Gianluca Torta

Model-Based diagnosis through OBDD compilation: a complexity analysis

Since it is known that Model-Based Diagnosis may suffer from a potentially exponential size of the search space, a number of techniques have been proposed for alleviating the problem. Among them, some forms of compilation of the domain model have been investigated. In the present paper we address the problem of evaluating the complexity of diagnostic problem solving when Ordered Binary Decision Diagrams are adopted for representing the normal and faulty behavior of the system to be diagnosed and the solution space. In particular we analyze the case of the diagnosis of static models that exhibit a directionality from inputs to outputs (an important example of this type of models is the class of combinatorial digital circuits). We show that the problem of determining the set of all diagnoses and of determining the minimum cardinality diagnoses can be solved in time and space polynomial with respect to the size of the OBDD encoding the domain model. These results hold regardless of the degree of system observability including whether observations are precise or uncertain. We then analyze the complexity of refining the set of diagnoses by making additional observations and by using a test vector for troubleshooting the system. In particular we show that in the latter case we lose the formal guarantee that the diagnosis can be performed in polynomial time with respect to the size of the compiled domain model.

Computing Minimum-Cardinality Diagnoses Using OBDDs

The paper addresses the problem of solving diagnostic problems by exploiting OBDDs (Ordered Binary Decision Diagrams) as a way for compactly representing the set of alternative diagnoses. In the MBD (Model Based Diagnosis) community it is indeed well known that the number of diagnoses can be exponential in the system size even when restricted to preferred diagnoses (e.g. minimal diagnoses). In particular, the paper presents methods and heuristics for efficiently encoding the domain theory of the system model in terms of an OBDD. Such heuristics suggest suitable ordering of the OBDD variables which prevents the explosion of the OBDD size for some classes of domain theories. Moreover, we describe how to solve specific diagnostic problems represented as OBDDs and report some results on the computational complexity of such process. Finally, we introduce a mechanism for extracting diagnoses with the minimum number of faults from the OBDD which represents the entire space of diagnoses. Experimental results are collected and reported on a model representing a simplified propulsion subsystem of a spacecraft.

COMPACT DIAGNOSES REPRESENTATION IN DIAGNOSTIC PROBLEM SOLVING

The paper addresses the problem of finding a compact representation of the diagnoses within a model‐based approach to diagnosis. To this end, we introduce the notion of scenario, a special kind of CNF formula over the component variables, which can be used to encode a large number of diagnoses using the same amount of space needed for encoding just a single diagnosis. We show how the solutions to a diagnostic problem can be computed as sets of scenarios by presenting first an exhaustive algorithm and then an efficient algorithm, which exploits probabilistic information to restrict the result set to preferred scenarios. Finally, we discuss the issue of how to efficiently extract preferred diagnoses from sets of scenarios and characterize a class of system models for which our techniques perform particularly well. Concepts and algorithms introduced in the paper have been tested within the prototype of the diagnostic agent of a space robotic arm; resulting statistics are reported and critically discussed.

On the use of OBDDs in model-based diagnosis: an approach based on the partition of the model

In this paper, we discuss how Ordered Binary Decision Diagrams (OBDDs) can be exploited for the computation of consistency-based diagnoses in model-based diagnosis. Since it is not always possible to efficiently encode the whole system model within a single OBDD, we propose to build a set of OBDDs, each one encoding a portion of the original model. For each portion of the model, we compute an OBDD encoding the set of local diagnoses; the OBDD encoding global diagnoses is then obtained by merging all the local-diagnoses OBDDs. Finally, minimal-cardinality diagnoses can be efficiently computed and extracted. The paper reports formal results about soundness, completeness and computational complexity of the proposed algorithm. Thanks to the fact that encoding diagnoses is in general much simpler than encoding the whole system model, this approach allows for the successful computation of global diagnoses even if the system model could not be compiled into a single OBDD. This is exemplified referring to a challenging combinatorial digital circuit taken from the ISCAS85 benchmark.

