Catálogo de publicaciones - libros

We study the interaction between non-deterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been proposed previously. Here, we introduce a model that extends probabilistic automata to the continuous setting. We identify the class of schedulers that ensures measurability properties on executions, and show that such measurability properties are preserved by parallel composition. Finally, we demonstrate how these results allow us to define an alternative notion of weak bisimulation in our model.

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 λ ^ Δ 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. Keywords: Higher-dimensional automata, bisimulation, open maps, directed topology, fibrations.

The problems of contextual equivalence and approximation are studied for the third-order fragment of Idealized Algol with iteration ( ). They are approached via a combination of game semantics and language theory. It is shown that for each -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.

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.

Language-based and process calculi-based information security are well developed fields of computer security. Although these fields have much in common, it is somewhat surprising that the literature lacks a comprehensive account of a formal link between the two disciplines. This paper develops such a link between a language-based specification of security and a process-algebraic framework for security properties. Encoding imperative programs into a CCS-like process calculus, we show that timing-sensitive security for these programs exactly corresponds to the well understood process-algebraic security property of persistent bisimulation-based nondeducibility on compositions ( ). This rigorous connection opens up possibilities for cross-fertilization, leading to both flexible policies when specifying the security of heterogeneous systems and to a synergy of techniques for enforcing security specifications.

The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course, should be taken in conjunction with the well-established views and methods stemming from algebra, category theory, domain theory, logic, type theory,  etc . In support of this proposal I will show how such an approach leads to interesting connections between various areas of computer science and mathematics; concentrating on one such example in some detail. Specifically, I will consider the line of my research involving denotational models of the pi calculus and algebraic theories with variable-binding operators, indicating how the abstract mathematical structure underlying these models fits with that of Joyal’s combinatorial species of structures. This analysis suggests both the unification and generalisation of models, and in the latter vein I will introduce generalised species of structures and their calculus. These generalised species encompass and generalise various of the notions of species used in combinatorics. Furthermore, they have a rich mathematical structure (akin to models of Girard’s linear logic) that can be described purely within Lawvere’s generalised logic. Indeed, I will present and treat the cartesian closed structure, the linear structure, the differential structure,  etc. of generalised species axiomatically in this mathematical framework. As an upshot, I will observe that the setting allows for interpretations of computational calculi (like the lambda calculus, both typed and untyped; the recently introduced differential lambda calculus of Ehrhard and Regnier;  etc ) that can be directly seen as translations into a more basic elementary calculus of interacting agents that compute by communicating and operating upon structured data.

The arithmetic of natural numbers with addition and divisibility has been shown undecidable as a consequence of the fact that multiplication of natural numbers can be interpreted into this theory, as shown by J. Robinson [14]. The most important decidable subsets of the arithmetic of addition and divisibility are the arithmetic of addition, proved by M. Presburger [13], and the purely existential subset, proved by L. Lipshitz [11]. In this paper we define a new decidable fragment of the form where the only variable allowed to occur to the left of the divisibility sign is z . For this form, called in the paper, we show the existence of a quantifier elimination procedure which always leads to formulas of Presburger arithmetic. We generalize the   form to , where the only variables appearing on the left of divisibility are z _1, ..., z _ m . For this form, called , we show decidability of the positive fragment, namely by reduction to the existential theory of the arithmetic with addition and divisibility. The , fragments were inspired by a real application in the field of program verification. We considered the satisfiability problem for a program logic used for quantitative reasoning about memory shapes, in the case where each record has at most one pointer field. The reduction of this problem to the positive subset of is sketched in the end of the paper.

We introduce a domain-theoretic computational model for multi-variable differential calculus, which for the first time gives rise to data types for differentiable functions. The model, a continuous Scott domain for differentiable functions of n variables, is built as a sub-domain of the product of n + 1 copies of the function space on the domain of intervals by tupling together consistent information about locally Lipschitz (piecewise differentiable) functions and their differential properties (partial derivatives). The main result of the paper is to show, in two stages, that consistency is decidable on basis elements, which implies that the domain can be given an effective structure. First, a domain-theoretic notion of line integral is used to extend Green’s theorem to interval-valued vector fields and show that integrability of the derivative information is decidable. Then, we use techniques from the theory of minimal surfaces to construct the least and the greatest piecewise linear functions that can be obtained from a tuple of n + 1 rational step functions, assuming the integrability of the n -tuple of the derivative part. This provides an algorithm to check consistency on the rational basis elements of the domain, giving an effective framework for multi-variable differential calculus.

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.