Representation and reasoning about dynamic spatial phenomena requires at its foundation a formalism of spatial change. This paper extends our understanding of topological change, by providing a classification and analysis of events associated with changes in topological structures of spatial areal objects as they evolve through time. Tree structures are employed to represent topological relatio...

The centrepiece of this paper is a normal form for primitive elements which facilitates the use of induction arguments to prove properties of primitive elements. The normal form arises from an elementary algorithm for constructing a primitive element p in F(x, y) with a given exponent sum pair (X, Y ), if such an element p exists. Several results concerning the primitive elements of F(x, y) are...

Using an appropriate notion of equivalence, those classical Hamiltonian systems which admit a first integral of motion polynomial of degree one in momentum are classified. The classification is effected by means of finding a normal form for a skew-symmetric matrix under the action of orthogonal symmetry.

Although the history of a scientific discipline should be studied regardless of which year and anniversary it is, with an attention to the idea development, the interdependence of various topics and problems etc., a jubilee can represent a good opportunity to remind some important events that influenced the forthcoming development, or to find some new and unnoticed relations. Coincidentally, in...

Let f(x 1 ; : : : ; x n ) = _ I2F ^ i2I x i and g(x 1 ; : : : ; x n ) = _ I2G ^ i2I x i be a pair of dual monotone irredundant disjunctive normal forms, where F and G are the sets of the prime implicants of f and g, respectively. For a variable x i ; i = 1; : : : ; n, let i = #fI 2 F ji 2 Ig=jF j and i = #fI 2 Gji 2 Ig=jGj be the frequencies with which x i occurs in f and g. It is easily seen t...

Combinatorial and learnability results are proven for projective disjunctive normal forms, a class of DNF expressions introduced by Valiant. Dedicated to Prof. Peter Hammer on the occasion of his 70th birthday.

This paper investigates ways to reduce redundancy in forbidding sets for language forbidding-enforcing systems. A language forbidding set disallows combinations of subwords in a word, while permitting the presence of some parts of these combinations. Since a forbidding set is a potentially infinite set of finite sets of words, finding normal forms for forbidding sets is interesting from a combi...

We present the definition and a normal form of a class of operators on sets of natural numbers which generalize the enumeration operators.

—In this paper, we examine and compare de Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms in fuzzy settings. This generalizes papers of Turksen on the subject of Boolean-normal forms.

Heap-based data structures play an important role in modern programming concepts. However standard verification algorithms cannot cope with infinite state spaces as induced by these structures. A common approach to solve this problem is to apply abstraction techniques. Hyperedge replacement grammars provide a promising technique for heap abstraction as their production rules can be used to part...