In this paper, we propose a genetic algorithm for solving the shortest vector problem (SVP) based on sparse integer representations of short vectors in lattices as chromesomes, which, we prove, can guarantee finding the shortest lattice vector under a Markov chain analysis. Moreover, we also suggest some improvements by introducing heuristic techniques: local search and heuristic pruning. The e...

In this paper, the connection between triangular number , square number for construction and counting the lattice number in lattice vector quantization is presented. We also observe that unique hexagonal lattice can be formed from two triangular numbers and a square number combination. Furthermore, the number of multistage lattice is derived from lattice number . Analysis of the number of latti...

The Closest Vector Problem (CVP) is a computational problem on lattices closely related to SVP. (See Shortest Vector Problem.) Given a lattice L and a target point ~x, CVP asks to find the lattice point closest to the target. As for SVP, CVP can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A more relaxed version of the ...

Dislocations in crystals are linear crystallographic defects, which move in lattice when crystals are plastically deformed. Motion of a partial dislocation may remove or create stacking fault characterized with a partial of a lattice translation vector. Here we report that motion of partial dislocations inside an intermetallic compound result in a local composition deviation from its stoichiome...

In this paper, we propose approximate lattice algorithms for solving the shortest vector problem (SVP) and the closest vector problem (CVP) on an n-dimensional Euclidean integral lattice L. Our algorithms run in polynomial time of the dimension and determinant of lattices and improve on the LLL algorithm when the determinant of a lattice is less than 2 2/4. More precisely, our approximate SVP a...

We show that given oracle access to a subroutine which returns approximate closest vectors in a lattice, one may find in polynomial time approximate shortest vectors in a lattice. The level of approximation is maintained; that is, for any function f , the following holds: Suppose that the subroutine, on input a lattice L and a target vector w (not necessarily in the lattice), outputs v ∈ L such...

Recall that in the closest vector problem we are given a lattice and a target vector (which is usually not in the lattice) and we are supposed to find the lattice point that is closest to the target point. More precisely, one can consider three variants of the CVP, depending on whether we have to actually find the closest vector, find its distance, or only decide if it is closer than some given...

Monitoring global predicates is a fundamental concern in distributed and concurrent systems for its importance during the design, testing and debugging phases of program development. In this paper, we present a generalization of local predicates called the chain predicates. In the context of multithreaded programs, these predicates can be thought of as predicates defined over shared variables i...

Domain Wall Fermions (DWF) for lattice gauge theories were developed in [1]. Since then a wealth of activity has followed with the main focus being the application of DWF to chiral lattice gauge theories, but also to vector lattice gauge theories (see [2] and references therein). As a result of these works little doubt remains that DWF can be used to regularize vector gauge theories on the latt...

In this thesis, we construct and analyze multiple-description codes based on lattice vector quantization.