When a negation surrounds a formula in Disjunctive Normal Form (DNF), is the formula still in DNF?

For example: Would $\lnot((\lnot X\land \lnot Y) \lor (\lnot X \land Y))$ be classed as being in DNF, even though it is surrounded by a negation?


The usual definition of a formula in DNF excludes this. It shall be a disjonction of conjonctions of litterals. However your form is very closed to CNF form according to Morgan's laws:

$$\neg((\neg X \land \neg Y) \lor (\neg X \land Y))\equiv(X \lor Y) \land ( X\lor \neg Y)$$

In general converting a formula in DNF to an equivalent form in CNF may lead to an exponential growth.


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