How can I simplify a conjunction of disjunctions (CNF) statement if I can introduce extra variables?
To simplify a conjunction of disjunctions (CNF) statement by introducing extra variables, you can use techniques like variable elimination, subsumption, and resolution. The goal is to reduce the size and complexity of the CNF while preserving its logical equivalence. Here are the general steps you can follow: 1. **Introduce Extra Variables**: - Identify parts of the CNF formula that can be simplified by introducing extra variables. This is typically done by identifying common subexpressions that appear in multiple clauses. 2. **Replace Subexpressions**: - Create new variables to represent subexpressions that appear multiple times. For example, if you have clauses (A v B) and (B v C), you can introduce a new variable X and rewrite the clauses as (A v X) and (X v C). 3. **Apply Subsumption**: - Look for clauses that are subsumed by other clauses. A clause A subsumes a clause B if A is a superset of B. Remove subsumed clauses from the CNF. 4. **Apply Resolution**: - Look for