10,541 research outputs found
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
An adaptive prefix-assignment technique for symmetry reduction
This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie
Topological Defects and nano-Hz Gravitational Waves in Aligned Axion Models
We study the formation and evolution of topological defects in an aligned
axion model with multiple Peccei-Quinn scalars, where the QCD axion is realized
by a certain combination of the axions with decay constants much smaller than
the conventional Peccei-Quinn breaking scale. When the underlying U(1)
symmetries are spontaneously broken, the aligned structure in the axion field
space exhibits itself as a complicated string-wall network in the real space.
We find that the string-wall network likely survives until the QCD phase
transition if the number of the Peccei-Quinn scalars is greater than two. The
string-wall system collapses during the QCD phase transition, producing a
significant amount of gravitational waves in the nano-Hz range at present. The
typical decay constant is constrained to be below O(100) TeV by the pulsar
timing observations, and the constraint will be improved by a factor of 2 in
the future SKA observations.Comment: 23 pages, 7 figure
Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory
We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions
and we determine all four-dimensional gauge theories resulting from the
generalized dimensional reduction a la Forgacs-Manton over coset spaces,
followed by a subsequent application of the Wilson flux spontaneous symmetry
breaking mechanism. Our investigation is constrained only by the requirements
that (i) the dimensional reduction leads to the potentially phenomenologically
interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and
(ii) the Wilson flux mechanism makes use only of the freely acting discrete
symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty,
ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C
- …