Bounded query machines: On NP and PSPACE
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It is shown that NP is equal to PSPACE if and only if for every oracle set A, NP( A ) isequal to the class NPQUERY ( A ) of languages accepted by nondeterministic polynomial space-bounded oracle machines that are allowed to query the oracle for A only aPolynomial number of times.About:
This article is published in Theoretical Computer Science.The article was published on 1981-01-01 and is currently open access. It has received 35 citations till now. The article focuses on the topics: Low & NP-easy.read more
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Book
Structural Complexity II
TL;DR: This is the second volume of a systematic two-volume presentation of the various areas of research in the field of structural complexity, addressed to graduate students and researchers and assumes knowledge of the topics treated in the first volume but is otherwise nearly self-contained.
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The strong exponential hierarchy collapses
TL;DR: It is shown that the strong exponential hierarchy collapses to P NE, its Δ 2 level, using the use of partial census information and the exploitation of nondeterminism.
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Quantitative relativizations of complexity classes
TL;DR: This paper studies restrictions R on both the deterministic and also the nondeterministic polynomial time-bounded oracle machines such that the size of the set of strings queried by the oracle in computations of a machine on an input is bounded by aPolynomial in the length of the input.
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Query complexity, or why is it difficult to separateNP A ∩coNP A fromP A by random oraclesA?
TL;DR: It is conjecture that the analogues of these classes actually coincide in the query complexity model, thus indicating an answer to the question in the title, and proves the following result, where polynomial bounds refer to query complexity.
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Relativizing complexity classes with sparse oracles
Timothy J. Long,Alan L. Selman +1 more
TL;DR: It is shown that the polynomial hierarchy collapses if and only if there is a sparse set S , and similar results are obtained for several other complexity classes.
References
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Relationships between nondeterministic and deterministic tape complexities
TL;DR: The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.
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Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question
TL;DR: Relativized versions of the open question of whether every language accepted nondeterministically in polynomial time can be recognized deterministic in poynomial time are investigated.
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Separating Nondeterministic Time Complexity Classes
TL;DR: The strongest known dmgonalization results for both deterministic and nondetermlmstlc time complexity classes are reviewed and orgamzed for comparison with the results of the new padding technique.
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A hierarchy for nondeterministic time complexity
TL;DR: This paper proves the following theorem: For any real numbers r"1, r"2, [email protected]?r"1 , where r is the number of real numbers and 𝕂 is the inequality between real numbers.
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A hierarchy for nondeterministic time complexity
TL;DR: For any real numbers r1, r2, 1 ≤ r1 < r2 , there is a set A of strings which has nondeterministic time complexity nr2 but not nondeterdependencies nr1, and the computing devices are non-deterministic multitape Turing machines.