Constraint-Based Optimal Testing Using DNNF Graphs

Abstract

The goal of testing is to distinguish between a number of hypotheses about a system-for example, different diagnoses of faultsby 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.

Computing Cost-Optimal Definitely Discriminating Tests

“…This method is able to compute DDTs as a special case, and in that role exhibits much better performance than an earlier algorithm by Sachenbacher and Schwoon (2008) specialized for DDTs, as shown in (Schumann, Sachenbacher, and Huang 2009). Hence it represents the state of the art in DDT computation.…”

“…Heinz and Sachenbacher (2009) introduced optimal distinguishing tests (ODTs), which generalize DDTs by maximizing the ratio of distinguishing over non-distinguishing outcomes. An efficient method for computing ODTs was presented in (Schumann, Sachenbacher, and Huang 2009), based on encoding the ODT problem into a Boolean formula, and compiling the formula into a graph in decomposable negation normal form (DNNF) (Darwiche 2001;Darwiche and Marquis 2002). The DNNF allows efficient derivation of good upper bounds on ratios of model counts, which are then used to prune a systematic search for ODTs.…”

“…Hence it represents the state of the art in DDT computation. As also shown in (Schumann, Sachenbacher, and Huang 2009), however, it can still run out of memory on instances of moderate size, which can be explained by the fact that the final DNNF graph is computed based on a number of auxiliary DNNF graphs, and the compilation can require a multitude of auxiliary variables to be introduced, which leads to slower computation and higher memory requirements.…”

“…This representation is used to transform a quantified Boolean formula defining the DDT problem into a SAT problem that can be solved using an existing SAT solver. This leads to a significantly more efficient method for computing DDTs compared to that of (Schumann, Sachenbacher, and Huang 2009).…”

Propagation complete encodings of smooth DNNF theories

“…There are also approaches that resolve a conflict by extending the instance by clauses that contain auxiliary variables new in the instance by lazily expanding a corresponding part of a large known encoding of the constraint [3,20]. Specific situations, where a CNF encoding of a DNNF is suitable for use in a SAT instance are described in [29,32].…”