Analytics of Condition-Effect Rules

This thesis studies properties such as confluence and termination for a rule model with condition-effect rules. A rule model is first defined and the complexity of solving these problems is analysed. Analysis of both confluence and termination shows that they are PSPACE-complete for our rule model. We give algorithms for testing these properties. We also study certain syntactic and structural restrictions under which these problems become easier and can be solved in polynomial time for practical purposes

A More General Theory of Diagnosis from First Principles

Model-based diagnosis has been an active research topic in different communities including artificial intelligence, formal methods, and control. This has led to a set of disparate approaches addressing different classes of systems and seeking different forms of diagnoses. In this paper, we resolve such disparities by generalising Reiter's theory to be agnostic to the types of systems and diagnoses considered. This more general theory of diagnosis from first principles defines the minimal diagnosis as the set of preferred diagnosis candidates in a search space of hypotheses. Computing the minimal diagnosis is achieved by exploring the space of diagnosis hypotheses, testing sets of hypotheses for consistency with the system's model and the observation, and generating conflicts that rule out successors and other portions of the search space. Under relatively mild assumptions, our algorithms correctly compute the set of preferred diagnosis candidates. The main difficulty here is that the search space is no longer a powerset as in Reiter's theory, and that, as consequence, many of the implicit properties (such as finiteness of the search space) no longer hold. The notion of conflict also needs to be generalised and we present such a more general notion. We present two implementations of these algorithms, using test solvers based on satisfiability and heuristic search, respectively, which we evaluate on instances from two real world discrete event problems. Despite the greater generality of our theory, these implementations surpass the special purpose algorithms designed for discrete event systems, and enable solving instances that were out of reach of existing diagnosis approaches

Diagnosers and diagnosability of succinct transition systems

Reasoning about the knowledge of an agent is an important problem in many areas of AI. For example in diagnosis a basic question about a system is whether it is possible to diagnose it, that is, whether it is always possible to know whether a faulty beha

Diagnosers and diagnosability of succinct transition systems

Reasoning about the knowledge of an agent is an important problem in many areas of AI. For example in diagnosis a basic question about a system is whether it is possible to diagnose it, that is, whether it is always possible to know whether a faulty behavior has occurred. In this paper we investigate the complexity of this diagnosability problem and the size of automata that perform diagnosis. There are algorithms for testing diagnosability in polynomial time in the number of states in the system. For succinct system representations, which may be exponentially smaller than the state space of the system, the diagnosability problem is consequently in EXPTIME. We show that this upper bound is not tight and that the decision problem is in fact PSPACE-complete. On-line diagnosis can be carried out by diagnosers which are automata that recognize faulty behavior. We show that diagnosers in the worst case have a size that is exponential in the number of states, both for explicit and succinct system representations. This is a consequence of the diagnoser having to maintain beliefs about the state of the system.

Diagnosers and Diagnosability of Succinct Transition Systems

Reasoning about the knowledge of an agent is an important problem in many areas of AI. One of them is diagnosis/abduction where a basic question about a system is whether it is possible to diagnose it, that is, whether it is always possible to know whether the system has exhibited an erroneous behavior. In this paper we investigate the complexity of this diagnosability problem (existence of diagnosers) and the size of diagnosers. There are algorithms for testing diagnosability in polynomial time in the number of states in the system. Hence the decision problem for succinct representations is in EXPTIME. We show that this upper bound is not tight and that the decision problem is PSPACE-complete. On-line diagnosis can be carried out by diagnosers which are automata that recognize faulty behavior. We show that diagnosers in the worst case have a size that is exponential in the number of states, both for explicit and succinct system representations. This is a consequence of the diagnoser having to maintain beliefs about the state of the system.

Time Decomposition for Diagnosis of Discrete Event Systems

Artificial intelligence diagnosis is a research topic of knowledge representation and reasoning. This work addresses the problem of on-line model-based diagnosis of Discrete Event Systems (DES). A DES model represents state dynamics in a discrete manner. This work concentrates on the models whose scales are finite, and thus uses finite state machines as the DES representation. Given a flow of observable events generated by a DES model, diagnosis aims at deciding whether a system is running normally or is experiencing faulty behaviours. The main challenge is to deal with the complexity of a diagnosis problem, which has to monitor an observation flow on the fly, and generate a succession of the states that the system is possibly in, called belief state. Previous work in the literature has proposed exact diagnosis, which means that a diagnostic algorithm attempts to compute a belief state at any time that is consistent with the observation flow from the time when the system starts operating to the current time. The main drawback of such a conservative strategy is the inability to follow the observation flow for a large system because the size of each belief state has been proved to be exponential in the number of system states. Furthermore, the temporal complexity to handle the exact belief states remains a problem. Because diagnosis of DES is a hard problem, the use of faster diagnostic algorithms that do not perform an exact diagnosis is often inevitable. However, those algorithms may not be as precise as an exact model-based diagnostic algorithm to diagnose a diagnosable system. This Thesis has four contributions. First, Chapter 3 proposes the concept of simulation to verify the precision of an imprecise diagnostic algorithm w.r.t. a diagnosable DES model. A simulation is a finite state machine that represents how a diagnostic algorithm works for a particular DES model. Second, Chapter 4 proposes diagnosis using time decomposition, and studies window-based diagnostic algorithms, called Independent-Window Algorithms (IWAs). IWAs only diagnose on the very last events of the observation flow, and forget about the past. The precision of this approach is assessed by constructing a simulation. Third, Chapter 5 proposes a compromise between the two extreme strategies of exact diagnosis and IWAs. This work looks for the minimum piece of information to remember from the past so that a window-based algorithm ensures the same precision as using the exact diagnosis. Chapter 5 proposes Time-Window Algorithms (TWAs), which are extensions to IWAs. TWAs carry over some information about the current state of the system from one time window to the next. The precision is verified by constructing a simulation. Fourth, Chapter 6 evaluates IWAs and TWAs through experiments, and compares their performance with the exact diagnosis encoded by Binary Decision Diagrams (BDD). Chapter 6 also examines the impact of the time window selections on the performance of IWAs and TWAs