57,859 research outputs found
Bootstrapping Mixed Correlators in the 3D Ising Model
We study the conformal bootstrap for systems of correlators involving
non-identical operators. The constraints of crossing symmetry and unitarity for
such mixed correlators can be phrased in the language of semidefinite
programming. We apply this formalism to the simplest system of mixed
correlators in 3D CFTs with a global symmetry. For the leading
-odd operator and -even operator
, we obtain numerical constraints on the allowed dimensions
assuming that and are
the only relevant scalars in the theory. These constraints yield a small closed
region in space compatible with the known
values in the 3D Ising CFT.Comment: 39 pages, 6 figure
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Using Graph Transformations and Graph Abstractions for Software Verification
In this paper we describe our intended approach for the verification of software written in imperative programming languages. We base our approach on model checking of graph transition systems, where each state is a graph and the transitions are specified by graph transformation rules. We believe that graph transformation is a very suitable technique to model the execution semantics of languages with dynamic memory allocation. Furthermore, such representation allows us to investigate the use of graph abstractions, which can mitigate the combinatorial explosion inherent to model checking. In addition to presenting our planned approach, we reason about its feasibility, and, by providing a brief comparison to other existing methods, we highlight the benefits and drawbacks that are expected
Learning from the Success of MPI
The Message Passing Interface (MPI) has been extremely successful as a
portable way to program high-performance parallel computers. This success has
occurred in spite of the view of many that message passing is difficult and
that other approaches, including automatic parallelization and directive-based
parallelism, are easier to use. This paper argues that MPI has succeeded
because it addresses all of the important issues in providing a parallel
programming model.Comment: 12 pages, 1 figur
Symbolic Tensor Calculus -- Functional and Dynamic Approach
In this paper, we briefly discuss the dynamic and functional approach to
computer symbolic tensor analysis. The ccgrg package for Wolfram
Language/Mathematica is used to illustrate this approach. Some examples of
applications are attached
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