Low-dimensional k-ary n-cubes have been popular in recent multicomputers. These networks, however, suffer from high switching delays due to their high message distance. To overcome this problem, Dally has proposed a variation, called express k-ary n-cubes, with express channels that allow non-local messages to partially bypass clusters of nodes within a dimension. K-ary n-cubes are graph topolo...

In this paper, we present a strongly fault-tolerant design for the k-ary n-cube multiprocessor and examine its reconfigurability. Our design augments the k-ary n-cube with ( j ) n spare nodes; each set of j regular nodes is connected to a spare node and the spare nodes are interconnected as a ( j )-ary n-cube. Our approach utilizes the circuit-switched capabilities of the communication modules ...

An (n, a, b)-perfect double cube is a b × b × b sized n-ary periodic array containing all possible a × a × a sized n-ary array exactly once as subarray. A growing cube is an array whose cj × cj × cj sized prefix is an (nj, a, cj)-perfect double cube for j = 1, 2, . . ., where cj = n v/3 j , v = a 3 and n1 < n2 < · · ·. We construct the smallest possible perfect double cube (a 256×256×256 sized ...

The diierence among diierent topologies in interconnection networks is a debated issue among highly parallel machine designers, since opposing parameters innuence the network performance. This paper presents a new model, k-ary n-cube m-diags, which generalizes existing k-ary n-cube topologies to include hexagonal networks and their n-dimensional extensions. A performance analysis based on this ...

‎In 1970‎, ‎Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ Atti Accad‎. ‎Naz‎. ‎Lincei Rend‎. ‎Cl‎. ‎Sci‎. ‎Fis‎. ‎Mat‎. ‎Natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $IM$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎A group $G$ is said to have the $FM$...

The Semantic Web is a vision of the next generation Web, in which semantic markup will make Web resources more accessible to automatic processes. Description Logics (DLs) are of crucial importance to the development of the Semantic Web, where their role is to provide formal underpinnings and automated reasoning services for Semantic Web ontology languages such as DAML+OIL. In this paper, we sho...

The main purpose of this paper is to discuss the asymptotic behavior of the difference sq,k(P (n))−k(q−1)/2 where sq,k(n) denotes the sum of the first k digits in the q-ary digital expansion of n and P (x) is an integer polynomial. We prove that this difference can be approximated by a Brownian motion and obtain under special assumptions on P a Strassen’s type version of the law of the iterated...

In this note we study the linear symmetry group LS(f ) of a Boolean function f of n variables, that is, the set of all ∈ GLn(2) which leave f invariant, where GLn(2) is the general linear group on the field of two elements. The main problem is that of concrete representation: which subgroups G of GLn(2) can be represented as G= LS(f ) for some n-ary k-valued Boolean function f. We call such sub...