2,605 research outputs found
Symmetry within Solutions
We define the concept of an internal symmetry. This is a symmety within a
solution of a constraint satisfaction problem. We compare this to solution
symmetry, which is a mapping between different solutions of the same problem.
We argue that we may be able to exploit both types of symmetry when finding
solutions. We illustrate the potential of exploiting internal symmetries on two
benchmark domains: Van der Waerden numbers and graceful graphs. By identifying
internal symmetries we are able to extend the state of the art in both cases.Comment: AAAI 2010, Proceedings of Twenty-Fourth AAAI Conference on Artificial
Intelligenc
An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles
In 1991, Gnanajothi [4] proved that the path graph P_n with n vertex and n-1
edge is odd graceful, and the cycle graph C_m with m vertex and m edges is odd
graceful if and only if m even, she proved the cycle graph is not graceful if m
odd. In this paper, firstly, we studied the graph C_m P_m when m = 4,
6,8,10 and then we proved that the graph C_ P_n is odd graceful if m is
even. Finally, we described an algorithm to label the vertices and the edges of
the vertex set V(C_m P_n) and the edge set E(C_m P_n).Comment: 9 Pages, JGraph-Hoc Journa
Effectively Solving NP-SPEC Encodings by Translation to ASP
NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe Prolog and via Boolean satisfiability solvers. In this paper, we present translations from NP-SPEC into ASP, and provide an experimental evaluation of existing implementations and the proposed translations to ASP using various ASP solvers. The results show that translating to ASP clearly has an edge over the existing translation into SAT, which involves an intrinsic grounding process. We also argue that it might be useful to incorporate certain language constructs of NPSPEC into mainstream ASP
Translation-based Constraint Answer Set Solving
We solve constraint satisfaction problems through translation to answer set
programming (ASP). Our reformulations have the property that unit-propagation
in the ASP solver achieves well defined local consistency properties like arc,
bound and range consistency. Experiments demonstrate the computational value of
this approach.Comment: Self-archived version for IJCAI'11 Best Paper Track submissio
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
Fine Tuning Free Paradigm of Two Measures Theory: K-Essence, Absence of Initial Singularity of the Curvature and Inflation with Graceful Exit to Zero Cosmological Constant State
The dilaton-gravity sector of the Two Measures Field Theory (TMT)is explored
in detail in the context of cosmology. The model possesses scale invariance
which is spontaneously broken due to the intrinsic features of the TMT
dynamics. The effective model represents an explicit example of the effective
k-essence resulting from first principles without any exotic term in the
fundamental action. Depending of the choice of regions in the parameter space,
TMT exhibits different possible outputs for cosmological dynamics: a) Absence
of initial singularity of the curvature while its time derivative is singular.
This is a sort of "sudden" singularities studied by Barrow on purely kinematic
grounds. b) Power law inflation in the subsequent stage of evolution. Depending
on the region in the parameter space (but without fine tuning) the inflation
ends with a graceful exit either into the state with zero cosmological constant
(CC) or into the state driven by both a small CC and the field phi with a
quintessence-like potential. c) Possibility of resolution of the old CC
problem. From the point of view of TMT, it becomes clear why the old CC problem
cannot be solved (without fine tuning) in conventional field theories. d) TMT
enables two ways for achieving small CC without fine tuning of dimensionfull
parameters: either by a seesaw type mechanism or due to a correspondence
principle between TMT and conventional field theories (i.e theories with only
the measure of integration sqrt{-g} in the action. e) There is a wide range of
the parameters such that in the late time universe: the equation-of-state
w=p/\rho <-1; w asymptotically (as t\to\infty) approaches -1 from below; \rho
approaches a constant, the smallness of which does not require fine tuning of
dimensionfull parameters.Comment: 37 pages, 20 figures. Minor misprints corrected, reference added. The
final version published in Phys. Rev.
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