It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes. AMS classifications: Primary: 94A62, Secondary: 05B05.

We show that the number of satisfying assignments of a k-CNF formula is determined uniquely from the numbers of unsatisfying assignments for clause-sets of size up to ⌊log k⌋+ 2. The information of this size is also shown to be necessary. key words: combinatorial problems; SAT; k-CNF formula; counting; inclusion-exclusion

This note gives an explicit construction of the one-generated free domain semiring. In particular it is proved that the elements can be represented uniquely by finite antichains in the poset of finite strictly decreasing sequences of nonnegative integers. It is also shown that this domain semiring can be represented by sets of binary relations with union, composition and relational domain as op...

In this paper we present a new technique for visualizing multidimensional information. We describe objects of a higher dimensional information space as small closed free-form-surfaces in the visualization. The location, size and shape of these surfaces describe the original objects in information space uniquely. The underlying enhanced spring model is introduced. The technique is applied to two...

We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satis5es the “basic requirement for fuzzy reasoning”, proposed by Turksen and Tian (Fuzzy Sets and Systems 58 (1993) 3–40). We establish a...

The description of the error dynamics (30) in our paper [1] contains an omission that leads to some bounds used in the conditions of Theorem 8 and Corollary 2 in the paper to be incorrectly defined. In what follows, the correct error dynamics and the corresponding conditions are given. Instead of (30) in [1], the error dynamics are actually given by ė = m ∑ i=1 wi(z)[(Ai − LiC +MiAδi)e +Mi(Āδix̂...

Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...