We propose a term rewriting approach to verify observational congruence between guarded recursive (finite-state) CCS expressions. Starting from the complete axiomatization of observational congruence for this subset of CCS, a non-terminating rewriting relation has been defined. This rewriting relation is co-canonical over a subclass of infinite derivations, structured fair derivations, which co...

In groups, an abelian normal subgroup induces congruence. We construct a class of centrally nilpotent Moufang loops containing subloop that does not induce On the other hand, we prove in 6-divisible loops, every congruence solvability adopted from universal-algebraic commutator theory modular varieties is strictly stronger than classical group theory. It open problem whether two notions coincid...

Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

In this paper we introduce fuzzy congruence and fuzzy strong congruence of semi-hypergroups as well as polygroups. We obtain some results in this respect. We also prove that FC(H), the set of all fuzzy strong congruences on a polygroup H , consists a complete lattice and this lattice is isomorphic to FN (H), the lattice of fuzzy normal subpolygroups.

A lattice identity is given such that it holds but its dual fails in the normal subgroup lattices of metaabelian groups. Thus the congruence variety of metaabelian groups is not self-dual; this is the first example for a modular congruence variety which is not self-dual. For a ring R with unit element let L(R) denote the class of lattices embeddable in submodule lattices of R-modules. Then HL(R...

Abstract We consider a generalisation of the Basilica group to all odd primes: p -Basilica groups acting on -adic tree. show that have -congruence subgroup property but not congruence nor weak property. This provides first examples weakly branch with such properties. In addition, give branch, which are super strongly fractal. compute orders quotients these groups, enable us determine Hausdorff ...

Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group. We specialize the fundamental theorem into several varieties of loops, and also discus...

We show that the poset of regions (with respect to a canonical base region) of a supersolvable hyperplane arrangement is a congruence normal lattice. Specifically, the poset of regions of a supersolvable arrangement of rank k is obtained via a sequence of doublings from the poset of regions of a supersolvable arrangement of rank k − 1. An explicit description of the doublings leads to a proof t...

This paper contributes to the discrete differential geometry of triangle meshes, in combination with a study of discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ‘normal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of t...