Testing membership in lattices is of practical relevance, with applications to integer programming, error detection in lattice-based communication and cryptography. In this work, we initiate a systematic study of local testing for membership in lattices, complementing and building upon the extensive body of work on locally testable codes. In particular, we formally define the notion of local te...

In this paper, we draw a connection between ideal lattices and Gröbner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in Z[x]/〈f〉 (Lyubashevsky & Micciancio, 2006) to ideal lattices in Z[x1, . . . , xn]/a, the multivariate case, where f is a polynomial in Z[X] and a is an ideal in Z[x1, . . . , xn]. Ideal lattices in univariate case are interprete...

Lattice based cryptography is gaining more and more importance in the cryptographic community. It is a common approach to use a special class of lattices, so-called ideal lattices, as the basis of lattice based crypto systems. This speeds up computations and saves storage space for cryptographic keys. The most important underlying hard problem is the shortest vector problem. So far there is no ...

The Heart of Mersey cardiovascular disease prevention programme in the UK Launched in 2003, following a visit to Finland, the Heart of Mersey (HoM) cardiovascular disease (CVD) prevention programme aims to improve the health of the local population through structural changes at regional, national and European level.(1) Based on the evidence (ie raised blood cholesterol and blood pressure, and t...

What we propose here is to reduce the size of Galois lattices still conserving their formal structure and exhaustivity. For that purpose we use a preliminary partition of the instance set, representing the association of a “type” to each instance. By redefining the notion of extent of a term in order to cope, to a certain degree (denoted as α), with this partition, we define a particular family...

Abstract. Studied is the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modeling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (PortRoyal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in O(e) elementary arithmetic operations, where e denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorit...

We show that the variety of ortholattices has the strong amalgamation property and that the variety of orthomodular lattices has the strong Boolean amalgamation property, i.e. that two orthomodular lattices can be strongly amalgamated over a common Boolean subalgebra. We give examples to show that the variety orthomodular lattices does not have the amalgamation property and that the variety of ...

In this talk we will present and analyze the efficiency of various algorithms in lattice theory. For finite lattices this will include recognition of various properties such as subdirect irreducibility, semidistributivity, and boundedness (in the sense of McKenzie) as well as efficient algorithms for computing the congruence lattice. For free and finitely presented lattices we will discuss algo...

A golden lattice is an even unimodular Z[ 1+ √ 5 2 ]-lattice of which the Hilbert theta series is an extremal Hilbert modular form. We construct golden lattices from extremal even unimodular lattices and obtain families of dense modular lattices.