Learning 3-CNFs

cosmos 6th March 2017 at 12:24pm

See Probably approximately correct

{c1c2...cm}\{c_1 \wedge c_2 \wedge ... \wedge c_m\} | each cic_i is a disjunction on at most 3-literals, known as clauses.

Can we efficiently PAC-learn 3-CNF?

We will map it to an easy problem (in P?) to show that it is, by doing a kind of Feature expansion.. Apply conjunction learning algorithm without negated literals.

3-term DNF:

ϕ=T1T2T3=l1T1,l2T2,l3T3(l1l2l3)\phi = T_1 \vee T_2 \vee T_3 = \wedge_{l_1 \in T_1, l_2 \in T_2, l_3 \in T_3} ( l_1 \vee l_2 \vee l_3)

can learn 3-DNF data using an equivalent 3-CNF. However, getting the 3-DNF back is hard..