A Parametric Hierarchical Planner for Experimenting Abstraction Techniques

In Model-Based Diagnosis (MBD), the problem of computing a diagnosis in a strong-fault model (SFM) is computationally much harder than in a weak-fault model (WFM). For example, in propositional Horn models, computing the first minimal diagnosis in a weak-fault model (WFM) is in P but is NP-hard for strong-fault models. As a result, SFM problems of practical significance have not been studied in great depth within the MBD community. In this paper we describe an algorithm that renders the problem of computing a diagnosis in several important SFM subclasses no harder than a similar computation in a WFM. We propose an approach for efficiently computing minimal diagnoses for these subclasses of SFM that extends existing conflict-based algorithms like GDE (Sherlock) and CDA∗. Experiments on ISCAS85 combinational circuits show (1) inference speedups with CDA∗of up to a factor of 8, and (2) an average of 28% reduction in the average conflict size, at the price of an extra low-polynomial-time consistency check for a candidate diagnosis. 1 Modeling for Diagnostic Inference Model-based diagnosis (MBD), as formulated in terms of logic [Reiter, 1987], focuses on determining whether an assignment of failure status to a set of mode-variables is consistent with a system description and an observation (e.g., of sensor values). Hence, the diagnostic process consists of taking an observation OBS, and then inferring the failure-mode assignment (diagnosis) consistent with OBS. Within MBD, two broad classes of model types have been specified: weak-fault models WFM [de Kleer et al., 1992] and strong-fault models SFM [Struss and Dressler, 1989]. Traditionally, WFM has been considered to be computationally simple, and SFM computationally hard. Weakfault models describe a system only in terms of its normal (non-faulty) behaviour, whereas strong-fault models include a definition of some aspects of abnormal behaviour. Strongfault models can avoid violating physical rules (cf. [Struss and Dressler, 1989]), but at the cost of increased complexity: moving from a binary-valued model with n components (which is adequate for weak-fault models) to one withm+ 1 possible faulty values increases the maximum number of failure candidates from 2 to (m+ 1). In terms of worst-case complexity, finding the first minimal diagnosis for a Horn model in WFM can be done in polynomial time, but finding the next minimal diagnosis is NP-complete [Friedrich et al., 1990]. In contrast, inference in strong-fault models entails computing kernel diagnoses [de Kleer et al., 1992], which is a Σ2 -hard task and is known to be computationally intensive in practice; for example, kernel diagnoses are given by the prime implicants of the minimal conflicts [de Kleer et al., 1992]. Further, the average case complexity of reasoning in WFM versus SFM increases from poly-time in n (WFM) to exponential in n (SFM) [de Kleer et al., 1992]. Given this intractability associated with inference using SFM, we show that, by closer examination of SFM, there is a spectrum of model types, and corresponding inference complexities. We identify two main categories of SFM, which we call literal-based SFM, lSFM, and function-based SFM, fSFM, and show that lSFM has the same properties (including inference complexity) asWFM, whereas fSFM has the properties traditionally assigned to SFM. This paper is the first detailed analysis of SFM, to our knowledge, which exploits model structure for computational advantage. It demonstrates the spectrum of fault modeling choices available to the system designer, and the computational implications such choices impose on the resulting diagnostic inference. We propose a SFM algorithm that: (1) decomposes a strong-fault model into strong and weak sub-models; (2) computes diagnoses first in the “relaxed” weak sub-model; and then (3) discards any diagnosis which is not also a diagnosis in the strong sub-model. We identify classes of SFM in which the SFM diagnosis verification (step 3 above) can be done efficiently. Using ISCAS85 benchmark circuits, we have empirically demonstrated that: (1) our algorithm reduces the diagnosis computation time in CDA∗by up to a factor of 8; and (2) the average LTMS conflict size decreases (at the price of an extra consistency check, which has lowpolynomial or better time-complexity for several classes of propositional strong-fault models).