Christophe Morvan

Diagnosability of pushdown systems

Partial observation of discrete-event systems features a setting where events split into observable and unobservable ones. In this context, the diagnosis of a discrete-event system consists in detecting defects from the (partial) observation of its executions. Diagnosability is the property that any defect is eventually detected. Not surprisingly, it is a major issue in practical applications. We investigate diagnosability for classes of pushdown systems: it is undecidable in general, but we exhibit reasonably large classes of visibly pushdown systems where the problem is decidable. For these classes, we furthermore prove the decidability of a stronger property: the bounded latency, which guarantees the existence of a uniform bound on the respond delay after the defect has occurred. We also explore a generalization of the approach to higher-order pushdown systems.

PETRI NET REACHABILITY GRAPHS: DECIDABILITY STATUS OF FIRST-ORDER PROPERTIES ∗

We investigate the decidability and complexity status of model-checking prob- lems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques.

Diagnosis and opacity problems for infinite state systems modeled by recursive tile systems

The 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.

Analysis of partially observed recursive tile systems

The 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. We consider recursive tile systems, which are infinite systems generated by a finite collection of finite tiles, a simplified variant of deterministic graph grammars. Recursive tile systems are expressive enough to capture classical models of recursive systems, such as the pushdown systems and the recursive state machines. They are infinite-state in general and therefore standard 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 opacity and diagnosability.

Test generation from recursive tiles systems

In this paper we explore test generation for Recursive Tiles Systems (RTS) in the framework of the classical ioco testing theory. The RTS model allows the description of reactive systems with recursion, and is very similar to other models like Pushdown Automata, Hyperedge Replacement Grammars or Recursive State Machines. We first present an off-line test generation algorithm for Weighted RTS, a determinizable sub-class of RTS, and second, an on-line test generation algorithm for the full RTS model. Both algorithms use test purposes to guide test selection through targeted behaviours.

Petri Net Reachability Graphs: Decidability Status of FO Properties

We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order, modal and pattern-based languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques.

A grammatical approach to data-centric case management in a distributed collaborative environment

This paper presents a purely declarative approach to artifact-centric case management systems. Each case is presented as a tree-like structure; nodes bear information that combines data and computations. Each node belongs to a given stakeholder, and semantic rules govern the evolution of the tree structure, as well as how data values derive from information stemming from the context of the node. Stakeholders communicate through asynchronous message passing without shared memory, enabling convenient distribution.

Active workspaces: distributed collaborative systems based on guarded attribute grammars

This paper presents a purely declarative approach to artifact-centric collaborative systems, a model which we introduce in two stages. First, we assume that the workspace of a user is given by a mindmap, shortened to a map, which is a tree used to visualize and organize tasks in which he or she is involved, with the information used for the resolution of these tasks. We introduce a model of guarded attribute grammar, or GAG, to help the automation of updating such a map. A GAG consists of an underlying grammar, that specifies the logical structure of the map, with semantic rules which are used both to govern the evolution of the tree structure (how an open node may be refined to a subtree) and to compute the value of some of its attributes (which derives from contextual information). The map enriched with this extra information is termed an active workspace. Second, we define collaborative systems by making the various users active workspaces communicate with each other. The communication uses message passing without shared memory thus enabling convenient distribution on an asynchronous architecture. We present some formal properties of the model of guarded attribute grammars, then a language for their specification and we illustrate the approach on a case study for a disease surveillance system.

Probabilistic regular graphs

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.

Petri Nets with Structured Data

This paper proposes Structured Data Nets (StDN), a Petri net extension that describes transactional systems with data. In StDNs, tokens are structured documents. Each transition is attached to a query, guarded by patterns, (logical assertions on the contents of its preset) and transforms tokens. We define StDNs and their semantics. We then consider their formal properties: coverability of a marking, termination and soundness of transactions. Unrestricted StDNs are Turing complete, so these properties are undecidable. We thus use an order on documents, and show that under reasonable restrictions on documents and on the expressiveness of patterns and queries, StDNs are well-structured transition systems, for which coverability, termination and soundness are decidable.