Regular (or canonical) open neighborhoods

Canonical Regular Types

Regular types represent sets of structured data, and have been used in logic programming (LP) for verification. However, first-class regular type systems are uncommon in LP languages. In this paper we present a new approach to regular types, based on type canonization, aimed at providing a practical first-class regular type system. 1998 ACM Subject Classification D.3.3 Language Constructs and F...

Regular Neighborhoods Are Not Topologically Invariant

The canonical controllers and regular interconnection

We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the regularity of the canonical controllers, a...

Canonical Varieties of Completely Regular Semigroups

Completely regular semigroups CR are regarded here as algebras with multiplication and the unary operation of inversion. Their lattice of varieties is denoted by L.CR/. Let B denote the variety of bands and L.B/ the lattice of its subvarieties. The mapping V → V ∩ B is a complete homomorphism of L.CR/ onto L.B/. The congruence induced by it has classes that are intervals, say VB = [VB ;V B] for...

Regular Neighbourhoods and Canonical Decompositions for Groups

We find canonical decompositions for finitely presented groups which essentially specialise to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under automorphisms of the group. A crucial new ingredient is the concept of a regular neighbourhood of a family of almost invariant subsets of a group. An almo...