Abstract We define a linear graph to be a connected acyclic graph each of whose nodes is of degree one or two. We consider a flow problem in linear graphs in which a commodity flows from source nodes to sink nodes. Each source node has a specified value denoting an amount of a commodity to be disposed of and each sink node has a specified capacity denoting the maximum amount of the commodity it can absorb; edges are capable of carrying an arbitrary quantity of the commodity. A solution is a set of flows which transports the commodity from all source nodes to sink nodes without overfilling any sink. A solution is defined to be optimal if it is minimax, that is, the largest flow along any edge is as small as possible. We describe 0(n2) and 0(n) algorithms for finding optimal solutions.

This paper is concerned with the problem of realizing an arbitrary syndconous or asynchronous sequential machine using only monotone AMR (or decreasing) switching functions. It has been found that h ion always exist, that in the asynchronous case only nomal fundamental mode flow tables are considered. Univesl state assignmments resulting in monotone inceasing (or next-state funtions are characterized using the concept of an (i,j) completely separating system.

This paper gives a unified approach for describing various systematic ways of using built-in delays in normal fundamental mode circuits. The transition of the circuit from one total stable state to another is characterized by the constraints imposed upon the next-state functions, and the realization method is characterized by the conditions under which these constraints can be satisfied simultaneously.