A Survey of Space Complexity

@article{Michel1992ASO,
  title={A Survey of Space Complexity},
  author={Pascal Michel},
  journal={Theor. Comput. Sci.},
  year={1992},
  volume={101},
  pages={99-132}
}
  • Pascal Michel
  • Published 13 July 1992
  • Mathematics
  • Theor. Comput. Sci.
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20 Citations
Highly Influential Citations
1
Background Citations
7

20 Citations

Citation Type

Citation Type

Separating the Lower Levels of the Sublogarithmic Space Hierarchy
TLDR
It is shown that for each S between loglogn and logn, Σ2SPACE(S) and Σ3SPACE (S) are not closed under complement, which implies the hierarchy Σ1SPACE(-1,2,3) ⊂Σ2 SPACE(-3,4) and the power of weak and strong sublogarithmic space bounded ATMs is compared.
The Sublogarithmic Alternating Space World
This paper tries to fully characterize the properties and relationships of space classes defined by Turing machines that use less than logarithmic space -- may they be deterministic, nondeterministic…
SIGACT News Complexity Theory Column 10
TLDR
This work presents recent advances on space-efficient deterministic simulation of probabilistic automata in both finite-state automata and logarithmic-space-bounded Turing machines.
The Separation of NP and PSPACE
TLDR
This paper shows that NP 6= PSPACE via the premise of NTIME[S(n)] ⊆ DSPACE[S (n)], and then by diagonalization over all polynomial-time nondeterministic Turing machines via universal nondetergetic Turing machine M0 running in O(n ) space for any k ∈ N1.
Some Accepting Powers of Three-Dimensional Synchronized Alternating Turing Machines
  • Ito
  • Business
  • 2007
This paper introduces a three-dimensional synchronized alternating Turing machine (3-SATM), and investigates fundamental properties of 3-SATM ′s whose input tapes are restricted to cubic ones. The…
Some Accepting Powers of Three-Dimensional Synchronized Alternating Turing Machines
This paper introduces a three-dimensional synchronized alternating Turing machine (3-SATM), and investigates fundamental properties of 3-SATM 0 s whose input tapes are restricted to cubic ones. The…
Guest Column: One-Tape Turing Machine Variants and Language Recognition
TLDR
Two restricted versions of one-tape Turing machines are presented and for d = 2 deterministic limited automata are equivalent to deterministic pushdown automata, namely they characterize deterministic context-free languages.
Restricted Turing Machines and Language Recognition
TLDR
In 1965 Hennie proved that one-tape deterministic Turing machines working in linear time are equivalent to finite automata, namely they characterize regular languages, and in 1967 Hibbard proved that for each integer \(d\ge 2\), one-Tape Turing machines that are allowed to rewrite each tape cell only in the first d visits are equivalents to pushdown automata.
Nondeterministic One-Tape Off-Line Turing Machines and Their Time Complexity
TLDR
This paper shows that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n log n, and proves that under this measure, each accepting computation should exhibit a crossing sequence of length at least log log n.
Resolution of The Linear-Bounded Automata Question
This work resolve a longstanding open question in automata theory, i.e. the linear-bounded automata question ( shortly, LBA question), which can also be phrased succinctly in the language of…
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References

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On Non- uniform Polynomial Space
TLDR
Some properties of a dual class defined by exponential lower bounds are shown, as a version of Lupanov theorem and a characterization in terms of oracle Turing machines.
Limitations on Separating Nondeterministic Complexity Classes
TLDR
If the time bounds defining two nondeterministic complexity classes are too close for separation by the two known techniques, then they are almost too close to separation by any relativizable technique, implying $\operatorname{NSPACE}(\log n) = \operatORName{DSPACE})$.
Relating Refined Space Complexity Classes
Space Bounded Computations: Review and New Separation Results
Languages that Capture Complexity Classes
  • N. Immerman
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1987
TLDR
It is shown that projection translations are a uniform version of Valiant’s projections, and that the usual complete problems remain complete via these very restrictive reductions.
Uniform Characterizations of Non-Uniform Complexity Measures
Some connections between nonuniform and uniform complexity classes
TLDR
This work aims to understand when nonuniform upper bounds can be used to obtain uniform upper bounds, and how to relate it to more common notions.
On some "non-uniform" complexity measures
TLDR
The initial index of languages is introduced by means of several computational models and is shown to be closely related to context-free cost, boolean circuits, straight line programs, and Turing machines with sparse oracles and time or space bounds.
Some Results on Tape-Bounded Turing Machines
TLDR
It is shown that the lower bounds on tape complexity of [1] depend on neither the halting assumption nor determinism, and that below log n tape complexity there exists a dense hierarchy of complexity classes for two-way nondeterministic devices.
Space-Bounded Hierarchies and Probabilistic Computations
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