41 research outputs found
On detectability of labeled Petri nets and finite automata
Detectability is a basic property of dynamic systems: when it holds an observer can use the current and past values of the observed output signal produced by a system to reconstruct its current state. In this paper, we consider properties of this type in the framework of discrete-event systems modeled by labeled Petri nets and finite automata. We first study weak approximate detectability. This property implies that there exists an infinite observed output sequence of the system such that each prefix of the output sequence with length greater than a given value allows an observer to determine if the current state belongs to a given set. We prove that the problem of verifying this property is undecidable for labeled Petri nets, and PSPACE-complete for finite automata. We also consider one new concept called eventual strong detectability. The new property implies that for each possible infinite observed output sequence, there exists a value such that each prefix of the output sequence with length greater than that value allows reconstructing the current state. We prove that for labeled Petri nets, the problem of verifying eventual strong detectability is decidable and EXPSPACE-hard, where the decidability result holds under a mild promptness assumption. For finite automata, we give a polynomial-time verification algorithm for the property. In addition, we prove that strong detectability is strictly stronger than eventual strong detectability for labeled Petri nets and even for deterministic finite automata
A new approach for diagnosability analysis of Petri nets using Verifier Nets
In this paper, we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a fixed bound of K event occurrences after the fault. We give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verifier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented
On detectability of labeled Petri nets and finite automata
We study detectability properties for labeled Petri nets and finite automata.
We first study weak approximate detectability (WAD) that implies that there
exists an infinite observed output sequence of the system such that each prefix
of the output sequence with length greater than a given value allows an
observer to determine if the current state belongs to a given set. We also
consider two new concepts called instant strong detectability (ISD) and
eventual strong detectability (ESD). The former property implies that for each
possible infinite observed output sequence each prefix of the output sequence
allows reconstructing the current state. The latter implies that for each
possible infinite observed output sequence, there exists a value such that each
prefix of the output sequence with length greater than that value allows
reconstructing the current state.
Results: WAD: undecidable for labeled Petri nets, PSPACE-complete for finite
automata ISD: decidable and EXPSPACE-hard for labeled Petri nets, belongs to P
for finite automata ESD: decidable under promptness assumption and
EXPSPACE-hard for labeled Petri nets, belongs to P for finite automata SD:
belongs to P for finite automata, strengthens Shu and Lin's 2011 results based
on two assumptions of deadlock-freeness and promptness ISD<SD<ESD<WD<WAD for
both labeled Petri nets and finite automataComment: 44 pages, 21 figure
The Complexity of Diagnosability and Opacity Verification for Petri Nets
International audienceDiagnosability and opacity are two well-studied problems in discrete-event systems. We revisit these two problems with respect to expressiveness and complexity issues. We first relate different notions of diagnosability and opacity. We consider in particular fairness issues and extend the definition of Germanos et al. [ACM TECS, 2015] of weakly fair diagnosability for safe Petri nets to general Petri nets and to opacity questions. Second, we provide a global picture of complexity results for the verification of diagnosability and opacity. We show that diagnosability is NL-complete for finite state systems, PSPACE-complete for safe Petri nets (even with fairness), and EXPSPACE-complete for general Petri nets without fairness, while non diagnosability is inter-reducible with reachability when fault events are not weakly fair. Opacity is ESPACE-complete for safe Petri nets (even with fairness) and undecidable for general Petri nets already without fairness
Diagnosis and Opacity Problems for Infinite State Systems Modeled by Recursive Tile Systems
International audienceThe analysis of discrete event systems under partial observation is an important topic, with major applications such as the detection of information flow and the diagnosis of faulty behaviors. These questions have, mostly, not been addressed for classical models of recursive systems, such as pushdown systems and recursive state machines. In this paper, we consider recursive tile systems, which are recursive infinite systems generated by a finite collection of finite tiles, a simplified variant of deterministic graph grammars (slightly more general than pushdown systems). Since these systems are infinite-state in general powerset constructions for monitoring do not always apply. We exhibit computable conditions on recursive tile systems and present non-trivial constructions that yield effective computation of the monitors.We apply these results to the classic problems of state-based opacity and diagnosability (off-line verification of opacity and diagnosability, and also run-time monitoring of these properties). For a decidable subclass of recursive tile systems, we also establish the decidability of the problems of state-based opacity and diagnosability
Twinâengined diagnosis of discreteâevent systems
Diagnosis of discrete-event systems (DESs) is computationally complex. This is why a variety of knowledge compilation techniques have been proposed, the most notable of them rely on a diagnoser. However, the construction of a diagnoser requires the generation of the whole system space, thereby making the approach impractical even for DESs of moderate size. To avoid total knowledge compilation while preserving efficiency, a twin-engined diagnosis technique is proposed in this paper, which is inspired by the two operational modes of the human mind. If the symptom of the DES is part of the knowledge or experience of the diagnosis engine, then Engine 1 allows for efficient diagnosis. If, instead, the symptom is unknown, then Engine 2 comes into play, which is far less efficient than Engine 1. Still, the experience acquired by Engine 2 is then integrated into the symptom dictionary of the DES. This way, if the same diagnosis problem arises anew, then it will be solved by Engine 1 in linear time. The symptom dic- tionary can also be extended by specialized knowledge coming from scenarios, which are the most critical/probable behavioral patterns of the DES, which need to be diagnosed quickly
Hyper Partial Order Logic
We define HyPOL, a local hyper logic for partial order models, expressing properties of sets of runs. These properties depict shapes of causal dependencies in sets of partially ordered executions, with similarity relations defined as isomorphisms of past observations. Unsurprisingly, since comparison of projections are included, satisfiability of this logic is undecidable. We then address model checking of HyPOL and show that, already for safe Petri nets, the problem is undecidable. Fortunately, sensible restrictions of observations and nets allow us to bring back model checking of HyPOL to a decidable problem, namely model checking of MSO on graphs of bounded treewidth