Model-Based Diagnosis (MBD) approaches often yield a large number of diagnoses, severely limiting their practical utility. This paper presents a novel active testing approach based on MBD techniques, called FRACTAL (FRamework for ACtive Testing ALgorithms), which, given a system description, computes a sequence of control settings for reducing the number of diagnoses. The approach complements probing, sequential diagnosis, and ATPG, and applies to systems where additional tests are restricted to setting a subset of the existing system inputs while observing the existing outputs. This paper evaluates the optimality of FRACTAL, both theoretically and empirically. FRACTAL generates test vectors using a greedy, next-best strategy and a low-cost approximation of diagnostic information entropy. Further, the approximate sequence computed by FRACTAL’s greedy approach is optimal over all poly-time approximation algorithms, a fact which we confirm empirically. Extensive experimentation with ISCAS85 combinational circuits shows that FRACTAL reduces the number of remaining diagnoses according to a steep geometric decay function, even when only a fraction of inputs are available for active testing.

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generation (ATPG) and Model-Based Diagnosis (MBD) into a framework called Fractal (FRamework for ACtive Testing ALgorithms). Apart from the inputs and outputs that connect a system to its environment, in active testing we consider additional input variables to which a sequence of test vectors can be supplied. We address the computationally hard problem of computing optimal control assignments (as defined in Fractal) in terms of a greedy approximation algorithm called Fractal G. We compare the decrease in the number of remaining minimal cardinality diagnoses of Fractal G to that of two more Fractal algorithms: Fractal ATPG and Fractal P. Fractal ATPG is based on ATPG and sequential diagnosis while Fractal P is based on probing and, although not an active testing algorithm, provides a baseline for comparing the lower bound on the number of reachable diagnoses for the Fractal algorithms. We empirically evaluate the trade-offs of the three Fractal algorithms by performing extensive experimentation on the ISCAS85/74XXX benchmark of combinational circuits. 1.

The goal of testing is to distinguish between a number of hypotheses about a system—for example, different diagnoses of faults— by applying input patterns and verifying or falsifying the hypotheses from the observed outputs. Optimal distinguishing tests (ODTs) are those input patterns that are most likely to distinguish between hypotheses about non-deterministic systems. Finding ODTs is practically important, but it amounts in general to determining a ratio of model counts and is therefore computationally very expensive. In this paper, we present a novel approach to constraint-based ODT generation, which uses structural properties of the system to limit the complexity of computation. We first construct a compact graphical representation of the testing problem via compilation into decomposable negation normal form. Based on this compiled representation, we show how one can evaluate distinguishing tests in linear time, which allows us to efficiently determine an ODT. Experimental results from a real-world application show that our method can compute ODTs for instances that were intractable for previous approaches.

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The goal of testing is to discriminate between multiple hypotheses about a system—for example, different fault diagnoses—by applying input patterns and verifying or falsifying the hypotheses from the observed outputs. Definitely discriminating tests (DDTs) are those input patterns that are guaranteed to discriminate between different hypotheses of non-deterministic systems. Finding DDTs is important in practice, but can be very expensive ( ∑p 2-complete). Even more challenging is the problem of finding a DDT that minimizes the cost of the testing process, i.e., an input pattern that can be most cheaply enforced and that is a DDT. This paper addresses both problems. We show how we can transform a given problem into a Boolean structure in decomposable negation normal form (DNNF), and extract from it a Boolean formula whose models correspond to DDTs. This allows us to harness recent advances in both knowledge compilation and satisfiability for efficient and scalable DDT computation in practice. Furthermore, we show how we can generate a DNNF structure compactly encoding all DDTs of the problem and use it to obtain a cost-optimal DDT in time linear in the size of the structure. Experimental results from a realworld application show that our method can compute DDTs in less than 1 second for instances that were previously intractable, and cost-optimal DDTs in less than 20 seconds where previous approaches could not even compute an arbitrary DDT.