Key-homomorphic properties of cryptographic objects have proven to be useful, both from a theoretical as well as a practical perspective. Important cryptographic objects such as pseudorandom functions or (public key) encryption have been studied previously with respect to key-homomorphisms. Interestingly, however, signature schemes have not been explicitly investigated in this context so far. W...

1. In a recent paper [18], A. Kleppner proved that every Haar measurable homomorphism 4 : G ~ H between locally compact groups G, H is continuous. This result also follows from a measure theoretic result by D. H. Fremlin [8], (see also [9, 19]), which provides a technique to prove measurability of uncountable unions of measurable sets. The purpose of this note is to present a different and new ...

Following E. Kirchberg, [3], we call a bifunctor (A,B) → A⊗α B a C -algebraic tensor product functor if it is obtained by completing of the algebraic tensor product A ⊙ B of C-algebras in a functional way with respect to a suitable C-norm ‖ · ‖α. We call such a functor symmetric if the standard isomorphism A ⊙ B ∼= B ⊙ A extends to an isomorphism A⊗αB ∼= B⊗αA. Similarly, we call it associative ...

Abstract Let XY L , T consist of all countable -structures M that satisfy the axioms and in which homomorphisms type X (these could be plain homomorphisms, monomorphisms, or isomorphisms) between finite substructures are restrictions an endomorphism Y (for example, automorphism a surjective endomorphism). Lockett Truss introduced 18 such classes for relational structures. For given pair however...

In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To purpose prove that can be characterized as the concatenation of finite tree (WFTA) and specific class homomorphism. We show series recognized by is closed under inverses homomorphisms, but not homomorphisms. logical automata, which uses MSO logic trees. Finally investigat...

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensiv...

In this paper X is a BCI-algebra and n is an element of N. Let D be a set, let f be a function from N into D, and let n be a natural number. Then f(n) is an element of D. Let G be a non empty BCI structure with 0. The functor BCI-powerG yielding a function from (the carrier of G) × N into the carrier of G is defined as follows: (Def. 1) For every element x of G holds (BCI-powerG)(x, 0) = 0G and...

Let CABA be the category of complete and atomic boolean algebras homomorphisms, let CSL meet-semilattices meet-homomorphisms. We show that forgetful functor from to has a left adjoint. This allows us describe an endofunctor H on such Alg(H) for is dually equivalent Coalg(P) coalgebras powerset P Set. As consequence, we derive Thomason duality Tarski duality, thus paralleling how J\'onsson-Tarsk...

This paper begins by introducing the concept of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which is a natural generalization of hom-Lie algebras introduced in a previous paper [14]. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by homomorphisms, twisting the Jacobi identity and skew-symmetry. The nat...

A quandle is an algebraic system with a binary operation satisfying three axioms modelled on the Reidemeister moves of planar diagrams links in 3-space. The paper establishes new relationship between cohomology, extensions and automorphisms quandles. We derive four term exact sequence relating 1-cocycles, second cohomology certain group abelian extension non-abelian counterpart this involving d...