A sequential machine for which any input sequence of a specified length is a distinguishing sequence is said to be definitely diagnosable. A method is developed to obtain for any arbitrary sequential machine a corresponding machine which contains the original one and which is definitely diagnosable. Similarly, these techniques are applied to embed machines which are not information lossless of finite order, or which do not have the finite-memory property, into machines which contain either of these properties. Simple and systematic techniques are presented for the construction, and the determination of the length, of the distinguishing sequences of these machines. Efficient fault-detection experiments are developed for machines possessing certain special distinguishing sequences. A procedure is proposed for the design of sequential machines such that they will possess these special sequences, and for which short fault-detection experiments can be constructed.

It is shown that the cycles sets of a linear sequential machine with a constant input having no stable state, are derivable from the cycle sets of that same linear sequential machine with a constant 0 input. It is shown that the level sets are independent of the input. A synthesis procedure and an example are presented. The objective of this short paper is to show the relation between the cycle set and level set of a linear sequential autonomous circuit and the cycle set and level set of a linear sequential circuit with a constant input. It was shown Srinivasan [1] that in response to a constant input, the cycle set (C) obtained, is exactly that obtained when another input was applied repetitively, provided that for both these inputs, there exists a stable state (under an input, the next state equals the present state). We ask now if the levels sets (L) are also identical and, more important, what is the state graph of a linear sequential circuit in response to a constant input under which no stable state exists. The parameters cycle sets (number and length of cycles) [2] and level sets (number of states per level in a tree) [3] are examined to see if a constant input will alter them; only the cycle sets are altered, if at all, by a constant input.

In this short paper it is shown how some simple concepts of group theory are used in the analysis of singular linear sequential machines: specifically it is shown that a set of states called the junction states form a group and more important a subgroup of the group (the set of junction states which belongs to the set of states mapping into the 0 state after 1 unit of time) plays a fundamental role in its relation to synthesis.