EXPTIME

In computational complexity theory, the complexity class EXPTIME (sometimes called EXP) is the set of all decision problems solvable by a deterministic Turing machine in O(2p(n)) time, where p(n) is a polynomial function of n.

In terms of DTIME,

\mbox{EXPTIME} = \bigcup_{k\in\mathbb{N}} \mbox{DTIME}\left(2^{n^k}\right).

We know

P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ EXPSPACE

and also

P ⊂ EXPTIME

(by the time hierarchy theorem), so at least one of the inclusions on the first line must be proper (most experts believe all the inclusions are proper).

The complexity class EXPTIME-complete is also a set of decision problems. A decision problem is in EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. In other words, there is a polynomial-time algorithm that transforms instances of one to instances of the other with the same answer. EXPTIME-complete might be thought of as the hardest problems in EXPTIME.

Examples of EXPTIME-complete problems include the problem of looking at a generalized Chess, Checkers, or Go position, and determining whether the first player can force a win. These games are EXPTIME-complete because games can last for a number of moves that is exponential in the size of the board. (By contrast, generalized games that can last for a number of moves that is polynomial in the size of the board are often PSPACE-complete.)


Important complexity classes
P | NP | Co-NP | NP-C | Co-NP-C | NP-hard | UP | #P | #P-C | NC | P-C
PSPACE | PSPACE-C | EXPTIME | EXPSPACE | BQP | BPP | RP | ZPP | PCP | IP | PH


es:EXPTIME

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