algorithm - Reduce 0-1 knapsack prob. to a SAT prob -

is there way reduce 0-1 knapsack problem sat problem in conjunctive norm form?

you work out digital circuits necessary implement adders , comparators , turn result of conjunctive normal form. can circuits cnf form without expanding them exponentially making intermediate variables represent outputs of small sections of circuit.

each node of circuit amounts a=f(b, c) output, b , c input, , f simple function & or |. can create cnf function true when result of f(b, c) , can't unwieldy, because function on 3 variables.

you can rewrite circuit large number of terms of form a=f(b, c) , have cnf versions of these , them together. assuming want solve output being true, stick on output variable final component of big and.