The consecutive retrieval (CR) property has been defined as the property of a query that can be answered by the retrieval of consecutive records in a file. In this correspondence we add some observations about boundary conditions to Gosh's study of the CR property.

This correspondence demonstrates an improvement on Winogard's algorithm for inner products as applied to the multiplication of two matrices.

This work is a solution to the generalization of the by now classical problem of Minsky, namely, the firing squad problem.

The inversion process which entails the interchange of two adjacent elements in a list is fundamental to most practical sorting algorithms.Consequently, one can utilize the inversions associated with a given permutation as its measure of complexity. To this end a recurrence relation is established.

A one-dimensional array of finite-state machines is being considered as a model for sequence replication. The authors consider the initial state of the first k machines in the array as representing the sequence of k symbols to be replicated along the array. A construction scheme is developed which allows for such replication to take place. It is also shown that the speed of replication approaches synchronous speed.

In this paper the construction of a switching network capable of n !-permutation of its n input terminals to its n output terminals is described. The building blocks for this network are binary cells capable of permuting their two input terminals to their two output terminals. The number of cells used by the network is 〈 n · log 2 n - n + 1〉 = Σ n k =1 〈log 2 k 〉. It could be argued that for such a network this number of cells is a lower bound, by noting that binary decision trees in the network can resolve individual terminal assignments only and not the partitioning of the permutation set itself which requires only 〈log 2 n !〉 = 〈Σ n k =1 log 2 k 〉 binary decisions. An algorithm is also given for the setting of the binary cells in the network according to any specified permutation.

No abstract available.

Abstract—A class of networks is described that has the capability of permuting in an arbitrary manner a set of n digital input lines onto a set of n digital output lines. The circuitry of the networks is arranged in cellular form, i. e., in a two-dimensional iterative pattern with mainly local intercell connections, where the basic cell behaves as a reversing switch with a single memory flip-flop. Various network forms are described, differing in the number of cells needed, in the shape of the array, and in the length and regularity of intercell connections. Also discussed are some ways of setting up the array to achieve a desired permutation.