Criminal justice procedures admit process flow diagram representations, which in effect induce equivalences on the data available in public records. Interrogations of the data in the context of such diagrams induce further equivalences. A task for the engineer in the study of criminal justice systems is to develop data display capabilities that reconcile the requirements of these two forms of equivalences. The work reported herein describes all these concepts in detail and illustrates them for jurisdiction in St. Joseph and Marion Counties, State of Indiana.

Abstract—This paper states the necessary and sufficient conditions for the existence of a feedforward inverse for a feedforward linear sequential circuit and gives an implicit procedure for constructing such inverses. It then goes on to give the necessary and sufficient conditions for the existence of general inverses with finite delay and gives procedures for constructing a class of such inverses. The discussion considers both the transfer function matrix description and the structural matrix description of the linear sequential circuit, together with the complementary nature of the results obtained from these two viewpoints. Finally, a large part of the work is motivated by results and techniques which have been applied in the study of continuous-time linear dynamical systems and thus serves to point out the advantages which may accrue through simultaneous study of both continuous-time systems and linear sequential circuits.

A study of linear estimators that minimize the variance of the error squared is reported. A projection principle and a sufficiency test establish and verify minimality. When the signal process and the data process are jointly Gaussian, the problem is completely solved for unique absolutely minimizing operators, which are found to be a cascade of the classical minimum-mean-squared error estimator and an amplifier.