4,694 research outputs found
Simulating counting oracles with cooperation
We prove that monodirectional shallow chargeless P systems with active
membranes and minimal cooperation working in polynomial time precisely characterise
P#P
k , the complexity class of problems solved in polynomial time by deterministic
Turing machines with a polynomial number of parallel queries to an oracle for a counting
problem
Gate-Level Simulation of Quantum Circuits
While thousands of experimental physicists and chemists are currently trying
to build scalable quantum computers, it appears that simulation of quantum
computation will be at least as critical as circuit simulation in classical
VLSI design. However, since the work of Richard Feynman in the early 1980s
little progress was made in practical quantum simulation. Most researchers
focused on polynomial-time simulation of restricted types of quantum circuits
that fall short of the full power of quantum computation. Simulating quantum
computing devices and useful quantum algorithms on classical hardware now
requires excessive computational resources, making many important simulation
tasks infeasible. In this work we propose a new technique for gate-level
simulation of quantum circuits which greatly reduces the difficulty and cost of
such simulations. The proposed technique is implemented in a simulation tool
called the Quantum Information Decision Diagram (QuIDD) and evaluated by
simulating Grover's quantum search algorithm. The back-end of our package,
QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability
to efficiently represent many seemingly intractable combinatorial structures.
This reliance on a well-established area of research allows us to take
advantage of existing software for BDD manipulation and achieve unparalleled
empirical results for quantum simulation
On the complexity of solving linear congruences and computing nullspaces modulo a constant
We consider the problems of determining the feasibility of a linear
congruence, producing a solution to a linear congruence, and finding a spanning
set for the nullspace of an integer matrix, where each problem is considered
modulo an arbitrary constant k>1. These problems are known to be complete for
the logspace modular counting classes {Mod_k L} = {coMod_k L} in special case
that k is prime (Buntrock et al, 1992). By considering variants of standard
logspace function classes --- related to #L and functions computable by UL
machines, but which only characterize the number of accepting paths modulo k
--- we show that these problems of linear algebra are also complete for
{coMod_k L} for any constant k>1.
Our results are obtained by defining a class of functions FUL_k which are low
for {Mod_k L} and {coMod_k L} for k>1, using ideas similar to those used in the
case of k prime in (Buntrock et al, 1992) to show closure of Mod_k L under NC^1
reductions (including {Mod_k L} oracle reductions). In addition to the results
above, we briefly consider the relationship of the class FUL_k for arbitrary
moduli k to the class {F.coMod_k L} of functions whose output symbols are
verifiable by {coMod_k L} algorithms; and consider what consequences such a
comparison may have for oracle closure results of the form {Mod_k L}^{Mod_k L}
= {Mod_k L} for composite k.Comment: 17 pages, one Appendix; minor corrections and revisions to
presentation, new observations regarding the prospect of oracle closures.
Comments welcom
On the possible Computational Power of the Human Mind
The aim of this paper is to address the question: Can an artificial neural
network (ANN) model be used as a possible characterization of the power of the
human mind? We will discuss what might be the relationship between such a model
and its natural counterpart. A possible characterization of the different power
capabilities of the mind is suggested in terms of the information contained (in
its computational complexity) or achievable by it. Such characterization takes
advantage of recent results based on natural neural networks (NNN) and the
computational power of arbitrary artificial neural networks (ANN). The possible
acceptance of neural networks as the model of the human mind's operation makes
the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of
Liverpool, UK. 23 page
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Elimination of Spurious Ambiguity in Transition-Based Dependency Parsing
We present a novel technique to remove spurious ambiguity from transition
systems for dependency parsing. Our technique chooses a canonical sequence of
transition operations (computation) for a given dependency tree. Our technique
can be applied to a large class of bottom-up transition systems, including for
instance Nivre (2004) and Attardi (2006)
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