1,363 research outputs found
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
Computing with and without arbitrary large numbers
In the study of random access machines (RAMs) it has been shown that the
availability of an extra input integer, having no special properties other than
being sufficiently large, is enough to reduce the computational complexity of
some problems. However, this has only been shown so far for specific problems.
We provide a characterization of the power of such extra inputs for general
problems. To do so, we first correct a classical result by Simon and Szegedy
(1992) as well as one by Simon (1981). In the former we show mistakes in the
proof and correct these by an entirely new construction, with no great change
to the results. In the latter, the original proof direction stands with only
minor modifications, but the new results are far stronger than those of Simon
(1981). In both cases, the new constructions provide the theoretical tools
required to characterize the power of arbitrary large numbers.Comment: 12 pages (main text) + 30 pages (appendices), 1 figure. Extended
abstract. The full paper was presented at TAMC 2013. (Reference given is for
the paper version, as it appears in the proceedings.
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
Probabilistic Simulations
The results of this paper concern the question of how fast machines with one type of storage media can simulate machines with a different type of storage media. Most work on this question has focused on the question of how fast one deterministic machine can simulate another. In this paper we shall look at the question of how fast a probabilistic machine can simulate another. This approach should be of interest in its own right, in view of the great attention that probabilistic algorithms have recently attracted
A Quantum Time-Space Lower Bound for the Counting Hierarchy
We obtain the first nontrivial time-space lower bound for quantum algorithms
solving problems related to satisfiability. Our bound applies to MajSAT and
MajMajSAT, which are complete problems for the first and second levels of the
counting hierarchy, respectively. We prove that for every real d and every
positive real epsilon there exists a real c>1 such that either: MajMajSAT does
not have a quantum algorithm with bounded two-sided error that runs in time
n^c, or MajSAT does not have a quantum algorithm with bounded two-sided error
that runs in time n^d and space n^{1-\epsilon}. In particular, MajMajSAT cannot
be solved by a quantum algorithm with bounded two-sided error running in time
n^{1+o(1)} and space n^{1-\epsilon} for any epsilon>0. The key technical
novelty is a time- and space-efficient simulation of quantum computations with
intermediate measurements by probabilistic machines with unbounded error. We
also develop a model that is particularly suitable for the study of general
quantum computations with simultaneous time and space bounds. However, our
arguments hold for any reasonable uniform model of quantum computation.Comment: 25 page
Computability and Complexity from a Programming Perspective (MFPS Draft preview)
AbstractThe author's forthcoming book proves central results in computability and complexity theory from a programmer-oriented perspective. In addition to giving more natural definitions, proofs and perspectives on classical theorems by Cook, Hartmanis, Savitch, etc., some new results have come from the alternative approach.One: for a computation model more natural than the Turing machine, multiplying the available problem-solving time provably increases problem-solving power (in general not true for Turing machines). Another: the class of decision problems solvable by Wadler's “treeless” programs [8], or by cons-free programs on Lisp-like lists, are identical with the well-studied complexity class LOGSPACE.A third is that cons-free programs augmented with recursion can solve all and only PTIME problems. Paradoxically, these programs often run in exponential time (not a contradiction, since they can be simulated in polynomial time by memoization.) This tradeoff indicates a tension between running time and memory space which seems worth further investigation
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