There are two laws pertinent to the question of what the law permits in DC, along with some understanding of a term of art. DC law generally allows pocket knives with blades under three inches. Federal law is ambiguous.

One may not bring a "dangerous" or "deadly weapon" onto federal property unless one is a law enforcement officer in the performance of his (or her) duties. The federal law states that a "dangerous" or "deadly weapon", per se, does not include a knife with a blade length under two and a half inches. The law is ambiguous with respect to, say, pocket knives with three inch blades. (Per se dangerous or deadly weapons include firearms and switchblades.) If it is not clear that an item is per se dangerous or deadly, a court or prosecutor will look to intent. If one is carrying a pocket knife for benign, non-offensive uses, it is not a dangerous or deadly weapon. If, OTOH, one carries a pocket knife for self defense, it may well be found to be a dangerous or deadly weapon and the carrier may be violating the law.

So, what does the law permit one to carry in DC? Probably a pocket knife with a blade under three inches. The last time I visited the White House (post-9/11) the Secret Service had a sign posted by the East Wing stating that visitors could not bring into the building pocket knives with blades longer than three inches.

Disclaimer: This is not legal advice and I am not acting as anyone's attorney.