Lax Lean Archive

Gate clauses

Lax429075.Tseitin · concepts/Lax429075/Tseitin.lean · lax-429075

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    Natural Language Statement

    Definition

    The Tseitin encoding assigns one variable to each gate. At most three clauses enforce a gate's truth table, and a unit clause requires a true output. Input gates have no constraints.

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    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Lax429075.Circuits
    2
    3/-!
    4---
    5title: Gate clauses
    6type: definition
    7---
    8The Tseitin encoding assigns one variable to each gate. At most three
    9clauses enforce a gate's truth table, and a unit clause requires a true
    10output. Input gates have no constraints.
    11-/
    12
    13namespace Lax429075.Tseitin
    14
    15open CNF Circuits
    16
    17def positive (i : ℕ) : Literal := ⟨i, true⟩
    18def negative (i : ℕ) : Literal := ⟨i, false⟩
    19
    20def gateClauses (i : ℕ) : Gate → Formula
    21 | .input => []
    22 | .constant b => [[⟨i, b⟩]]
    23 | .neg a => [[positive i, positive a], [negative i, negative a]]
    24 | .conj a b => [[negative i, positive a], [negative i, positive b],
    25 [positive i, negative a, negative b]]
    26 | .disj a b => [[positive i, negative a], [positive i, negative b],
    27 [negative i, positive a, positive b]]
    28
    29def encode (C : Circuit) : Formula :=
    30 [[positive C.output]] ++ C.gates.zipIdx.flatMap (fun gi => gateClauses gi.2 gi.1)
    31
    32end Lax429075.Tseitin
    33
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