This paper presents a system that automatically refines the theory expressed in the function-free first-order logic. Our system can efficiently correct multiple faults in both the concept and subconcepts of the theory, given only the classified examples of the concept. It can refine larger classes of theory than existing systems can since it has overcome many of their limitations. Our system is based on a new combination of an inductive and an explanation-based learning algorithms, which we call the biggest-first multiple-example EBL (BM-EBL). From a learning perspective, our system is an improvement over the FOIL learning system in that our system can accept a theory as well as examples. An experiment shows that when our system is given a theory that has the classification error rate as high as 50%, it can still learn faster and with more accuracy than when it is not given any theory.

The single fault model is invalid in many cases. However, it is very difficult to generate tests for all multiple faults since an m-line circuit may have 3m --1 multiple faults. In this paper, we describe a method for generating tests for combinational circuits with multiple stuck-at faults. An input vector is a test for a fault on a target line, if it find the target line to be fault-free in the presence of undetected or undetectable lines. The test is called a robust test for fault on a target line. It is shown that the sensitizing input-pair for a completely single sensitized path can be a robust test-pair. The method described here consists of two procedures. We label these as SINGLE_SEN" procedure and DECISION" procedure. SINGLE_SEN generates a single sensitized path including a target line on it by using a PODEM-like method which uses a new seven-valued calculus. DECISION determines by utilizing the method proposed by H. Cox and J. Rajski whether the single sensitizing input-pair generated by the SINGLE_SEN is a robust test-pair. By using these two procedures the described method generates robust test-pairs for the combinational circuit with multiple stuck-at faults. Finally, we demonstrate by experimental results on the ISCAS85 benchmark circuits that SINGLE_SEN is effective for an algorithmic multiple fault test generation for circuits not including many XOR gates.