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Fengming Wang - One of the best experts on this subject based on the ideXlab platform.

  • extracting kolmogorov complexity with applications to dimension zero one laws
    Information & Computation, 2011
    Co-Authors: Lance Fortnow, John M Hitchcock, A Pavan, N V Vinodchandran, Fengming Wang
    Abstract:

    We apply results on extracting randomness from independent sources to ''extract'' Kolmogorov complexity. For any @a,@e>0, given a string x with K(x)>@a|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=@W(|x|), with K(y)>(1-@e)|y|. This result holds for both unbounded and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for the strong dimensions of complexity classes within ESPACE. The unbounded extraction procedure yields a zero-one law for the constructive strong dimensions of Turing degrees.

  • extracting kolmogorov complexity with applications to dimension zero one laws
    International Colloquium on Automata Languages and Programming, 2006
    Co-Authors: Lance Fortnow, John M Hitchcock, A Pavan, N V Vinodchandran, Fengming Wang
    Abstract:

    We apply recent results on extracting randomness from independent sources to “extract” Kolmogorov complexity. For any α, e> 0, given a string x with K(x) > α|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=Ω(|x|), with K(y) > (1–e)|y|. This result holds for both classical and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for polynomial-space strong dimension. Our results include: (i) If Dimpspace(E) > 0, then Dimpspace(E/O(1)) = 1. (ii) Dim(E/O(1) |ESPACE) is either 0 or 1. (iii) Dim(E/poly |ESPACE) is either 0 or 1. In other words, from a dimension standpoint and with respect to a small amount of advice, the exponential-time class E is either minimally complex or maximally complex within ESPACE.

Ralf Lehnert - One of the best experts on this subject based on the ideXlab platform.

  • Classical-physics applications for Finsler $b$ space
    Bulletin of the American Physical Society, 2015
    Co-Authors: Joshua Foster, Ralf Lehnert
    Abstract:

    Article history: Received 26 January 2015 Received in revised form 30 March 2015 Accepted 22 April 2015 Available online 24 April 2015 Editor: A. Ringwald The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

  • Classical-physics applications for Finsler $b$ space
    Physics Letters B, 2015
    Co-Authors: Joshua Foster, Ralf Lehnert
    Abstract:

    Abstract The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler b space parametrized by a prescribed background covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler b space and constructs a geodesic for a sample non-constant choice for the background covector. The existence of these classical analogues demonstrates that Finsler b spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.

Lance Fortnow - One of the best experts on this subject based on the ideXlab platform.

  • extracting kolmogorov complexity with applications to dimension zero one laws
    Information & Computation, 2011
    Co-Authors: Lance Fortnow, John M Hitchcock, A Pavan, N V Vinodchandran, Fengming Wang
    Abstract:

    We apply results on extracting randomness from independent sources to ''extract'' Kolmogorov complexity. For any @a,@e>0, given a string x with K(x)>@a|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=@W(|x|), with K(y)>(1-@e)|y|. This result holds for both unbounded and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for the strong dimensions of complexity classes within ESPACE. The unbounded extraction procedure yields a zero-one law for the constructive strong dimensions of Turing degrees.

  • extracting kolmogorov complexity with applications to dimension zero one laws
    International Colloquium on Automata Languages and Programming, 2006
    Co-Authors: Lance Fortnow, John M Hitchcock, A Pavan, N V Vinodchandran, Fengming Wang
    Abstract:

    We apply recent results on extracting randomness from independent sources to “extract” Kolmogorov complexity. For any α, e> 0, given a string x with K(x) > α|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=Ω(|x|), with K(y) > (1–e)|y|. This result holds for both classical and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for polynomial-space strong dimension. Our results include: (i) If Dimpspace(E) > 0, then Dimpspace(E/O(1)) = 1. (ii) Dim(E/O(1) |ESPACE) is either 0 or 1. (iii) Dim(E/poly |ESPACE) is either 0 or 1. In other words, from a dimension standpoint and with respect to a small amount of advice, the exponential-time class E is either minimally complex or maximally complex within ESPACE.

Toniann Pitassi - One of the best experts on this subject based on the ideXlab platform.

  • exponential time space speedups for resolution and the pspace completeness of black white pebbling
    Foundations of Computer Science, 2007
    Co-Authors: P Herte, Toniann Pitassi
    Abstract:

    The complexity of the Black-White Pebbling Game has remained open for 30 years. It was devised to capture the power of non-deterministic space bounded computation. Since then it has been applied to problems in diverse areas of computer science including VLSI design and more recently propositional proof complexity. In this paper we show that the Black-While Pebbling Game is PSPACE-complete. We then use similar ideas in a more complicated reduction to prove the PSPACE-completeness of Resolution space. The reduction also yields a surprising exponential time/space speedup for Resolution in which an increase of 3 units of space results in an exponential decrease in proof-size.

  • an exponential time space speedup for resolution
    Electronic Colloquium on Computational Complexity, 2007
    Co-Authors: Philipp Hertel, Toniann Pitassi
    Abstract:

    Satisfiability algorithms have become one of the most practi cal and successful approaches for solving a variety of real-world problems, including hardware verifi cation, experimental design, planning and diagnosis problems. The main reason for the success is due to highly optimized algorithms for SAT based on resolution. The most successful of these is clause learning, a DPLL scheme based on caching intermediate clauses that are “learned” throughout the backtrack search procedure. The main bottleneck to this approach is space, and thus there has been a tremendous amount of research aimed at identifying good heuristics for deciding what information to cache. Haken first suggested a formal approach to this issue, and Ben-Sasson [3] posed the question of whether there is a time/space tradeoff for resolution. Our main result is an optimal time/space tradeoff for resolution. Namely, we present an infinite family of propositional formulas whose minimal space proofs all have exponential time, but if just three extra units of storage are allowed, then the formulas can be proved in linear time. We also prove another related theorem. Given an unsatisfiabl e formula F and an integer k, the resolution space problem is to determine if F has a resolution proof which can be verified using space k. We prove that this problem is PSPACE complete.

N V Vinodchandran - One of the best experts on this subject based on the ideXlab platform.

  • extracting kolmogorov complexity with applications to dimension zero one laws
    Information & Computation, 2011
    Co-Authors: Lance Fortnow, John M Hitchcock, A Pavan, N V Vinodchandran, Fengming Wang
    Abstract:

    We apply results on extracting randomness from independent sources to ''extract'' Kolmogorov complexity. For any @a,@e>0, given a string x with K(x)>@a|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=@W(|x|), with K(y)>(1-@e)|y|. This result holds for both unbounded and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for the strong dimensions of complexity classes within ESPACE. The unbounded extraction procedure yields a zero-one law for the constructive strong dimensions of Turing degrees.

  • extracting kolmogorov complexity with applications to dimension zero one laws
    International Colloquium on Automata Languages and Programming, 2006
    Co-Authors: Lance Fortnow, John M Hitchcock, A Pavan, N V Vinodchandran, Fengming Wang
    Abstract:

    We apply recent results on extracting randomness from independent sources to “extract” Kolmogorov complexity. For any α, e> 0, given a string x with K(x) > α|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=Ω(|x|), with K(y) > (1–e)|y|. This result holds for both classical and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for polynomial-space strong dimension. Our results include: (i) If Dimpspace(E) > 0, then Dimpspace(E/O(1)) = 1. (ii) Dim(E/O(1) |ESPACE) is either 0 or 1. (iii) Dim(E/poly |ESPACE) is either 0 or 1. In other words, from a dimension standpoint and with respect to a small amount of advice, the exponential-time class E is either minimally complex or maximally complex within ESPACE.