Gap-deenability and the gap-closure operator were deened in FFK91]. Few complexity classes were known at that time to be gap-deenable. In this paper, we give simple characterizations of both gap-deenability and the gap-closure operator, and we show that many complexity classes are gap-deenable, including P #P , P #P1] , PSPACE, EXP, NEXP, MP, and BP P. If a class is closed under union, intersec...

In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of ahyper K-algebra, and we prove a ...

Triadic Formal Concept Analysis (3FCA) was introduced by Lehman and Wille almost two decades ago. And many researchers work in Data Mining and Formal Concept Analysis using the notions of closed sets, Galois and closure operators, closure systems, but up-to-date even though that different researchers actively work on mining triadic and n-ary relations, a proper closure operator for enumeration ...

Because antimatroid closure spaces satisfy the anti-exchange axiom, it is easy to show that they are uniquely generated. That is, the minimal set of elements determining a closed set is unique. A prime example is a discrete geometry in Euclidean space where closed sets are uniquely generated by their extreme points. But, many of the geometries arising in computer science, e.g. the world wide we...

background: the ductus arteriosus connects the main pulmonary trunk to the descending aorta. the incidence of isolated patent ductus arteriosus (pda) in full-term infants is about 1 in 2000. the amplatzer ductal occluder (ado) is recommended for pdas with sizes larger than 2 mm. in this procedure, we must confirm the ado position in pda by aortogram from the arterial line. the purpose of this s...

This paper concerns residuated lattice-ordered idempotent commutative monoids that are subdirect products of chains. An algebra of this kind is a generalized Sugihara monoid (GSM) if it is generated by the lower bounds of the monoid identity; it is a Sugihara monoid if it has a compatible involution ¬. Our main theorem establishes a category equivalence between GSMs and relative Stone algebras ...

The interest in a further pruning of the set of frequent patterns that can be drawn from real-life datasets is growing up. In fact, it is a quite survival reflex towards providing a manageably-sized and reliable knowledge. This fact is witnessed by the proliferation of what is called concise representation of frequent patterns. In this paper, we propose an exact concise representation that expl...