The polynomial hierarchy starts with familiar classes on level one: Σ1 = NP and Π1 = coNP. For all i ≥ 1, it includes two classes, Σi and Πi, which are defined as follows: Definition 2 Σk is the class of all problems such that there is a polynomial time computable F (·, ..., ·) and k polynomials p1(), ..., pk() such that x is a YES-instance⇔ ∃y1 ∈ {0, 1}1.∀y2 ∈ {0, 1}p2(|x|). . . . . . . ∀/∃ k ...

This concise text focuses on the Oxford Record Linkage Studies of factors associated with sudden infant death and the Foundation for the Study of Infant Death surveys of psychosocial stress experienced by bereaved parents. Its focus is on sudden infant deaths in Britain, but the authors make frequent reference to North American studies as well. The book begins with a brief history of sudden inf...

In this lecture, we will discuss the maxima problem defined as follows. Let (x1, y1) and (x2, y2) be two different points in R. We say that the former dominates the latter if x1 ≥ x2 and y1 ≥ y2 (note that the two equalities cannot hold simultaneously because these are two different points). Let P be a set of n points in R. A point p ∈ P is a maximal point of P if p is not dominated by any poin...

The difficulty here is to know which term M of type τ to use to instantiante the quantifier. This problem is not specific to linear logic but arises in all logics that permit quantification. The general idea is simply to postpone the choice of M , just as we postponed splitting the resources in the multiplicative rules. M , in effect, becomes a metavariable or logic variable or existential vari...

Considering two large surfaces far away from each other, it is clear that if each surface is subdivided into k elements, then computing k2 form factors to represent the exchange of energy between the two surfaces is an overkill. While the energy arriving at a surface must be represented accurately using many elements, when the surface is functioning as a light source, the variations in energy b...

In this lecture we will start the transition from C0 to C. In some ways, the lecture is therefore about knowledge rather than principles. The underlying issue that we are trying to solve in this lecture is nevertheless a deep one: how can a language support generic implementations of data structures that accomodate data elements of different types. The name polymorphism derives from the fact th...

Cet ouvrage de François Rastier présente une vue articulée de différents domaines de la linguistique – y compris le traitement automatique du langage – auxquels l’auteur a contribué. Par ses travaux antérieurs, la linguistique de corpus est l’angle d’attaque permettant des propositions, aussi bien épistémologiques qu’applicatives. François Rastier présente des cas concrets de méthodes applicati...

Consider a bilateral trading market where there is one potential buyer and one potential seller of an object. The value that the buyer and seller place on the object depends on the product’s quality, . In particular, assume the value to the buyer is vB and the value to the seller is vS : Assume that the quality of the good is uniformly distributed between 0 and 1, U [0; 1]: Tomake the problem i...