We propose the following computational assumption: in general if we try to compress the depth of a circuit family (parallel time) more than a constant factor we will suffer super-quasipolynomial blowup in the size (number of processors). This assumption is only slightly stronger than the popular assumption about the robustness of NC, and we observe that it has surprising consequences. Note also...

Any monotone Boolean function on a lattice can be described by the set of its minimal 1 values. If a lattice is given as a concept lattice, this set can be represented by the set of minimal hypotheses of a classification context. Enumeration of minimal hypotheses in output polynomial time is shown to be impossible unless P = NP, which shows that dualization of monotone functions on lattices wit...

Despite significant research on state-space reductions, the poor scalability of model checking for reasoning about behavioral models of large, complex systems remains the chief obstacle to its broad acceptance. One strategy for making further progress is to exploit characteristics of classes of systems to develop domain-specific reductions. In this paper, we identify a structural property of sy...

Fagin et al. characterized those symmetric Boolean functions which can be computed by small AND/OR circuits of constant depth and unbounded fan-in. Here we provide a similar characterization for d-perceptrons | AND/OR circuits of constant depth and unbounded fan-in with a single MAJORITY gate at the output. We show that a symmetric function has small (quasipolynomial, or 2 log O(1) n size) d-pe...

In his well-known paper dealing with the construction of the injective hull of a metric space Isbell introduced the concept of an endpoint of a (compact) metric space. In the present article we introduce similarly the notion of an endpoint in a (joincompact) T0-quasi-metric space. It turns out that in a (joincompact) T0-quasi-metric space there is a dual concept which we shall call a startpoint...

The object of the present paper is to study quasi-conformally flat generalized Sasakian-space-forms. Also we study quasi-conformally semisymmetric generalized Sasakian-space-forms. As a consequence of the results, we obtain some important corollaries.

Let H d (t ≥ −d, t > −3) be the reproducing kernel Hilbert space on the unit ball B d with kernel k(z, w) = 1 (1− 〈z, w〉)d+t+1 . We prove that if an ideal I ⊳ C [z1 , . . . , zd] (not necessarily homogeneous) has what we call the approximate stable division property, then the closure of I in H d is p-essentially normal for all p > d. We then show that all quasi homogeneous ideals in two variabl...

Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius t = 1 or dimension n = 1, 2. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the best alternative to the perfect codes. In this paper we firstly highlight the relationships between subset sums, Cayley graphs, and Lee linear codes and present...

We study the coarse geometry of the Teichmüller space of a compact orientable surface in the Teichmüller metric. We describe when this admits a quasi-isometric embedding of a euclidean space, or a euclidean half-space. We prove quasi-isometric rigidity for Teichmüller space of a surface of complexity at least 2: a result announced independently by Eskin, Masur and Rafi. We deduce that, apart fr...