choosing a method.

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A witness does not replace the complete ordered truth outputs.