Lecture 9

SAT §

Input: Given f in CNF with n variables and m clauses
Output: Assignment satisfying f if one exists and no if no SAT exists.

2-SAT §

Same but input $f$ has clauses of size $\le$ 2.

You can solve the 2-SAT problem using the SCC algorithm.

For all unit clauses (clauses of size 1):

• satisfy it, call it a: so set $a_i=T$
• remove all clauses containing $a_i$, these are satisfied
• drop all occurrences of $\overline{a}$
• Let f’ be new formula

In general for clause $(\alpha \wedge \beta )$, add edges $\overline{\alpha }\to \beta$ and $\overline{\beta }\to \alpha$.