Explaining interdependent action delays in multiagent plans execution

In this paper we address the problem of diagnosing the execution of Multiagent Plans with interdependent action delays. To this end, we map our problem to the Model-Based Diagnosis setting, and solve it by devising a novel modeling and reasoning method to infer preferred diagnoses based on partial observation of the start and end times of plan actions. Interestingly, we show that the kind of problem we address can be seen as an extension to the well known disjunctive temporal problem with preferences, augmented with a (qualitative) Bayesian network that models dependencies among action delays. An extensive set of tests performed with a prototype implementation on two different problem domains proves the feasibility of the proposed methodology.

A Multi-UAS Cooperative Mission Over Non-Segregated Civil Areas

In this paper we describe an experience of multi UAS civil mission management derived from our participation to the Industrial Research Project SMAT-F1, which focused on UAV missions for monitoring the territory for civil purposes. After describing the operational framework and the system architecture, we present in some detail the computer-supported design of a Mission Plan. The main focus of the article is on the flight experience made; in particular, we discuss the capabilities of the system to supply clear situation comprehension to the operators, the operation coordination issues and the operational results achieved during the mission. Finally, future extensions of mission planning support capabilities are discussed.

Diagnosing delays in multi-agent plans execution

The paper introduces the notion of Temporal Multi-Agent Plan (TMAP) and proposes a methodology, based on Simple Temporal Problems (STP), for detecting and diagnosing action execution delays. Actions are characterized by a finite set of behavioral modes, and each behavioral mode is a continuous interval of possible durations of the action. Nominal modes represent the expected durations, whereas faulty modes represent delays. Solving such diagnostic problems requires to find an assignment of modes to the actions that is consistent with the received observations and maximizes the likelihood of the delayed durations. An implementation of the approach and some preliminary experimental results are also discussed.

Parametric abstraction of behavioral modes for model-based diagnosis

In the present paper we address the problem of automatically abstracting the behavioral modes of system components on the basis of their indiscriminability in a diagnostic setting. Our goal is to abstract the original model in such a way as to provide more informative results to the supervisor, without loosing any relevant diagnostic information. This paper extends and complements existing work on automatic abstraction in MBD in different directions: we propose a framework to integrate different parameters (system observability, context restriction and status restriction) that can influence the abstractions; we develop an algorithm for the computation of abstractions that can take advantage of the symbolic compilation of the system model for giving both theoretical guarantees about the computational cost and good experimental performance on non-trivial domains; finally, we discuss the properties of the abstractions resulting by the combination of a-priori, user-provided abstractions with the ones automatically computed by our algorithm.

Formalizing the abstraction process in model-based diagnosis

Several theories have been proposed to capture the essence of abstraction. Among these, the KRA model offers a framework where a set of generic abstraction operators allows abstraction to be automated. In this paper we show how to describe component-based abstraction for the Model-Based Diagnosis task within the KRA framework, and we discuss the benefits of such a formalization. The clear and explicit partition of the system model into different levels required by KRA (going from the perception level up to the theory level) opens the way to explore richer and better founded kinds of abstraction to apply to the MBD task. Another noticeable advantage is that, by suitably personalizing the generic abstraction operators of KRA, the whole abstraction process, from the definition of abstract (macro)components to the computation of their behaviors starting from those of the ground components, can be performed automatically in such a way that important relationships between ground and abstract diagnoses are guaranteed.

Mixed-Initiative management of online calendars

Calendar management has been recognized as a complex, highly personal type of activity, which must take individual preferences and constraints into account in the formulation of satisfactory schedules. Current calendar management services are affected by two limitations: most of them lack any reasoning capabilities and thus cannot help the user in the management of tight schedules, which make the allocation of new tasks particularly challenging. Others are too impositive because they proactively schedule events without involving the user in the decision process.