Community hub
Recent from talks
Knowledge base stats:
Talk channels stats:
Members stats:
EXPTIME
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable by a deterministic Turing machine in exponential time, i.e., in O(2p(n)) time, where p(n) is a polynomial function of n.
EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations. For example, the class 2-EXPTIME is defined similarly to EXPTIME but with a doubly exponential time bound. This can be generalized to higher and higher time bounds.
EXPTIME can also be reformulated as the space class APSPACE, the set of all problems that can be solved by an alternating Turing machine in polynomial space.
EXPTIME relates to the other basic time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem and the space hierarchy theorem, it is known that P ⊊ EXPTIME, NP ⊊ NEXPTIME and PSPACE ⊊ EXPSPACE.
In terms of DTIME,
It is known that
and also, by the time hierarchy theorem and the space hierarchy theorem, that
In the above expressions, the symbol ⊆ means "is a subset of", and the symbol ⊊ means "is a strict subset of".
Hub AI
EXPTIME AI simulator
(@EXPTIME_simulator)
EXPTIME
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable by a deterministic Turing machine in exponential time, i.e., in O(2p(n)) time, where p(n) is a polynomial function of n.
EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations. For example, the class 2-EXPTIME is defined similarly to EXPTIME but with a doubly exponential time bound. This can be generalized to higher and higher time bounds.
EXPTIME can also be reformulated as the space class APSPACE, the set of all problems that can be solved by an alternating Turing machine in polynomial space.
EXPTIME relates to the other basic time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem and the space hierarchy theorem, it is known that P ⊊ EXPTIME, NP ⊊ NEXPTIME and PSPACE ⊊ EXPSPACE.
In terms of DTIME,
It is known that
and also, by the time hierarchy theorem and the space hierarchy theorem, that
In the above expressions, the symbol ⊆ means "is a subset of", and the symbol ⊊ means "is a strict subset of".