In this paper, we study two questions related to the problem of testing whether a function is close to a homomorphism. For two finite groups (not necessarily Abelian), an arbitrary map , and a parameter , say that is -close to a homomorphism if there is some homomorphism such that and differ on at most elements of , and say that is -far otherwise. For a given and , a homomorphism tester should ...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

For graphs G and H , a homomorphism from G to H is a function φ : V (G) → V (H), which maps vertices adjacent in G to adjacent vertices of H . A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H . Many cases of graph homomorphism and locally injective graph homomorphism are NPcomplete, so there is little hope to design polynomial-time...

We define the Homomorphism Extension (HomExt) problem: given a group G, a subgroup M ≤ G and a homomorphism φ : M → H , decide whether or not there exists a homomorphism φ̃ : G → H extending φ, i.e., φ̃|M = φ. This problem arose in the context of list-decoding homomorphism codes but is also of independent interest, both as a problem in computational group theory and as a new and natural problem i...

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices. Define...

We study the complexity of structurally restricted homomorphism and constraint satisfaction problems. For every class of relational structures C, let LHOM(C, _) be the problem of deciding whether a structure A ∈ C has a homomorphism to a given arbitrary structure B, when each element in A is only allowed a certain subset of elements of B as its image. We prove, under a certain complexity-theore...