theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally, these theorems say that given...

analogous theorems for time are the time hierarchy theorems. The foundation for the hierarchy theorems lies in the intuition that with either more time or more...

time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem and...

conjecture that the polynomial time hierarchy of complexity classes is infinite. The compression theorem is an important theorem about the complexity of computable...

the time hierarchy theorem. They are important because the time hierarchy theorem relies on Turing machines that must determine in O(f(n)) time whether...

classes can be defined similarly. Because of the time hierarchy theorem, these classes form a strict hierarchy; we know that P ⊊ E X P T I M E {\displaystyle...

Open mapping theorem (functional analysis) Product topology Riemann integral Time hierarchy theorem Deterministic time hierarchy theorem Furstenberg's...

proven that these problems cannot be verified in polynomial time, by the time hierarchy theorem. An important set of NEXPTIME-complete problems relates to...

The time and space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem tells...

and cannot compute languages beyond this complexity class. The time hierarchy theorem implies that E L E M E N T A R Y {\displaystyle {\mathsf {ELEMENTARY}}}...

computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize...

The non-deterministic time hierarchy theorem says that nondeterministic machines can solve more problems in asymptotically more time. NTIME is also related...

the Gap Theorem does not imply anything interesting for complexity classes such as P or NP, and it does not contradict the time hierarchy theorem or space...

theorem is a result in computational complexity theory that was proven by Seinosuke Toda in his paper "PP is as Hard as the Polynomial-Time Hierarchy"...

The time and space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem establishes...

more than polynomial time. In fact, by the time hierarchy theorem, they cannot be solved in significantly less than exponential time. Examples include finding...

The only known strict inclusions come from the time hierarchy theorem and the space hierarchy theorem, and respectively they are N P ⊊ N E X P T I M E...

Polynomial-time Turing reduction Savitch's theorem Space hierarchy theorem Speed Prior Speedup theorem Subquadratic time Time hierarchy theorem See the list...

science) Time hierarchy theorem (computational complexity theory) Toda's theorem (computational complexity theory) Universal approximation theorem (artificial...

Cook's theorem List of complexity classes Polynomial hierarchy Exponential hierarchy NP-complete Time hierarchy theorem Space hierarchy theorem Natural...

and lower-order terms. It ignores the size of the exponent. The time hierarchy theorem proves the existence of problems in P requiring arbitrarily large...

problems nondeterministically in a smaller amount of time, violating the time hierarchy theorem. Therefore, the existence of algorithm A {\displaystyle...

2307/1994208, JSTOR 1994208, MR 0170805. Contains the time hierarchy theorem, one of the theorems that shaped the field of computational complexity theory...

theorem. Williams (2011) proves that ACC0 does not contain NEXPTIME. The proof uses many results in complexity theory, including the time hierarchy theorem...

ZPP = EXPTIME. A proof for ZPP = EXPTIME would imply that P ≠ ZPP, as P ≠ EXPTIME (see time hierarchy theorem). BPP RP Complexity Zoo: ZPP Class ZPP...

theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. The statement of Post's theorem uses...

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej...

according to the time required to solve them. They went on to prove a number of fundamental results such as the Time hierarchy theorem. In his own Turing...

model of arithmetic Fast-growing hierarchy Paris–Harrington theorem Kanamori–McAloon theorem Kruskal's tree theorem Kirby & Paris 1982. Rathjen 2014,...

version of Karp–Lipton theorem states that if every language in NP has polynomial size circuits then the polynomial time hierarchy collapses to SP 2. This...