Promise problem

In computational complexity theory, a promise problem is a generalization of a decision problem where the input is promised to belong to a subset of all possible inputs. Unlike decision problems, the yes instances (the inputs for which an algorithm must return yes) and no instances do not exhaust the set of all inputs. Intuitively, the algorithm has been promised that the input does indeed belong to set of yes instances or no instances. There may be inputs which are neither yes or no. If such an input is given to an algorithm for solving a promise problem, the algorithm is allowed to output anything, and may even not halt.

Formal definition

A decision problem can be associated with a language , where the problem is to accept all inputs in and reject all inputs not in . For a promise problem, there are two languages, and , which must be disjoint, which means , such that all the inputs in are to be accepted and all inputs in are to be rejected. The set is called the promise. There are no requirements on the output if the input does not belong to the promise. If the promise equals , then this is also a decision problem, and the promise is said to be trivial.

My Last

"My Last" is the first single by American rapper Big Sean from his debut album Finally Famous. The song features R&B singer Chris Brown. The song is produced by No I.D..

Background

Originally, Sean performed both the verses and the chorus but after Brown turned up at one of Sean's shows, the pair connected and Brown suggested the two work together on a song which resulted in Brown singing the chorus. Brown has also done a freestyle over the track. The extended version of the track features Chris Brown's freestyle verse leading the song to 5min19seconds.

Production

The songs instrumental was described by Rap-Up as a "bouncy piano-laced beat". DJBooth.net described the beat as "soft keyboard chords that transition well into the hook where a low bass and snare set the pace for Sean's first verse." Sean revealed he originally rejected the beat but gave it a chance after pressurings by the song's producer No I.D.. The song's melody is sampled from the 1988 New Edition hit "Can You Stand the Rain".