224,661 research outputs found
Quantum Histories
There are good motivations for considering some type of quantum histories
formalism. Several possible formalisms are known, defined by different
definitions of event and by different selection criteria for sets of histories.
These formalisms have a natural interpretation, according to which nature
somehow chooses one set of histories from among those allowed, and then
randomly chooses to realise one history from that set; other interpretations
are possible, but their scientific implications are essentially the same.
The selection criteria proposed to date are reasonably natural, and certainly
raise new questions. For example, the validity of ordering inferences which we
normally take for granted --- such as that a particle in one region is
necessarily in a larger region containing it --- depends on whether or not our
history respects the criterion of ordered consistency, or merely consistency.
However, the known selection criteria, including consistency and medium
decoherence, are very weak. It is not possible to derive the predictions of
classical mechanics or Copenhagen quantum mechanics from the theories they
define, even given observational data in an extended time interval. Attempts to
refine the consistent histories approach so as to solve this problem by finding
a definition of quasiclassicality have so far not succeeded.
On the other hand, it is shown that dynamical collapse models, of the type
originally proposed by Ghirardi-Rimini-Weber, can be re-interpreted as set
selection criteria within a quantum histories framework, in which context they
appear as candidate solutions to the set selection problem. This suggests a new
route to relativistic generalisation of these models, since covariant
definitions of a quantum event are known.Comment: 19 pages, TeX with harvmac. Contribution to Proceedings of the 104th
Nobel Symposium, ``Modern Studies of Basic Quantum Concepts and Phenomena'',
Gimo, June 1997. To appear in Physica Script
Learning Weak Constraints in Answer Set Programming
This paper contributes to the area of inductive logic programming by
presenting a new learning framework that allows the learning of weak
constraints in Answer Set Programming (ASP). The framework, called Learning
from Ordered Answer Sets, generalises our previous work on learning ASP
programs without weak constraints, by considering a new notion of examples as
ordered pairs of partial answer sets that exemplify which answer sets of a
learned hypothesis (together with a given background knowledge) are preferred
to others. In this new learning task inductive solutions are searched within a
hypothesis space of normal rules, choice rules, and hard and weak constraints.
We propose a new algorithm, ILASP2, which is sound and complete with respect to
our new learning framework. We investigate its applicability to learning
preferences in an interview scheduling problem and also demonstrate that when
restricted to the task of learning ASP programs without weak constraints,
ILASP2 can be much more efficient than our previously proposed system.Comment: To appear in Theory and Practice of Logic Programming (TPLP),
Proceedings of ICLP 201
Bisymmetric and quasitrivial operations: characterizations and enumerations
We investigate the class of bisymmetric and quasitrivial binary operations on
a given set and provide various characterizations of this class as well as
the subclass of bisymmetric, quasitrivial, and order-preserving binary
operations. We also determine explicitly the sizes of these classes when the
set is finite.Comment: arXiv admin note: text overlap with arXiv:1709.0916
New developments in the theory of Groebner bases and applications to formal verification
We present foundational work on standard bases over rings and on Boolean
Groebner bases in the framework of Boolean functions. The research was
motivated by our collaboration with electrical engineers and computer
scientists on problems arising from formal verification of digital circuits. In
fact, algebraic modelling of formal verification problems is developed on the
word-level as well as on the bit-level. The word-level model leads to Groebner
basis in the polynomial ring over Z/2n while the bit-level model leads to
Boolean Groebner bases. In addition to the theoretical foundations of both
approaches, the algorithms have been implemented. Using these implementations
we show that special data structures and the exploitation of symmetries make
Groebner bases competitive to state-of-the-art tools from formal verification
but having the advantage of being systematic and more flexible.Comment: 44 pages, 8 figures, submitted to the Special Issue of the Journal of
Pure and Applied Algebr
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