214 research outputs found
Solving Set Constraint Satisfaction Problems using ROBDDs
In this paper we present a new approach to modeling finite set domain
constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We
show that it is possible to construct an efficient set domain propagator which
compactly represents many set domains and set constraints using ROBDDs. We
demonstrate that the ROBDD-based approach provides unprecedented flexibility in
modeling constraint satisfaction problems, leading to performance improvements.
We also show that the ROBDD-based modeling approach can be extended to the
modeling of integer and multiset constraint problems in a straightforward
manner. Since domain propagation is not always practical, we also show how to
incorporate less strict consistency notions into the ROBDD framework, such as
set bounds, cardinality bounds and lexicographic bounds consistency. Finally,
we present experimental results that demonstrate the ROBDD-based solver
performs better than various more conventional constraint solvers on several
standard set constraint problems
On Folding and Twisting (and whatknot): towards a characterization of workspaces in syntax
Syntactic theory has traditionally adopted a constructivist approach, in
which a set of atomic elements are manipulated by combinatory operations to
yield derived, complex elements. Syntactic structure is thus seen as the result
or discrete recursive combinatorics over lexical items which get assembled into
phrases, which are themselves combined to form sentences. This view is common
to European and American structuralism (e.g., Benveniste, 1971; Hockett, 1958)
and different incarnations of generative grammar, transformational and
non-transformational (Chomsky, 1956, 1995; and Kaplan & Bresnan, 1982; Gazdar,
1982). Since at least Uriagereka (2002), there has been some attention paid to
the fact that syntactic operations must apply somewhere, particularly when
copying and movement operations are considered. Contemporary syntactic theory
has thus somewhat acknowledged the importance of formalizing aspects of the
spaces in which elements are manipulated, but it is still a vastly
underexplored area. In this paper we explore the consequences of
conceptualizing syntax as a set of topological operations applying over spaces
rather than over discrete elements. We argue that there are empirical
advantages in such a view for the treatment of long-distance dependencies and
cross-derivational dependencies: constraints on possible configurations emerge
from the dynamics of the system.Comment: Manuscript. Do not cite without permission. Comments welcom
Numerical Linear Algebra applications in Archaeology: the seriation and the photometric stereo problems
The aim of this thesis is to explore the application of Numerical Linear Algebra to Archaeology. An ordering problem called the seriation problem, used for dating findings and/or artifacts deposits, is analysed in terms of graph theory. In particular, a Matlab implementation of an algorithm for spectral seriation, based on the use of the Fiedler vector of the Laplacian matrix associated with the problem, is presented. We consider bipartite graphs for describing the seriation problem, since the interrelationship between the units (i.e. archaeological sites) to be reordered, can be described in terms of these graphs. In our archaeological metaphor of seriation, the two disjoint nodes sets into which the vertices of a bipartite graph can be divided, represent the excavation sites and the artifacts found inside
them.
Since it is a difficult task to determine the closest bipartite network to a given one, we describe how a starting network can be approximated by a bipartite one by solving a sequence of fairly simple optimization problems.
Another numerical problem related to Archaeology is the 3D reconstruction of the shape of an object from a set of digital pictures. In particular, the Photometric Stereo (PS) photographic technique is considered
Continuity argument revisited: geometry of root clustering via symmetric products
We study the spaces of polynomials stratified into the sets of polynomial
with fixed number of roots inside certain semialgebraic region , on its
border, and at the complement to its closure. Presented approach is a
generalisation, unification and development of several classical approaches to
stability problems in control theory: root clustering (-stability) developed
by R.E. Kalman, B.R. Barmish, S. Gutman et al., -decomposition(Yu.I.
Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A.
Fam, J. Meditch, J.Ackermann).
Our approach is based on the interpretation of correspondence between roots
and coefficients of a polynomial as a symmetric product morphism.
We describe the topology of strata up to homotopy equivalence and, for many
important cases, up to homeomorphism. Adjacencies between strata are also
described. Moreover, we provide an explanation for the special position of
classical stability problems: Hurwitz stability, Schur stability,
hyperbolicity.Comment: 45 pages, 4 figure
Preimages for SHA-1
This research explores the problem of finding a preimage — an input that, when passed through a particular function, will result in a pre-specified output — for the compression function of the SHA-1 cryptographic hash. This problem is much more difficult than the problem of finding a collision for a hash function, and preimage attacks for very few popular hash functions are known. The research begins by introducing the field and giving an overview of the existing work in the area. A thorough analysis of the compression function is made, resulting in alternative formulations for both parts of the function, and both statistical and theoretical tools to determine the difficulty of the SHA-1 preimage problem. Different representations (And- Inverter Graph, Binary Decision Diagram, Conjunctive Normal Form, Constraint Satisfaction form, and Disjunctive Normal Form) and associated tools to manipulate and/or analyse these representations are then applied and explored, and results are collected and interpreted. In conclusion, the SHA-1 preimage problem remains unsolved and insoluble for the foreseeable future. The primary issue is one of efficient representation; despite a promising theoretical difficulty, both the diffusion characteristics and the depth of the tree stand in the way of efficient search. Despite this, the research served to confirm and quantify the difficulty of the problem both theoretically, using Schaefer's Theorem, and practically, in the context of different representations
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