Abstract—A system is linear if and only if it is zero-state linear, zero-input linear, and its input-output state equation has the decompostion property. In this note, it is shown that zero-state linearity is sufficient to imply that the set of states accessible from the zero state can be made into a vector space over the output field and the zeroinput response is a homomorphism on this vector space to the output space of the system. An application of the theorem to finite-state systems is given.

The problem considered in this paper is the design of a checking experiment which will determine from observation of input-output behavior whether a sequential switching circuit is operating correctly. An input sequence is applied to the circuit, and the output sequence is observed and compared to the correct output sequence which has been determined from the state table corresponding to the correctly operating circuit. The sequential machines under consideration here must be 1) strongly connected, 2) reduced, and 3) have a distinguishing sequence [1]. The malfunctions which occur in the circuit are assumed to be those which do not increase the number of states in the circuit. In Hennie [1], a general synthesis procedure is proposed for checking experiments on machines in the class defined previously. The procedure to be proposed here is a modification of that procedure for which the upper bound on the length is reduced. Familiarity with at least the first portion of Hennie [1] on the synthesis of checking experiments for machines having distinguishing sequences is assumed.

There are several experiences proving a linear relationship between information content of signs or events and reaction or perception time of the human operator (fig. l,2). As information is a function of probability there must be a convergence, called informational accomodation, of subjective to objective information if the (subjective) probability approaches the (objective) frequency. The speed of this process is correlated with intelligence, measured by success at school (average grades). The information of a sign or event multiplied by its frequency is called its striking valueA_i. It is shown, that the estimationss_iof frequencies equal the relative striking valuesa_i, even beyondh = 1/e \approx37% ifSsare not too aged, intelligent or experienced in giving estimates (fig.3). Other experiences show the influence of thea_ieven during the process of informational accommodation (fig.4,5).