Abstract A balanced switching network is a multistage switching network where all channel graphs G(α, β) (the union of all paths from the input switch α to the output switch β) are isomorphic. In this paper we: (1) derive some necessary conditions for the existence of balanced switching networks realizing various types of channel graphs, (2) solve completely the problem of the construction of 3‐stage balanced switching networks, and (3) give a recursive procedure to construct a class of balanced switching networks with more than three stages.

In this paper we present a new algorithm for merging two linearly ordered sets which requires substantially fewer comparisons than the commonly used tape merge or binary insertion algorithms. Bounds on the difference between the number of comparisons required by this algorithm and the information theory lower bounds are derived. Results from a computer implementation of the new algorithm are given and compared with a similar implementation of the tape merge algorithm.

This paper solves a problem relating to Turing machines arising in connection with the Busy Beaver logical game [21.Specifically, with the help of a computer program, the values of two very well-defined positive integers ~(3) and SH(3) are determined to b~ 6 and 21 respectively.The functions Y2(n) and SH(n), however, are noncomputable fune.tions.