Classically, null designs were defined on the poset of subsets of a given finite set (boolean algebra). A null design is defined as a collection of weighted k-subsets such that the sum of the weights of ksubsets containing a t-subset is 0 for every t-subset, where 0 ≤ t < k ≤ n. Null designs are useful to understand designs or to construct new designs from a known one. They also deserve researc...

We consider finite colourings of products $$X_1\times X_2\times \cdot \times X_n$$ infinite sets and determine what is the minimal number colours a subproduct $$Y_1\times Y_2\times Y_n$$ subsets could achieve.

This paper describes a compositional approach to generate the labeled transition system representing the behavior of a Lotos program by repeatedly alternating composition and reduction operations on subsets of its processes. To restrict the size of the intermediate Ltss generated, we generalize to the Lotos parallel composition operator the results proposed in GS90], which consist in representi...

Let $D$ denote the distance matrix for an $n+1$ point metric space $(X,d)$. In case that $X$ is unweighted tree, sum of entries in $D^{-1}$ always equal to $2/n$. Such trees can be considered as affinely independent subsets Hamming cube $H_n$, and it was conjectured value $2/n$ minimal among all such subsets. this paper we confirm conjecture give a geometric interpretation our result which appl...

Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of SAT involve solving function as opposed to decision problems. Concrete examples include computing minimal unsatisfiable subsets, minimal correction subsets, pr...

The project first makes the attempt to formally address the problem of authorized data deduplication. Here apart from the traditional deduplication systems, the differential privileges of users are further considered in duplicate check besides the data itself. It shows the proposed authorized duplicate check scheme incurs minimal overhead compared to normal operations. The one of the advantage ...

Let $\mathscr {R}$ be an $\mathrm {NIP}$ expansion of $(\mathbb {R},<,+)$ by closed subsets $\mathbb {R}^n$ and continuous functions $f : \mathbb {R}^m \to {R}^n$. Then is generically locally o-minimal. This follows from a more general theorem on expansions compact groups, which itself result quotients definable sets in $\aleph _1$-saturated structures equivalence relations are both externally ...

Classical Multi-color Ramsey Theory pertains to the existence of monochromatic subsets of structured multicolored sets such that the subsets have a given property or structure. This paper examines a generalization of Ramsey theory that allows the subsets to have specified groupings of colors. By allowing more than one color in subsets, the corresponding minimal sets for finite cases tend to be ...