56,554 research outputs found
On the time complexity of 2-tag systems and small universal Turing machines
We show that 2-tag systems efficiently simulate Turing machines. As a
corollary we find that the small universal Turing machines of Rogozhin, Minsky
and others simulate Turing machines in polynomial time. This is an exponential
improvement on the previously known simulation time overhead and improves a
forty year old result in the area of small universal Turing machines.Comment: Slightly expanded and updated from conference versio
Quick and energy-efficient Bayesian computing of binocular disparity using stochastic digital signals
Reconstruction of the tridimensional geometry of a visual scene using the
binocular disparity information is an important issue in computer vision and
mobile robotics, which can be formulated as a Bayesian inference problem.
However, computation of the full disparity distribution with an advanced
Bayesian model is usually an intractable problem, and proves computationally
challenging even with a simple model. In this paper, we show how probabilistic
hardware using distributed memory and alternate representation of data as
stochastic bitstreams can solve that problem with high performance and energy
efficiency. We put forward a way to express discrete probability distributions
using stochastic data representations and perform Bayesian fusion using those
representations, and show how that approach can be applied to diparity
computation. We evaluate the system using a simulated stochastic implementation
and discuss possible hardware implementations of such architectures and their
potential for sensorimotor processing and robotics.Comment: Preprint of article submitted for publication in International
Journal of Approximate Reasoning and accepted pending minor revision
Self-Replication and Self-Assembly for Manufacturing
It has been argued that a central objective of nanotechnology is to make
products inexpensively, and that self-replication is an effective approach
to very low-cost manufacturing. The research presented here is intended to
be a step towards this vision. We describe a computational simulation of
nanoscale machines floating in a virtual liquid. The machines can bond
together to form strands (chains) that self-replicate and self-assemble
into user-specified meshes. There are four types of machines and the
sequence of machine types in a strand determines the shape of the mesh
they will build. A strand may be in an unfolded state, in which the bonds
are straight, or in a folded state, in which the bond angles depend on the
types of machines. By choosing the sequence of machine types in a strand,
the user can specify a variety of polygonal shapes. A simulation typically
begins with an initial unfolded seed strand in a soup of unbonded machines.
The seed strand replicates by bonding with free machines in the soup. The
child strands fold into the encoded polygonal shape, and then the polygons
drift together and bond to form a mesh. We demonstrate that a variety of
polygonal meshes can be manufactured in the simulation, by simply changing
the sequence of machine types in the seed
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
- …