Catálogo de publicaciones - libros

Aspects have emerged as a powerful tool in the design and development of systems. Aspect-orientation ideas are paradigm independent and have been developed for object-oriented, imperative and functional languages. This talk will discuss a suite of results that aim to level the foundational playing field between aspects and other programming paradigms. In this context, we will argue that aspects are no more intractable than stateful higher order programs. The talk is based on joint work with Glenn Bruns, Alan Jeffrey, Corin Pitcher and James Riely.

Timed automata can be studied in not only a dense-time setting but also a discrete-time setting. The most common example of discrete-time semantics is the so called sampled semantics (i.e., discrete semantics with a fixed time granularity ε ). In the real-time setting, the universality problem is known to be undecidable for timed automata. In this work, we study the universality question for the languages accepted by timed automata with sampled semantics. On the negative side, we show that deciding whether for all sampling periods ε a timed automaton accepts all timed words in ε -sampled semantics is as hard as in the real-time case, i.e., undecidable. On the positive side, we show that checking whether there is a sampling period such that a timed automaton accepts all untimed words in ε -sampled semantics is decidable. Our proof uses clock difference relations, developed to characterize the reachability relation for timed automata in connection with sampled semantics.

System $\mathcal{L}$ is a linear λ -calculus with numbers and an iterator, which, although imposing linearity restrictions on terms, has all the computational power of Gödel’s System $\mathcal{T}$ . System $\mathcal{L}$ owes its power to two features: the use of a closed reduction strategy (which permits the construction of an iterator on an open function, but only iterates the function after it becomes closed), and the use of a liberal typing rule for iterators based on iterative types. In this paper, we study these new types, and show how they relate to intersection types. We also give a sound and complete type reconstruction algorithm for System $\mathcal{L}$ .

An extension of the λ -calculus is proposed, to study resource usage analysis and verification. Resources can be dynamically created, and passed / returned by functions; their usages have side effects, represented by events. Usage policies are properties over histories of events, and have a possibly nested, local scope. A type and effect system over-approximates the set of histories a program can generate at run-time. A crucial point solved here concerns correctly associating fresh resources with their usages within approximations. A second issue is that these approximations may contain an unbounded number of fresh resources. Despite of that, we have devised a technique to model-check validity of approximations. A program with a valid approximation is resource-safe: no run-time monitor is needed to safely drive its executions.

In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP -complete or PSPACE -complete, depending on the set of temporal operators used . If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This paper undertakes a systematic study of satisfiability for LTL formulae over restricted sets of propositional and temporal operators. Since every propositional operator corresponds to a Boolean function, there exist infinitely many propositional operators. In order to systematically cover all possible sets of them, we use Post’s lattice. With its help, we determine the computational complexity of LTL satisfiability for all combinations of temporal operators and all but two classes of propositional functions. Each of these infinitely many problems is shown to be either PSPACE -complete, NP -complete, or in P . Keywords: computational complexity, linear temporal logic.

We formalise the pi-calculus using the nominal datatype package, a package based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a unison manner. We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover. A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.

The last few years have seen the development of the rewriting calculus (also called rho-calculus or ρ -calculus) that uniformly integrates first-order term rewriting and λ -calculus. The combination of these two latter formalisms has been already handled either by enriching first-order rewriting with higher-order capabilities, like in the Combinatory Reduction Systems (CRS), or by adding to λ -calculus algebraic features. In a previous work, the authors showed how the semantics of CRS can be expressed in terms of the ρ -calculus. The converse issue is adressed here: rewriting calculus derivations are simulated by Combinatory Reduction Systems derivations. As a consequence of this result, important properties, like standardisation, are deduced for the rewriting calculus.

Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types. Our interpretation is based on Reynolds’s relational parametricity, and it provides a formal connection between separation logic and data abstraction.

We consider the model of priced (a.k.a. weighted) timed automata, an extension of timed automata with cost information on both locations and transitions. We prove that model-checking this class of models against the logic WCTL, CTL with cost-constrained modalities, is PSPACE -complete under the “single-clock” assumption. In contrast, it has been recently proved that the model-checking problem is undecidable for this model as soon as the system has three clocks. We also prove that the model-checking of WCTL* becomes undecidable, even under this “single-clock” assumption.

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski’s decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist.