Learn Turn a finite specification into logical formulas, distinguish witnesses from universal certificates, and prove circuit correctness with an explicit work/depth model. Normal forms provide supporting depth.
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An existential witness and a universal certificate answer different questions.
No. One matching row establishes agreement only there. A counterexample refutes equivalence; checking every assignment of a specified finite input set proves it on that domain.
Material implication is a truth condition, not a promise of causation.
Yes. A→B is false only when A is true and B false. This differs from A AND B and from the converse B→A.
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Assumptions, hidden variables and circuit families
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Translate requirements into truth conditions and choose the right evidence for satisfiability, validity, equivalence and entailment.
8 practice tasks.
Supporting depth: build canonical DNF and CNF, prove their meaning row by row, and separate finite decidability from efficient representation.
6 practice tasks.
Construct a bounded-fan-in alarm circuit, prove its specification for every input, and audit padding, parallel depth and shared gates.
6 practice tasks.