Catálogo de publicaciones - libros

We consider model-checking algorithms for durational probabilistic systems, which are systems exhibiting nondeterministic, probabilistic and discrete-timed behaviour. We present two semantics for durational probabilistic systems, and show how formulae of the probabilistic and timed temporal logic Ptctl can be verified on such systems. We also address complexity issues, in particular identifying the cases in which model checking durational probabilistic systems is harder than verifying non-probabilistic durational systems.

The finite π -calculus has an explicit set-theoretic functor-category model that is known to be fully abstract for strong late bisimulation congruence. We characterize this as the initial free algebra for an appropriate set of operations and equations in the enriched Lawvere theories of Plotkin and Power. Thus we obtain a novel algebraic description for models of the π -calculus, and validate an existing construction as the universal such model. The algebraic operations are intuitive, covering name creation, communication of names over channels, and nondeterminism; the equations then combine these features in a modular fashion. We work in an enriched setting, over a “possible worlds” category of sets indexed by available names. This expands significantly on the classical notion of algebraic theories, and in particular allows us to use nonstandard arities that vary as processes evolve. Based on our algebraic theory we describe a category of models for the π -calculus, and show that they all preserve bisimulation congruence. We develop a direct construction of free models in this category; and generalise previous results to prove that all free-algebra models are fully abstract.

We investigate a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of distinction . The key aspect of this model is to consider functors over the category of irreflexive, symmetric finite relations. The models previously proposed for the notions of “variables” and “names” embed faithfully in the new one, and initial algebra/final coalgebra constructions can be transferred from the formers to the latter. Moreover, the new model admits a definition of distinction-aware simultaneous substitutions. As a substantial application example, we give the first semantic interpretation of Miller-Tiu’s $FO\lambda^{\nabla}$ logic.

We show how parallel composition of higher-dimensional automata (HDA) can be expressed categorically in the spirit of Winskel & Nielsen. Employing the notion of computation path introduced by van Glabbeek, we define a new notion of bisimulation of HDA using open maps. We derive a connection between computation paths and carrier sequences of dipaths and show that bisimilarity of HDA can be decided by the use of geometric techniques.

The problems of contextual equivalence and approximation are studied for the third-order fragment of Idealized Algol with iteration ( IA $^*_{3}$ ). They are approached via a combination of game semantics and language theory. It is shown that for each ( IA $^{*}_{3}$ )-term one can construct a pushdown automaton recognizing a representation of the strategy induced by the term. The automata have some additional properties ensuring that the associated equivalence and inclusion problems are solvable in Ptime . This gives an Exptime decision procedure for contextual equivalence and approximation for β -normal terms. Exptime -hardness is also shown in this case, even in the absence of iteration.

Fault diagnosis consists in observing behaviours of systems, and in detecting online whether an error has occurred or not. In the context of discrete event systems this problem has been well-studied, but much less work has been done in the timed framework. In this paper, we consider the problem of diagnosing faults in behaviours of timed plants. We focus on the problem of synthesizing fault diagnosers which are realizable as deterministic timed automata, with the motivation that such diagnosers would function as efficient online fault detectors. We study two classes of such mechanisms, the class of deterministic timed automata (DTA) and the class of event-recording timed automata (ERA). We show that the problem of synthesizing diagnosers in each of these classes is decidable, provided we are given a bound on the resources available to the diagnoser. We prove that under this assumption diagnosability is 2EXPTIME-complete in the case of DTA’s whereas it becomes PSPACE-complete for ERA’s.

In this paper, we prove decidability of the optimal conditional reachability problem for multi-priced timed automata, an extension of timed automata with multiple cost variables evolving according to given rates for each location. More precisely, we consider the problem of determining the minimal cost of reaching a given target state, with respect to some primary cost variable, while respecting upper bound constraints on the remaining (secondary) cost variables. Decidability is proven by constructing a zone-based algorithm that always terminates while synthesizing the optimal cost with a single secondary cost variable. The approach is then lifted to any number of secondary cost variables.

A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem. This gives a new class of timed languages which is closed under boolean operations and which has an effective presentation. We prove that the complexity of the emptiness problem for alternating timed automata with one clock is non-primitive recursive. The proof gives also the same lower bound for the universality problem for nondeterministic timed automata with one clock thereby answering a question asked in a recent paper by Ouaknine and Worrell.

The problem of finding a fully abstract model for the polymorphic π -calculus was stated in Pierce and Sangiorgi’s work in 1997 and has remained open since then. In this paper, we show that a slight variant of their language has a direct fully abstract model, which does not depend on type unification or logical relations. This is the first fully abstract model for a polymorphic concurrent language. In addition, we discuss the relationship between our work and Pierce and Sangiorgi’s, and show that their conjectured fully abstract model is, in fact, sound but not complete.

A timed extension of π -calculus with a transaction construct – the calculus Web π – is studied. The underlying model of Web π relies on networks of processes; time proceeds asynchronously at the network level, while it is constrained by the local urgency at the process level. Namely process reductions cannot be delayed to favour idle steps. The extensional model – the timed bisimilarity – copes with time and asynchrony in a different way with respect to previous proposals. In particular, the discriminating power of timed bisimilarity is weaker when local urgency is dropped. A labelled characterization of timed bisimilarity is also discussed.