Most current systems for mechanical program verification are not fully automatic, since the user himself must provide the intermediate inductive assertions. This paper describes an interactive computer program, called ADI, which automatically generates the needed inductive assertions. ADI is also able to extend partial loop assertions supplied by the user to form complete assertions. The implementation (written in QLISP and INTERLISP) is based on both the algorithmic and the heuristic approaches introduced by Katz and Manna in "Logical Analysis of Programs" [25]. For the algorithmic subsystem ADI includes: Difference Equations Constructor, Difference Equations Solver, and Invariants from Conditional Statements Generator. The heuristic subsystem includes: Exit Rules Package, Bounding Variables Component, Strengthening Executer, Weakening Executer, and a Heuristic Invariant Matcher-which is the actual implementation of two new heuristics, MATCHPQ and MATCHPT. ADI is a small step toward interactive, practical program verification.

Recent developments in modern control theory and high-speed computation techniques have enabled extensive treatment of complex processes. A method is presented for building a model of an R& D process utilizing the state space approach. The specific model described in this paper contains 21 state variables and a control vector of 6 components. Its formulation leads to the Mayer's problem with inequality constraints imposed on the control vector. An algorithm based on the adjoint system technique is used for simultaneous optimization and simplification. The computation for the preceding model lasts 2.5 min and is completed within 5 iterations. It results in an improvement factor of three for the chosen index of performance. Simplification of the model reduces the 21 state variables and 6 control components into 1 state variable and 1 control component.