22,393 research outputs found
Synthesizing Finite-state Protocols from Scenarios and Requirements
Scenarios, or Message Sequence Charts, offer an intuitive way of describing
the desired behaviors of a distributed protocol. In this paper we propose a new
way of specifying finite-state protocols using scenarios: we show that it is
possible to automatically derive a distributed implementation from a set of
scenarios augmented with a set of safety and liveness requirements, provided
the given scenarios adequately \emph{cover} all the states of the desired
implementation. We first derive incomplete state machines from the given
scenarios, and then synthesis corresponds to completing the transition relation
of individual processes so that the global product meets the specified
requirements. This completion problem, in general, has the same complexity,
PSPACE, as the verification problem, but unlike the verification problem, is
NP-complete for a constant number of processes. We present two algorithms for
solving the completion problem, one based on a heuristic search in the space of
possible completions and one based on OBDD-based symbolic fixpoint computation.
We evaluate the proposed methodology for protocol specification and the
effectiveness of the synthesis algorithms using the classical alternating-bit
protocol.Comment: This is the working draft of a paper currently in submission.
(February 10, 2014
Systoles of 2-complexes, Reeb graph, and Grushko decomposition
Let X be a finite 2-complex with unfree fundamental group. We prove lower
bounds for the area of a metric on X, in terms of the square of the least
length of a noncontractible loop in X. We thus establish a uniform systolic
inequality for all unfree 2-complexes. Our inequality improves the constant in
M. Gromov's inequality in this dimension. The argument relies on the Reeb graph
and the coarea formula, combined with an induction on the number of freely
indecomposable factors in Grushko's decomposition of the fundamental group.
More specifically, we construct a kind of a Reeb space ``minimal model'' for X,
reminiscent of the ``chopping off long fingers'' construction used by Gromov in
the context of surfaces. As a consequence, we prove the agreement of the
Lusternik-Schnirelmann and systolic categories of a 2-complex.Comment: 29 pages; to appear in Int. Math. Res. Notice
Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity
The prescription of Silva to derive superpotential equations from variational
derivatives rather than from Lagrangian densities is applied to theories of
gravity derived from Lovelock Lagrangians in the Palatini representation.
Spacetimes are without torsion and isolated sources of gravity are minimally
coupled. On a closed boundary of spacetime, the metric is given and the
connection coefficients are those of Christoffel. We derive equations for the
superpotentials in these conditions. The equations are easily integrated and we
give the general expression for all superpotentials associated with Lovelock
Lagrangians. We find, in particular, that in Einstein's theory, in any number
of dimensions, the superpotential, valid at spatial and at null infinity, is
that of Katz, Bicak and Lynden-Bell, the KBL superpotential. We also give
explicitly the superpotential for Gauss-Bonnet theories of gravity. Finally, we
find a simple expression for the superpotential of Einstein-Gauss-Bonnet
theories with an anti-de Sitter background: it is minus the KBL superpotential,
confirming, as it should, the calculation of the total mass-energy of spacetime
at spatial infinity by Deser and Tekin.Comment: Scheduled to appear in Class. Quantum Grav. August 200
On the mass of a Kerr-anti-de Sitter spacetime in D dimensions
We show how to compute the mass of a Kerr-anti-de Sitter spacetime with
respect to the anti-de Sitter background in any dimension, using a
superpotential which has been derived from standard Noether identities. The
calculation takes no account of the source of the curvature and confirms
results obtained for black holes via the first law of thermodynamics.Comment: minor changes; accepted by CQ
Investigation of light scattering in high reflecting pigmented coatings quarterly report, 1 may - 1 aug. 1965
Application of light scattering theories to highly pigmented coating
- …