1,502 research outputs found
Uncountable realtime probabilistic classes
We investigate the minimum cases for realtime probabilistic machines that can
define uncountably many languages with bounded error. We show that logarithmic
space is enough for realtime PTMs on unary languages. On binary case, we follow
the same result for double logarithmic space, which is tight. When replacing
the worktape with some limited memories, we can follow uncountable results on
unary languages for two counters.Comment: 12 pages. Accepted to DCFS201
Chaos and quantum-nondemolition measurements
The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ‘‘deterministic randomness’’ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity
On Many-Minds Interpretations of Quantum Theory
This paper is a response to some recent discussions of many-minds
interpretations in the philosophical literature. After an introduction to the
many-minds idea, the complexity of quantum states for macroscopic objects is
stressed. Then it is proposed that a characterization of the physical structure
of observers is a proper goal for physical theory. It is argued that an
observer cannot be defined merely by the instantaneous structure of a brain,
but that the history of the brain's functioning must also be taken into
account. Next the nature of probability in many-minds interpretations is
discussed and it is suggested that only discrete probability models are needed.
The paper concludes with brief comments on issues of actuality and identity
over time.Comment: 16 pages, plain TeX, no macros required. Revised following comments
November 199
On the Consistent Effect Histories Approach to Quantum Mechanics
A formulation of the consistent histories approach to quantum mechanics in
terms of generalized observables (POV measures) and effect operators is
provided. The usual notion of `history' is generalized to the notion of `effect
history'. The space of effect histories carries the structure of a D-poset.
Recent results of J.D. Maitland Wright imply that every decoherence functional
defined for ordinary histories can be uniquely extended to a bi-additive
decoherence functional on the space of effect histories. Omnes' logical
interpretation is generalized to the present context. The result of this work
considerably generalizes and simplifies the earlier formulation of the
consistent effect histories approach to quantum mechanics communicated in a
previous work of this author.Comment: LaTeX 2.09 version replaced by LaTeX2e version, minor change
- …