31,852 research outputs found
On the Complexity of Simulating Auxiliary Input
We construct a simulator for the simulating auxiliary input problem with
complexity better than all previous results and prove the optimality up to
logarithmic factors by establishing a black-box lower bound. Specifically, let
be the length of the auxiliary input and be the
indistinguishability parameter. Our simulator is
more complicated than the distinguisher family.
For the lower bound, we show the relative complexity to the distinguisher of a
simulator is at least assuming the simulator is
restricted to use the distinguishers in a black-box way and satisfy a mild
restriction
Computations on Nondeterministic Cellular Automata
The work is concerned with the trade-offs between the dimension and the time
and space complexity of computations on nondeterministic cellular automata. It
is proved, that
1). Every NCA \Cal A of dimension , computing a predicate with time
complexity T(n) and space complexity S(n) can be simulated by -dimensional
NCA with time and space complexity and
by -dimensional NCA with time and space complexity .
2) For any predicate and integer if \Cal A is a fastest
-dimensional NCA computing with time complexity T(n) and space
complexity S(n), then .
3). If is time complexity of a fastest -dimensional NCA
computing predicate then T_{r+1,P} &=O((T_{r,P})^{1-r/(r+1)^2}),
T_{r-1,P} &=O((T_{r,P})^{1+2/r}). Similar problems for deterministic CA are
discussed.Comment: 18 pages in AmsTex, 3 figures in PostScrip
Simulating Auxiliary Inputs, Revisited
For any pair of correlated random variables we can think of as a
randomized function of . Provided that is short, one can make this
function computationally efficient by allowing it to be only approximately
correct. In folklore this problem is known as \emph{simulating auxiliary
inputs}. This idea of simulating auxiliary information turns out to be a
powerful tool in computer science, finding applications in complexity theory,
cryptography, pseudorandomness and zero-knowledge. In this paper we revisit
this problem, achieving the following results:
\begin{enumerate}[(a)] We discuss and compare efficiency of known results,
finding the flaw in the best known bound claimed in the TCC'14 paper "How to
Fake Auxiliary Inputs". We present a novel boosting algorithm for constructing
the simulator. Our technique essentially fixes the flaw. This boosting proof is
of independent interest, as it shows how to handle "negative mass" issues when
constructing probability measures in descent algorithms. Our bounds are much
better than bounds known so far. To make the simulator
-indistinguishable we need the complexity in time/circuit size, which is better by a
factor compared to previous bounds. In particular, with our
technique we (finally) get meaningful provable security for the EUROCRYPT'09
leakage-resilient stream cipher instantiated with a standard 256-bit block
cipher, like .Comment: Some typos present in the previous version have been correcte
A New Approximate Min-Max Theorem with Applications in Cryptography
We propose a novel proof technique that can be applied to attack a broad
class of problems in computational complexity, when switching the order of
universal and existential quantifiers is helpful. Our approach combines the
standard min-max theorem and convex approximation techniques, offering
quantitative improvements over the standard way of using min-max theorems as
well as more concise and elegant proofs
Models to Reduce the Complexity of Simulating a Quantum Computer
Recently Quantum Computation has generated a lot of interest due to the
discovery of a quantum algorithm which can factor large numbers in polynomial
time. The usefulness of a quantum com puter is limited by the effect of errors.
Simulation is a useful tool for determining the feasibility of quantum
computers in the presence of errors. The size of a quantum computer that can be
simulat ed is small because faithfully modeling a quantum computer requires an
exponential amount of storage and number of operations. In this paper we define
simulation models to study the feasibility of quantum computers. The most
detailed of these models is based directly on a proposed imple mentation. We
also define less detailed models which are exponentially less complex but still
pro duce accurate results. Finally we show that the two different types of
errors, decoherence and inaccuracies, are uncorrelated. This decreases the
number of simulations which must be per formed.Comment: 25 page
Reversible Simulation of Irreversible Computation by Pebble Games
Reversible simulation of irreversible algorithms is analyzed in the stylized
form of a `reversible' pebble game. While such simulations incur little
overhead in additional computation time, they use a large amount of additional
memory space during the computation. The reacheable reversible simulation
instantaneous descriptions (pebble configurations) are characterized
completely. As a corollary we obtain the reversible simulation by Bennett and
that among all simulations that can be modelled by the pebble game, Bennett's
simulation is optimal in that it uses the least auxiliary space for the
greatest number of simulated steps. One can reduce the auxiliary storage
overhead incurred by the reversible simulation at the cost of allowing limited
erasing leading to an irreversibility-space tradeoff. We show that in this
resource-bounded setting the limited erasing needs to be performed at precise
instants during the simulation. We show that the reversible simulation can be
modified so that it is applicable also when the simulated computation time is
unknown.Comment: 11 pages, Latex, Submitted to Physica
An in-between "implicit" and "explicit" complexity: Automata
Implicit Computational Complexity makes two aspects implicit, by manipulating
programming languages rather than models of com-putation, and by internalizing
the bounds rather than using external measure. We survey how automata theory
contributed to complexity with a machine-dependant with implicit bounds model
Introduction to Quantum Algorithms for Physics and Chemistry
In this introductory review, we focus on applications of quantum computation
to problems of interest in physics and chemistry. We describe quantum
simulation algorithms that have been developed for electronic-structure
problems, thermal-state preparation, simulation of time dynamics, adiabatic
quantum simulation, and density functional theory.Comment: 44 pages, 5 figures; comments or suggestions for improvement are
welcom
Sublogarithmic uniform Boolean proof nets
Using a proofs-as-programs correspondence, Terui was able to compare two
models of parallel computation: Boolean circuits and proof nets for
multiplicative linear logic. Mogbil et. al. gave a logspace translation
allowing us to compare their computational power as uniform complexity classes.
This paper presents a novel translation in AC0 and focuses on a simpler
restricted notion of uniform Boolean proof nets. We can then encode
constant-depth circuits and compare complexity classes below logspace, which
were out of reach with the previous translations.Comment: In Proceedings DICE 2011, arXiv:1201.034
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