A note on sparse oracles for NP
TLDR
A single construction yields Mahaney's result for sparse ⩽TP-complete sets for NP and also the corresponding result for co-sparse⩽ TP-complete set for NP, which strengthen the earlier work of Karp, Lipton, and Sipser.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1982-04-01 and is currently open access. It has received 30 citations till now. The article focuses on the topics: Sparse language & Hierarchy (mathematics).read more
Citations
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Book
Complexity theory of real functions
TL;DR: " polynomial complexity theory extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems.
Journal ArticleDOI
ERRATUM: the polynomial time hierarchy collapses if the boolean hierarchy collapses
TL;DR: It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that ${\text{co-NP}} \subseteq {\text{ NP}}^S $, and therefore the polynomial time hierarchy (PH) col...
Proceedings Article
P NP [log n] and sparse turing complete sets for NP.
TL;DR: In this article, it was shown that if there exists a sparse set S ϵ NP such that co-NP ( NPs) is contained in PNP[O(log n), then the polynomial hierarchy (PH) of PNP(n) = DP.
Journal ArticleDOI
The polynomial-time hierarchy and sparse oracles
TL;DR: It is proved that the polynomial-time hierarchy collapses if and only if for every sparse set S, the hierarchy relative to S collapses and the question is answered if it is answered for any arbitrary sparse oracle set.
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On relativized exponential and probabilistic complexity classes
TL;DR: An oracle X is constructed such that the exponential complexity class Δ EP, X 2 equals the probabilistic class R(R( X )), which shows that it will be difficult to prove that Δ EP 2 is different from R( R), although it seems very unlikely that these two classes are equal.
References
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Book ChapterDOI
Reducibility Among Combinatorial Problems
TL;DR: The work of Dantzig, Fulkerson, Hoffman, Edmonds, Lawler and other pioneers on network flows, matching and matroids acquainted me with the elegant and efficient algorithms that were sometimes possible.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
The polynomial-time hierarchy☆
TL;DR: The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.
Proceedings ArticleDOI
The equivalence problem for regular expressions with squaring requires exponential space
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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.