This paper extends the lattice-based linearly homomorphic signature to have multiple signers with the security proof. In our construction, we assume that there are one trusted dealer and either single signer or multiple signers for a message. The dealer pre-shares the message vector v during the set-up phase and issues a pre-shared vector vi to each signer. Then, from partial signatures σi of v...

The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance. We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog monadic linear Datalog with at most one EDB per rule, and also in the smallest non-linear extension of this fragment. We give combinatorial and al...

Let K and L be lattices, and let φ be a homomorphism of K into L. Then φ induces a natural 0-preserving join-homomorphism of ConK into ConL. Extending a result of A. Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectiv...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...

A graph K is called multiplicative if whenever a categorical product of two graphs admits a homomorphism to K, then one of the factors also admits a homomorphism to K. We prove that all circular graphs Kk/d such that k/d < 4 are multiplicative. This is done using semi-lattice endomorphism in (the skeleton of) the category of graphs to prove the multiplicativity of some graphs using the known mu...

Min-Max orderings correspond to conservative lattice polymorphisms. Digraphs with Min-Max orderings have polynomial time solvable minimum cost homomorphism problems. They can also be viewed as digraph analogues of proper interval graphs and bigraphs. We give a forbidden structure characterization of digraphs with a Min-Max ordering which implies a polynomial time recognition algorithm. We also ...

We study the lattice finite representability of the Bochner space Lp(μ1, Lq(μ2)) in `p{`q}, 1 ≤ p, q < ∞, and then we characterize the ideal of the operators which factor through a lattice homomorphism between L∞(μ) and Lp(μ1, Lq(μ2)).

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H . We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.