1,407 research outputs found
An Exact Fluctuating 1/2-BPS Configuration
This work explores the role of thermodynamic fluctuations in the two
parameter giant and superstar configurations characterized by an ensemble of
arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis
illustrates that the chemical and state-space geometric descriptions exhibit an
intriguing set of exact pair correction functions and the global correlation
lengths. The first principle of statistical mechanics shows that the possible
canonical fluctuations may precisely be ascertained without any approximation.
Interestingly, our intrinsic geometric study exemplifies that there exist exact
fluctuating 1/2-BPS statistical configurations which involve an ensemble of
microstates describing the liquid droplets or fuzzballs. The Gaussian
fluctuations over an equilibrium chemical and state-space configurations
accomplish a well-defined, non-degenerate, curved and regular intrinsic
Riemannian manifolds for all physically admissible domains of black hole
parameters. An explicit computation demonstrates that the underlying chemical
correlations involve ordinary summations, whilst the state-space correlations
may simply be depicted by standard polygamma functions. Our construction
ascribes definite stability character to the canonical energy fluctuations and
to the counting entropy associated with an arbitrary choice of excited boxes
from an ensemble of ample boxes constituting a variety of Young tableaux.Comment: Minor changes, added references, 30 pages, 4 figures, PACS numbers:
04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.50.Gh
Higher-dimensional black holes, black strings, and related objects; 04.60.Cf
Gravitational aspects of string theory, accepted for publication in JHE
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
The safety of infinite state systems can be checked by a backward
reachability procedure. For certain classes of systems, it is possible to prove
the termination of the procedure and hence conclude the decidability of the
safety problem. Although backward reachability is property-directed, it can
unnecessarily explore (large) portions of the state space of a system which are
not required to verify the safety property under consideration. To avoid this,
invariants can be used to dramatically prune the search space. Indeed, the
problem is to guess such appropriate invariants. In this paper, we present a
fully declarative and symbolic approach to the mechanization of backward
reachability of infinite state systems manipulating arrays by Satisfiability
Modulo Theories solving. Theories are used to specify the topology and the data
manipulated by the system. We identify sufficient conditions on the theories to
ensure the termination of backward reachability and we show the completeness of
a method for invariant synthesis (obtained as the dual of backward
reachability), again, under suitable hypotheses on the theories. We also
present a pragmatic approach to interleave invariant synthesis and backward
reachability so that a fix-point for the set of backward reachable states is
more easily obtained. Finally, we discuss heuristics that allow us to derive an
implementation of the techniques in the model checker MCMT, showing remarkable
speed-ups on a significant set of safety problems extracted from a variety of
sources.Comment: Accepted for publication in Logical Methods in Computer Scienc
Rigged configuration bijection and proof of the conjecture for nonexceptional affine types
We establish a bijection between rigged configurations and highest weight
elements of a tensor product of Kirillov-Reshetikhin crystals for all
nonexceptional types. A key idea for the proof is to embed both objects into
bigger sets for simply-laced types or , whose bijections
have already been established. As a consequence we settle the conjecture
in full generality for nonexceptional types. Furthermore, the bijection extends
to a classical crystal isomorphism and sends the combinatorial -matrix to
the identity map on rigged configurations.Comment: 30 pages, 2 figures; v2 Referenced Naoi's work in the introduction,
clarified some notation; v3 Various additions for more self-containment
(e.g., the signature rule) and typos fixe
Tableaux Modulo Theories Using Superdeduction
We propose a method that allows us to develop tableaux modulo theories using
the principles of superdeduction, among which the theory is used to enrich the
deduction system with new deduction rules. This method is presented in the
framework of the Zenon automated theorem prover, and is applied to the set
theory of the B method. This allows us to provide another prover to Atelier B,
which can be used to verify B proof rules in particular. We also propose some
benchmarks, in which this prover is able to automatically verify a part of the
rules coming from the database maintained by Siemens IC-MOL. Finally, we
describe another extension of Zenon with superdeduction, which is able to deal
with any first order theory, and provide a benchmark coming from the TPTP
library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117
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