A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this en...

The Strong Perfect Graph Conjecture, suggested by Claude Berge in 1960, had a major impact on the development of graph theory over the last forty years. It has led to the definitions and study of many new classes of graphs for which the Strong Perfect Graph Conjecture has been verified. Powerful concepts and methods have been developed to prove the Strong Perfect Graph Conjecture for these spec...

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and ...

In this article, we present a characterization of basic graphs in terms of forbidden induced subgraphs. This class of graphs was introduced by Conforti, Cornuéjols and Vušković [3], and it plays an essential role in the announced proof of the Strong Perfect Graph Conjecture by Chudnovsky, Robertson, Seymour and Thomas [2]. Then we apply the Reducing Pseudopath Method [13] to characterize the su...

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...

We compare three notions of knowledge in concurrent system: memoryless knowledge, knowledge of perfect recall, and causal knowledge. Memoryless knowledge is based only on the current state of a process, knowledge of perfect recall can take into account the local history of a process, and causal knowledge depends on the causal past of a process, which comprises the information a process can obta...

The standard solution concept for perfect-information extensive form games is subgame perfect Nash equilibrium. However, humans do not always play according to a subgame perfect Nash equilibrium, especially in games where it is possible for all the players to obtain much higher payoffs if they place some trust in each other (and this trust is not violated). In this paper, we introduce a new sol...

The assessment of military information systems is an art form that has evolved substantially since the mid-1970s.1 Until then, national security assessments generally neglected information system issues. Such systems were either assumed to be “perfect” (i.e., providing perfect information with no time delays), capable of no more than secondor third-order effects, or totally irrelevant. When the...

We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the expectation value of wealth, buying insurance is only rational at a price that makes it irrational to sell insurance. There is no price that is beneficial to both the buyer and the seller of an ins...

We consider discounted and undiscounted stochastic games with perfect information in the form of a natural BWR-model with positions of three types: VB Black, VW White, VR Random. These BWR-games lie in the complexity class NP∩CoNP and contain the well-known cyclic games (when VR is empty) and Markov decision processes (when VB or VW is empty). We show that the BWR-model is polynomial-time equiv...