Further research along the line shows that expert users can use Boolean Conjunctive Normal Form expansion to improve retrieval performance by 50-300 % over unexpanded keyword queries.
12.
This resolution technique uses proof by contradiction and is based on the fact that any sentence in propositional logic can be transformed into an equivalent sentence in conjunctive normal form.
13.
The name of the switching lemma stems from the following observation : Take an arbitrary formula in conjunctive normal form, which is in particular a depth-2 circuit.
14.
The first example is also in conjunctive normal form and the last two are in both conjunctive normal form and disjunctive normal form, but the second example is in neither.
15.
The first example is also in conjunctive normal form and the last two are in both conjunctive normal form and disjunctive normal form, but the second example is in neither.
16.
If and only if the original argument was valid will the theorem in conjunctive normal form be a contradiction, and if it is then that it is will be apparent.
17.
Given that any proposition containing conjunction, disjunction, and negation can be equivalently rephrased using conjunction and negation alone ( the conjunctive normal form ), we can now handle any compound proposition.
18.
As there exist polynomial-time algorithms to convert any Boolean expression to conjunctive normal form such as Tseitin's algorithm, posing SAT problems in CNF does not change their computational difficulty.
19.
CNF is the infimum of the numbers ? such that satisfiability of conjunctive normal form formulas without clause length limits can be solved in time O ( 2 ? " n " ).
20.
Another important NL-complete problem is 2-satisfiability ( Papadimitriou 1994 Thrm . 16.3 ), the problem of determining whether a boolean formula in conjunctive normal form with two variables per clause is satisfiable.
