Space hierarchy theorem information

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

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

\log(n)} is a space-constructible function. Time-constructible functions are used in results from complexity theory such as the time hierarchy theorem. They are...

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

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

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

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

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

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...

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

metric spaces) Baker's theorem (number theory) Balian–Low theorem (Fourier analysis) Balinski's theorem (combinatorics) Banach–Alaoglu theorem (functional...

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

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...

Together with the speedup theorem, the gap theorem and the time and space hierarchy theorems it is a basis for hirarchies in complexity theory. McCreight, E...

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

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

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...

space usage and proved the first space hierarchy theorem. In the same year they also proved that every context-free language has deterministic space complexity...

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...

separable metric space. Then X as a Borel space is isomorphic to one of R, Z, a finite space. (This result is reminiscent of Maharam's theorem.) Considered...

to show that Borel sets in Polish spaces have regularity properties such as the perfect set property. The theorem is also known for its metamathematical...