12,280 research outputs found
Strong Equivalence Relations for Iterated Models
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical
representation, has become standard for applying topological reasoning to
distributed computing. Its modular structure makes it easier to analyze than
the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS).
It is known that AS and IIS are equivalent with respect to \emph{wait-free
task} computability: a distributed task is solvable in AS if and only if it
solvable in IIS. We observe, however, that this equivalence is not sufficient
in order to explore solvability of tasks in \emph{sub-models} of AS (i.e.
proper subsets of its runs) or computability of \emph{long-lived} objects, and
a stronger equivalence relation is needed. In this paper, we consider
\emph{adversarial} sub-models of AS and IIS specified by the sets of processes
that can be \emph{correct} in a model run. We show that AS and IIS are
equivalent in a strong way: a (possibly long-lived) object is implementable in
AS under a given adversary if and only if it is implementable in IIS under the
same adversary. %This holds whether the object is one-shot or long-lived.
Therefore, the computability of any object in shared memory under an
adversarial AS scheduler can be equivalently investigated in IIS
The Faddeev-Jackiw Approach and the Conformal Affine sl(2) Toda Model Coupled to Matter Field
The conformal affine sl(2) Toda model coupled to matter field is treated as a
constrained system in the context of Faddeev-Jackiw and the (constrained)
symplectic schemes. We recover from this theory either, the sine-Gordon or the
massive Thirring model, through a process of Hamiltonian reduction, considering
the equivalence of the Noether and topological currrents as a constraint and
gauge fixing the conformal symmetry.Comment: 15 pages. Minor changes and references added in section
On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators
Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern
the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general
Iterated Monoidal Categories
We develop a notion of iterated monoidal category and show that this notion
corresponds in a precise way to the notion of iterated loop space. Specifically
the group completion of the nerve of such a category is an iterated loop space
and free iterated monoidal categories give rise to finite simplicial operads of
the same homotopy type as the classical little cubes operads used to
parametrize the higher H-space structure of iterated loop spaces. Iterated
monoidal categories encompass, as a special case, the notion of braided tensor
categories, as used in the theory of quantum groups.Comment: 55 pages, 3 PostScript figure
Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences
We consider a real Lagrangian off-critical submodel describing the soliton
sector of the so-called conformal affine Toda model coupled to
matter fields (CATM). The theory is treated as a constrained system in the
context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent
Lagrangian nature of the model from which generalizations of the sine-Gordon
(GSG) or the massive Thirring (GMT) models are derivable. The dual description
of the model is further emphasized by providing the relationships between
bilinears of GMT spinors and relevant expressions of the GSG fields. In this
way we exhibit the strong/weak coupling phases and the (generalized)
soliton/particle correspondences of the model. The case is also
outlined.Comment: 22 pages, LaTex, some comments and references added, conclusions
unchanged, to appear in J. Math. Phy
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