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Searching for authors named "Christopher Umans" – sorted by Relevance.

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  • Hardness of Approximating Sigma_2^p Minimization Problems  
  • by Christopher Umans — 1999 — in Proc. 40th IEEE Symp. on Foundations of Computer Science
  • …We show that a number of natural optimization problems in the second level of the Polynomial Hierarchy are \Sigma p 2 -hard to approximate to within n ffl factors, for specific ffl ? 0. The main technical tool is the use of explicit dispersers to achieve strong, direct inapproximability results.…
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  • On the Complexity and Inapproximability of Shortest Implicant Problems  
  • by Christopher Umans — 1999 — In Automata, Languages and Programming, 26th International Colloquium (ICALP 99
  • …. We investigate the complexity and approximability of a basic optimization problem in the second level of the Polynomial Hierarchy, that of finding shortest implicants. We show that the DNF variant of this problem is complete for a complexity class in the second level of the hierarchy utilizing…
  • Cited by 5 (2 self) – Add To MetaCart
  • Reconstructive dispersers and hitting set generators  
  • by Christopher Umans — 2005 — In APPROXRANDOM
  • …Abstract. We give a generic construction of an optimal hitting set generator (HSG) from any good “reconstructive ” disperser. Past constructions of optimal HSGs have been based on such disperser constructions, but have had to modify the construction in a complicated way to meet the stringent efficie…
  • Cited by 4 (2 self) – Add To MetaCart
  • Pseudo-random generators for all hardness  
  • by Christopher Umans — 2003 — Journal of Computer and System Science
  • …A pseudo-random generator (PRG) is a function that “stretches ” a short random seed into a longer pseudo-random output string that “fools ” small circuits: Definition 1 (ɛ-PRG) An ɛ-PRG for size s is a function G: {0, 1} t →{0, 1} m such that for all circuits C of size at most s: | Pr[C(G(z))=1]−Pr[…
  • Cited by 40 (8 self) – Add To MetaCart
  • The Minimum Equivalent DNF Problem and Shortest Implicants  
  • by Christopher Umans — 1998
  • …We prove that the Minimum Equivalent DNF problem is \Sigma p 2 -complete, resolving a conjecture due to Stockmeyer. The proof involves as an intermediate step a variant of a related problem in logic minimization, namely, that of finding the shortest implicant of a Boolean function. We also obtain …
  • Cited by 27 (2 self) – Add To MetaCart
  • Abstract  
  • by David Buchfuhrer, Christopher Umans — 2008
  • …The Minimum Equivalent Expression problem is a natural optimization problem in the second level of the Polynomial-Time Hierarchy. It has long been conjectured to be Σ P 2-complete and indeed appears as an open problem in Garey and Johnson [GJ79]. The depth-2 variant was only shown to be Σ P 2-comple…
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  • An Algorithm for Finding Hamiltonian Cycles in Grid Graphs Without Holes  
  • by Christopher M. Umans — 1996
  • …The Hamiltonian cycle problem for general grid graphs is NP-complete. However, it is conjectured that an efficient algorithm to solve the Hamiltonian cycle problem exists for a subclass of general grid graphs known as grid graphs without holes. This thesis contains a number of results concerning the…
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  • Pseudorandomness for approximate counting and sampling  
  • by Ronen Shaltiel, Christopher Umans — 2005 — In Proceedings of the 20th IEEE Conference on Computational Complexity
  • …We study computational procedures that use both randomness and nondeterminism. Examples are Arthur-Merlin games and approximate counting and sampling of NPwitnesses. The goal of this paper is to derandomize such procedures under the weakest possible assumptions. Our main technical contribution allow…
  • Cited by 15 (1 self) – Add To MetaCart
  • Unbalanced expanders and randomness extractors from parvaresh-vardy codes  
  • by Venkatesan Guruswami, Christopher Umans — 2007 — In Proceedings of the 22nd Annual IEEE Conference on Computational Complexity
  • …We give an improved explicit construction of highly unbalanced bipartite expander graphs with expansion arbitrarily close to the degree (which is polylogarithmic in the number of vertices). Both the degree and the number of right-hand vertices are polynomially close to optimal, whereas the previous …
  • Cited by 14 (3 self) – Add To MetaCart
  • Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator  
  • by Ronen Shaltiel, Christopher Umans — 2001 — Journal of the ACM
  • …A “randomness extractor ” is an algorithm that given a sample from a distribution with sufficiently high min-entropy and a short random seed produces an output that is statistically indistinguishable from uniform. (Min-entropy is a measure of the amount of randomness in a distribution). We present a…
  • Cited by 76 (18 self) – Add To MetaCart
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