No abstract available.

A formal verification system based on the use of automated reasoning techniques is described to validate fault tolerance. An extended Petri net representation, called a flow net, is described together with the theorem-proving implementation of a rule-based system for manipulating system descriptions. Examples taken from the literature are used to illustrate the representation and the capabilities of the formal verification system under development.>

Given N approximations to the zeros of an N th-degree polynomial, N circular regions in the complex z -plane are determined whose union contains all the zeros, and each connected component of this union consisting of K such circular regions contains exactly K zeros. The bounds for the zeros provided by these circular regions are not excessively pessimistic; that is, whenever the approximations are sufficiently well separated and sufficiently close to the zeros of this polynomial, the radii of these circular regions are shown to overestimate the errors by at most a modest factor simply related to the configuration of the approximations. A few numerical examples are included.