The theory of chi processes with the mismatch operator is studied. Two open congruence relations are investigated. These are weak early open congruence and weak late open congruence. Complete systems are given for both congruence relations. These systems use some new tau laws. The results of this paper correct some popular mistakes in literature.

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...

This paper deenes a congruence relation on Gamma programs. Based on this congruence relation, laws for transforming programs are derived. We deene an axiomatic semantics for Gamma based on Brookes' transition assertions. The deenition of the congruence is in terms of provable satissability of such assertions. We consider the relationship between our congruence and other orderings that have been...

We study congruences on the partial automorphism monoid of a finite rank free group action. determine decomposition congruence this into Rees congruence, Brandt semigroup and an idempotent separating congruence. The constituent parts are further described in terms subgroups direct semidirect products groups. utilize description to demonstrate how number depends

The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

An ω-language over a finite alphabet X is a set of infinite sequences of letters of X. Previously studied syntactic equivalence relations defined by ω-languages have mainly been relations on X∗. In this paper the emphasis is put on relations in Xω, by associating to an ω-language L a congruence on Xω, called the ω-syntactic congruence of L. Properties of this congruence and notions induced by i...

Since congruence modulo m is an equivalence relation, it partitions the universe of integers into equivalence classes, which we’ll call congruence classes modulo m. Within any one of these classes, all of the members are congruent to all of the other members; but congruence modulo m never holds between members of different equivalence classes. For instance, there are two congruence classes modu...

It is evident from the definition that the class of all BCK-algebras is a quasivariety. Yet it is not a variety, nor does the largest subvariety of BCK exist—as shown in Wroński [2], Kabziński & Wroński [3], respectively. Several subvarieties of BCK have been isolated and thoroughly investigated, which has led to a substantial body of results (cf. e.g., Blok & Raftery [4]). Nevertheless, the qu...