Modular Grammars and Splitting of Catamorphisms

An abstract context-free grammar can be viewed as a system of polynomial functors. The initial algebra of this functor coincides with its least fixed-point; and this fixed-point can be computed by a method of substitution using Bek\`{\i}c theorem. By doing so the system of polynomial functors is transformed into a related system of regular functors. We introduce a splitting operation on algebras producing an algebra for the resulting system of regular functors from an algebra of the original system of polynomial functors. This transformation preserves the interpretation function (catamorphism). The end result is a class of (extended) abstract context-free grammars, associated with regular functors. This class seems to be well-adapted to the modular design of domain-specific embedded languages

Polynomial Algorithms for the Synthesis of Bounded Nets

The so-called synthesis problem for nets, which consists in deciding whether a given graph is isomorphic to the case graph of some net, and then constructing the net, has been solved in the litterature for various types of nets, ranging from elementary nets to Petri nets. The common principle for the synthesis is the idea of regions in graphs, representing possible extensions of places in nets. However, no practical algorithm has been defined so far for the synthesis. We give here explicit algorithms solving in polynomial time the synthesis problem for bounded nets from regular languages or from finite automata

The Synthesis Problem for Elementary Net Systems is NP-Complete

The so-called synthesis problem consists in deciding for a class of nets whether a given graph is isomorphic to the case graph of some net and then constructing the net. This problem has been solved for various classes of nets, ranging from elementary nets to Petri nets. The general principle is to compute regions in the graph, i.e. subsets of nodes liable to represent extensions of places of an associated net. The naive method of synthesis which relies on this principle leads to exponential algorithms for an arbitrary class of nets. In an earlier study, we gave algorithms that solve the synthesis problem in polynomial time for the class of bounded Petri nets. We show here that in contrast the synthesis problem is indeed NP-complete for the class of elementary nets. This result is independent from the results of Kunihiko Hiraishi, showing that both problems of separation and inhibition by regions at a given node of the graph are NP-complete

Representations of Reversible Automata and State Graphs of Vector Addition Systems

Using the interpretation of a place of a vector addition system as a synchronic constraint we derive a characterization of the state graphs of vector addition systems as the maximal quotients of polyhedral automata. We give a classification of the representations of reversible automata (automata in which events are local bijections on states) as full subgraphs of Schreier graphs. We describe the computation of the canonical representation of a commutative automaton (automaton that fully embedds in the Cayley graph of an abelian group). We suggest on that basis an algorithm to decide whether a finite automaton is isomorphic to the state graph of a vector addition system. The correction of this algorithm however relies on the conjecture that the state graphs of vector addition systems are torsion-free

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, and a decentralization scheme for this model. 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

A symbolic algorithm for the synthesis of bounded Petri nets

This paper presents an algorithm for the synthesis of bounded Petri nets from transition systems. A bounded Petri net is always provided in case it exists. Otherwise, the events are split into several transitions to guarantee the synthesis of a Petri net with bisimilar behavior. The algorithm uses symbolic representations of multisets of states to efficiently generate all the minimal regions. The algorithm has been implemented in a tool. Experimental results show a significant net reduction when compared with approaches for the synthesis of safe Petri nets.Peer ReviewedPostprint (author's final draft

Opacité des artefacts d'un système workflow

International audienceA property (of an object) is opaque to an observer when he or she cannot deduce the property from its set of observations. If each observer is attached to a given set of properties (the so-called secrets), then the system is said to be opaque if each secret is opaque to the corresponding observer. Opacity has been studied in the context of discrete event dynamic systems where technique of control theory were designed to enforce opacity. To the best of our knowledge, this paper is the first attempt to formalize opacity of artifacts in data-centric workflow systems. We motivate this problem and give some assumptions that guarantee the decidability of opacity. Some techniques for enforcing opacity are indicated.Une propriété d'un objet est dite opaque pour un observateur si celui-ci ne peut déduire que la propriété est satisfaite sur la base de l'observation qu'il a de cet objet. Supposons qu'un certain de nombre de propriétés (appelées secrets) soient attachées à chaque intervenant d'un système, nous dirons alors que le système lui-même est opaque si chaque secret d'un observateur lui est opaque: il ne peut percer aucun des secrets qui lui ont été attachés. L'opacité a été étudiée préalablement dans le contexte des systèmes à événements discrets où différents jeux d'hypothèses ont pu être identifiés pour lesquels on pouvait d'une part décider de l'opacité d'un système et d'autre part développer des techniques pour diagnostiquer et/ou forcer l'opacité. Ce papier constitue, à notre connaissance, la première contribution au problème de l'opacité des artefacts d'un système à flots de tâches (système workflow). Notre propos est par conséquent de formaliser ce problème en dégageant les hypothèses qui doivent être posées sur ces systèmes pour que l'opacité soit décidable. Nous indiquons quelques techniques pour assurer l'opacité d'un système

Yet Another Implementation of Attribute Evaluation

We introduce another item in the already large list of techniques for attribute evaluation. Our algorithm consists in computing attributes by reductions to normal forms using a transducer operating on tree encodings of a cyclic representation of zippers. A zipper is a data structure introduced by Gérard Huet for representing a subtree together with its context, i.e. it is a tree with a focus that points to some node inside it. We mention some potential applications of this representation of attribute grammars as zipper transformers

Avant-propos

International audienceForeword to the special issue of ARIMA Journal dedicated to CARI'14Avant propos au numéro spécial de la revue ARIMA dédié au CARI'14