3,647 research outputs found
About some symmetries of negation
This paper deals with some structural properties of the sequent calculus and describes strong symmetries between cut-free derivations and derivations, which do not make use of identity axioms. Both of them are discussed from a semantic and syntactic point of view. Identity axioms and cuts are closely related to the treatment of negation in the sequent calculus, so the results of this article explain some nice symmetries of negatio
Relative Critical Points
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are
critical points of appropriate scalar functions parametrized by the Lie algebra
(or its dual) of the symmetry group. Setting aside the structures - symplectic,
Poisson, or variational - generating dynamical systems from such functions
highlights the common features of their construction and analysis, and supports
the construction of analogous functions in non-Hamiltonian settings. If the
symmetry group is nonabelian, the functions are invariant only with respect to
the isotropy subgroup of the given parameter value. Replacing the parametrized
family of functions with a single function on the product manifold and
extending the action using the (co)adjoint action on the algebra or its dual
yields a fully invariant function. An invariant map can be used to reverse the
usual perspective: rather than selecting a parametrized family of functions and
finding their critical points, conditions under which functions will be
critical on specific orbits, typically distinguished by isotropy class, can be
derived. This strategy is illustrated using several well-known mechanical
systems - the Lagrange top, the double spherical pendulum, the free rigid body,
and the Riemann ellipsoids - and generalizations of these systems
A Linear Category of Polynomial Diagrams
We present a categorical model for intuitionistic linear logic where objects
are polynomial diagrams and morphisms are simulation diagrams. The
multiplicative structure (tensor product and its adjoint) can be defined in any
locally cartesian closed category, whereas the additive (product and coproduct)
and exponential Tensor-comonoid comonad) structures require additional
properties and are only developed in the category Set, where the objects and
morphisms have natural interpretations in terms of games, simulation and
strategies.Comment: 20 page
Symmetry sensitivities of Derivative-of-Gaussian filters
We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories
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
Boolean derivatives and computation of cellular automata
The derivatives of a Boolean function are defined up to any order. The Taylor
and MacLaurin expansions of a Boolean function are thus obtained. The last
corresponds to the ring sum expansion (RSE) of a Boolean function, and is a
more compact form than the usual canonical disjunctive form. For totalistic
functions the RSE allows the saving of a large number of Boolean operations.
The algorithm has natural applications to the simulations of cellular automata
using the multi site coding technique. Several already published algorithms are
analized, and expressions with fewer terms are generally found.Comment: 15 page
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
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