We prove that, if A and B are complete normed non-associative algebras, and if B is strongly semisimple and algebraic, then dense range homomorphisms from A to B are continuous. As a consequence, we obtain that homomorphisms from complete normed algebras into a complete normed power-associative algebraic algebra B are continuous if and only if B has no nonzero elements with zero square. We also...

For many one-way homomorphisms used in cryptography, there exist efficient zero-knowledge proofs of knowledge of a preimage. Examples of such homomorphisms are the ones underlying the Schnorr or the Guillou-Quisquater identification protocols. In this paper we present, for the first time, efficient zero-knowledge proofs of knowledge for exponentiation ψ(x1) . = h1 1 and multi-exponentiation hom...

We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms...

We describe here the new concept of ǫ-Homomorphisms of Prob-abilistic Regulatory Gene Networks(PRN). The ǫ-homomorphisms are special mappings between two probabilistic networks, that consider the algebraic action of the iteration of functions and the probabilistic dynamic of the two networks. It is proved here that the class of PRN, together with the homo-morphisms, form a category with product...

Behaviour of systems is described by formal languages: the sets of all sequences of actions. Regarding abstraction, alphabetic language homomorphisms areion, alphabetic language homomorphisms are used to compute abstract behaviours. To avoid loss of important information when moving to the abstract level, abstracting homomorphisms have to satisfy a certain property called simplicity on the conc...