In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines...

space requirements, the answer to such questions is given by the time and space hierarchy theorems respectively. They are called hierarchy theorems because...

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

assumed. □ The above theorem implies the necessity of the space-constructible function assumption in the space hierarchy theorem. L = DSPACE(O(log n))...

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, NL ⊂ NPSPACE) and the fact that PSPACE = NPSPACE via Savitch's theorem. The second follows simply from the space hierarchy theorem...

Space-constructible functions are used similarly, for example in the space hierarchy theorem. This article incorporates material from constructible on PlanetMath...

_{c\in \mathbb {Z} ^{+}}{\mathsf {NSPACE}}(n^{c})} The space hierarchy theorem states that, for all space-constructible functions f ( n ) , {\displaystyle f(n)...

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

problem under logarithmic space many-one reductions but polyL does not due to the space hierarchy theorem. The space hierarchy theorem guarantees that DSPACE(logd...

science) Space hierarchy theorem (computational complexity theory) Speedup theorem (computational complexity theory) Structured program theorem (computer...

theorem states that there exists no largest complexity class, with computable boundary, which contains all computable functions. The space hierarchy theorems...

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

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

a small amount of space is strictly contained in PSPACE by the space hierarchy theorem. The transformations that are usually considered in defining PSPACE-completeness...

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 {\displaystyle...

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 hierarchy...

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

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

standard. In some contexts, such as the proof of the time and space hierarchy theorems, it is more useful to assume that the abstract machine defining...

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

Stearns also defined complexity classes based on space usage. They proveded the first space hierarchy theorem. In the same year they also proved that every...

research on counter machines, showing that they obeyed time hierarchy and space hierarchy theorems analogous to those for Turing machines. Fischer was an early...

and space O ( log ⁡ n ) {\displaystyle O(\log n)} .: 139  Unsolved problem in computer science Is the N C {\displaystyle {\mathsf {NC}}} hierarchy proper...

speedup theorem, the gap theorem and the time and space hierarchy theorems it is a basis for hierarchies in complexity theory. McCreight, E. M.; Meyer, A...

mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra...

finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages...

Thoroughbred racehorse Littlewood subordination theorem Subordinate partition of unity in paracompact space This disambiguation page lists articles associated...

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

are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast...