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Does the Polynomial Hierarchy Collapse if Onto Functions are Invertible?
"... Abstract. The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomialtime does this imply the polynomi ..."
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the polynomialtime hierarchy collapses? By computing a multivalued function in deterministic polynomialtime we mean on every input producing one of the possible values of the function on that input. We give a relativized negative answer to this question by exhibiting an oracle under which TFNP functions
Inverting Onto Functions and Polynomial Hierarchy
"... Abstract. The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomialtime does this imply the polynomi ..."
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Cited by 2 (0 self)
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the polynomialtime hierarchy collapses? By computing a multivalued function in deterministic polynomialtime we mean on every input producing one of the possible values of that function on that input. We give a relativized negative answer to this question by exhibiting an oracle under which TFNP functions
The Collapse of the Polynomial Hierarchy: NP = P (A Summary)
, 2009
"... We present a novel extension to the permutation group enumeration technique which is well known to have polynomial time algorithms. This extended technique allows each perfect matching in a bipartite graph on 2n nodes to be expressed as a unique directed path in a directed acyclic graph on O(n 3) no ..."
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. And thus we prove a result even more surprising than NP = P, that is, #P = FP, where FP is the class of functions, f: {0, 1} ∗ → N, computable in polynomial time on a deterministic model of computation. It is well established that NP ⊆ P #P, and hence the Polynomial Time Hierarchy collapses to P. 1
Inverting Onto Functions Might Not Be Hard
, 2006
"... The class TFNP, dened by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially veriable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomialtime does this imply the polynomialtime hierar ..."
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time hierarchy collapses? We give a relativized negative answer to this question by exhibiting an oracle under which TFNP functions are easy to compute but the polynomialtime hierarchy is innite. To create the oracle, we introduce Kolmogorovgeneric oracles where the strings placed in the oracle are derived
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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is to make each image value selectively reflect signal from the voxel it represents. [9] The term in brackets describes the spatial weighting of signal in . It is therefore called the corresponding voxel function: F ,(␥,) e ␥, (r). [10] Hence, the matrix F has to be chosen such that the resulting voxel
Every PolynomialTime 1Degree Collapses if and only if P = PSPACE
"... A set A is mreducible (or Karpreducible) to B if and only if there is a polynomialtime computable function f such that, for all x, x # A if and only if f(x) # B. Two sets are: . 1equivalent if and only if each is mreducible to the other by oneone reductions; . pinvertible equivalent ..."
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A set A is mreducible (or Karpreducible) to B if and only if there is a polynomialtime computable function f such that, for all x, x # A if and only if f(x) # B. Two sets are: . 1equivalent if and only if each is mreducible to the other by oneone reductions; . pinvertible equivalent
Every PolynomialTime 1Degree Collapses iff P = PSPACE
, 1996
"... A set A is mreducible (or Karpreducible) to B iff there is a polynomialtime computable function f such that, for all x, x 2 A () f(x) 2 B. Two sets are: ffl 1equivalent iff each is mreducible to the other by oneone reductions; ffl pinvertible equivalent iff each is mreducible to the othe ..."
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Cited by 5 (2 self)
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A set A is mreducible (or Karpreducible) to B iff there is a polynomialtime computable function f such that, for all x, x 2 A () f(x) 2 B. Two sets are: ffl 1equivalent iff each is mreducible to the other by oneone reductions; ffl pinvertible equivalent iff each is m
Collapsing threemanifolds under a lower curvature bound
 J. Differential Geom
"... Abstract The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension. Introduction We study the topology of threedimensional Riemannian manifolds ..."
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Cited by 30 (3 self)
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space (Y, y 0 ). As a crucial lemma (Key Lemma 3.6), we prove that dim Y = dim X+1 = 3. Since the convergence ( 0 ) does not collapse, a discussion using Perelman's Stability Theorem (Theorem 2.4) shows that int B i Y . The next step is to establish the Generalized Soul Theorem for threedimensional
Infeasibility of instance compression and succinct PCPs for NP
 Electronic Colloquium on Computational Complexity (ECCC
"... The ORSAT problem asks, given Boolean formulae φ1,..., φm each of size at most n, whether at least one of the φi’s is satisfiable. We show that there is no reduction from ORSAT to any set A where the length of the output is bounded by a polynomial in n, unless NP ⊆ coNP/poly, and the PolynomialTi ..."
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Cited by 70 (1 self)
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Time Hierarchy collapses. This result settles an open problem proposed by Bodlaender et. al. [4] and Harnik and Naor [15] and has a number of implications. • A number of parametric NP problems, including Satisfiability, Clique, Dominating Set and Integer Programming, are not instance compressible or polynomially
Results 1  10
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147