15,755 research outputs found
The Riddle of Gravitation
There is no doubt that both the special and general theories of relativity
capture the imagination. The anti-intuitive properties of the special theory of
relativity and its deep philosophical implications, the bizzare and dazzling
predictions of the general theory of relativity: the curvature of spacetime,
the exotic characteristics of black holes, the bewildering prospects of
gravitational waves, the discovery of astronomical objects as quasers and
pulsers, the expansion and the (possible) recontraction of the universe..., are
all breathtaking phenomena. In this paper, we give a philosophical
non-technical treatment of both the special and the general theory of
relativity together with an exposition of some of the latest physical theories.
We then give an outline of an axiomatic approach to relativity theories due to
Andreka and Nemeti that throws light on the logical structure of both theories.
This is followed by an exposition of some of the bewildering results
established by Andreka and Nemeti concerning the foundations of mathematics
using the notion of relativistic computers. We next give a survey on the
meaning and philosophical implications of the the quantum theory and end the
paper by an imaginary debate between Einstein and Neils Bohr reflecting both
Einstein's and Bohr's philosophical views on the quantum world.
The paper is written in a somewhat untraditional manner; there are too many
footnotes. In order not to burden the reader with all the details, we have
collected the more advanced material the footnotes. We think that this makes
the paper easier to read and simpler to follow. The paper in full is adressed
more to experts.Comment: 40 pages, LaTeX-fil
A Metric Encoding for Bounded Model Checking (extended version)
In Bounded Model Checking both the system model and the checked property are
translated into a Boolean formula to be analyzed by a SAT-solver. We introduce
a new encoding technique which is particularly optimized for managing
quantitative future and past metric temporal operators, typically found in
properties of hard real time systems. The encoding is simple and intuitive in
principle, but it is made more complex by the presence, typical of the Bounded
Model Checking technique, of backward and forward loops used to represent an
ultimately periodic infinite domain by a finite structure. We report and
comment on the new encoding technique and on an extensive set of experiments
carried out to assess its feasibility and effectiveness
Non-null Infinitesimal Micro-steps: a Metric Temporal Logic Approach
Many systems include components interacting with each other that evolve with
possibly very different speeds. To deal with this situation many formal models
adopt the abstraction of "zero-time transitions", which do not consume time.
These however have several drawbacks in terms of naturalness and logic
consistency, as a system is modeled to be in different states at the same time.
We propose a novel approach that exploits concepts from non-standard analysis
to introduce a notion of micro- and macro-steps in an extension of the TRIO
metric temporal logic, called X-TRIO. We use X-TRIO to provide a formal
semantics and an automated verification technique to Stateflow-like notations
used in the design of flexible manufacturing systems.Comment: 20 pages, 2 figures, submitted to the conference "FORMATS: Formal
Modelling and Analysis of Timed Systems" 201
An Algebra of Synchronous Scheduling Interfaces
In this paper we propose an algebra of synchronous scheduling interfaces
which combines the expressiveness of Boolean algebra for logical and functional
behaviour with the min-max-plus arithmetic for quantifying the non-functional
aspects of synchronous interfaces. The interface theory arises from a
realisability interpretation of intuitionistic modal logic (also known as
Curry-Howard-Isomorphism or propositions-as-types principle). The resulting
algebra of interface types aims to provide a general setting for specifying
type-directed and compositional analyses of worst-case scheduling bounds. It
covers synchronous control flow under concurrent, multi-processing or
multi-threading execution and permits precise statements about exactness and
coverage of the analyses supporting a variety of abstractions. The paper
illustrates the expressiveness of the algebra by way of some examples taken
from network flow problems, shortest-path, task scheduling and worst-case
reaction times in synchronous programming.Comment: In Proceedings FIT 2010, arXiv:1101.426
Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
What is the simplest Hamiltonian which can implement quantum computation
without requiring any control operations during the computation process? In a
previous paper we have constructed a 10-local finite-range interaction among
qubits on a 2D lattice having this property. Here we show that
pair-interactions among qutrits on a 2D lattice are sufficient, too, and can
also implement an ergodic computer where the result can be read out from the
time average state after some post-selection with high success probability.
Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle
located at a specific lattice site, the third state is its absence. Usual
hopping terms together with an attractive force among adjacent particles induce
a coupled quantum walk where the particle spins are subjected to spatially
inhomogeneous interactions implementing holonomic quantum computing. The
holonomic method ensures that the implemented circuit does not depend on the
time needed for the walk.
Even though the implementation of the required type of spin-spin interactions
is currently unclear, the model shows that quite simple Hamiltonians are
powerful enough to allow for universal quantum computing in a closed physical
system.Comment: More detailed explanations including description of a programmable
version. 44 pages, 12 figures, latex. To appear in PR
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