Abstract We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and Yaacov, Doucha, Nies, Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences the perturbation systems former paper, such as Banach‐Mazur distance Lipschitz between metric spaces. Our is characterized syntacticall...

The convex hull ψn,n of certain (n!) 2 tensors was considered recently in connection with graph isomorphism. We consider the convex hull ψn of the n! diagonals among these tensors. We show: 1. The polytope ψn is a face of ψn,n. 2. Deciding if a graph G has a subgraph isomorphic to H reduces to optimization over ψn. 3. Optimization over ψn reduces to optimization over ψn,n. In particular, this i...

In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism prob...

Let A and B be two factors. In this paper, it is proved that a not necessarily linear bijective map ? : satisfies ?([A, B]* C) = [?(A), ?(B)]* ?(C) for all A, B,C if only *-isomorphism, conjugate the negative of or *-isomorphism.

We prove that if the squaring map in the factor loop of a Moufang loop Q over its nucleus is surjective, then every half-isomorphism of Q onto a Moufang loop is either an isomorphism or an anti-isomorphism. This generalizes all earlier results in this vein.

Almost isomorphism is an equivalence relation on countable state Markov shifts which provides a strong version of Borel conjugacy; still, for mixing SPR shifts, entropy is a complete invariant of almost isomorphism [2]. In this paper, we establish a class of potentials on countable state Markov shifts whose thermodynamic formalism is respected by almost isomorphism.

Whittlesey 12,13,14] gave a criterion which decides when two nite 2-dimensional complexes are homeomorphic. We show that graph isomorphism can be reduced eeciently to 2-complex homeomorphism, and that Whittlesey's criterion can be reduced eeciently to graph isomorphism. Therefore graph isomorphism and 2-complex homeomorphism are polynomial-time equivalent.

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.