How to convert Pseudo boolean constraints to CNF format

for example L1 + … + Ln ≥ 1 is converted to L1 ∨ … ∨ Ln

but how about:

L1 + … + Ln ≥ k

L1 + … + Ln < k


L1 + L2 = k


2 L1 + 2 L2L3 + L4 ≥ 3

is it there a book that I could read to understand more?


1 Answer 1


Apply the Tseitin transform to a circuit with adders and comparators.

For the special case of $L_1 + \dots + L_n \ge k$ (or $\le k$), see Encoding 1-out-of-n constraint for SAT solvers and Reduce the following problem to SAT.


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