Catálogo de publicaciones - libros

In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatization of rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard Hennessy-Milner logic, graded modal logic and probabilistic modal logic.

We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for T-coalgebras and investigate under which circumstances it gives rise to a ‘concrete’ such logic, that is, a logic with an inductively defined syntax and proof system. We obtain a result that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.

As part of ongoing work on evaluating Milner’s bigraphical reactive systems, we investigate bigraphical models of , a facet of ubiquitous computing. We find that naively encoding such systems in bigraphs is somewhat awkward; and we propose a more sophisticated modeling technique, introducing , alleviating this awkwardness. We argue that such models are useful for simulation and point out that for reasoning about such bigraphical models, the bisimilarity inherent to bigraphical reactive systems is not enough in itself; an equivalence between the bigraphical reactive systems themselves is also needed.

Rewriting systems over adhesive categories have been recently introduced as a general framework which encompasses several rewriting-based computational formalisms, including various modelling frameworks for concurrent and distributed systems. Here we begin the development of a truly concurrent semantics for adhesive rewriting systems by defining the fundamental notion of process, well-known from Petri nets and graph grammars. The main result of the paper shows that processes capture the notion of true concurrency—there is a one-to-one correspondence between concurrent derivations, where the sequential order of independent steps is immaterial, and (isomorphism classes of) processes. We see this contribution as a step towards a general theory of true concurrency which specialises to the various concrete constructions found in the literature.

Metric Temporal Logic (MTL) is a real-time extension of Linear Temporal Logic that was proposed fifteen years ago and has since been extensively studied. Since the early 1990s, it has been widely believed that some very small fragments of MTL are undecidable (i.e., have undecidable satisfiability and model-checking problems). We recently showed that, on the contrary, some substantial and important fragments of MTL are decidable [19,20]. However, until now the question of the decidability of full MTL over infinite timed words remained open.

In this paper, we settle the question negatively. The proof of undecidability relies on a surprisingly strong connection between MTL and a particular class of faulty Turing machines, namely ‘insertion channel machines with emptiness-testing’.

We introduce a denotational semantics for non-linear hybrid automata, and relate it to the operational semantics given in terms of hybrid trajectories. The semantics is defined as least fixpoint of an operator on the continuous domain of functions of time that take values in the lattice of compact subsets of -dimensional Euclidean space. The semantic function assigns to every point in time the set of states the automaton can visit at that time, starting from one of its initial states. Our main results are the correctness and computational adequacy of the denotational semantics with respect to the operational semantics and the fact that the denotational semantics is computable.

Reversible computation has a growing number of promising application areas such as the modelling of biochemical systems, program debugging and testing, and even programming languages for quantum computing. We formulate a procedure for converting operators of standard algebraic process calculi such as CCS, ACP and CSP into reversible operators, while preserving their operational semantics.

A key problem in mixing operational (e.g., process–algebraic) and declarative (e.g., logical) styles of specification is how to deal with inconsistencies arising when composing processes under conjunction. This paper introduces a conjunction operator on labelled transition systems capturing the basic intuition of “”, and considers a naive preorder that demands that an inconsistent specification can only be refined by an inconsistent implementation.

The main body of the paper is concerned with characterising the largest precongruence contained in the naive preorder. This characterisation will be based on a novel semantics called ready–tree semantics, which refines ready traces but is coarser than ready simulation. It is proved that the induced ready–tree preorder is compositional and fully–abstract, and that the conjunction operator indeed reflects conjunction.

The paper’s results provide a foundation for, and an important step towards a unified framework that allows one to freely mix operators from process algebras and temporal logics.

We answer an open question related to bisimilarity checking on labelled transition systems generated by prefix rewrite rules on words. Stirling (1996, 1998) proved the decidability of bisimilarity for normed pushdown processes. This result was substantially extended by Sénizergues (1998, 2005) who showed the decidability for regular (or equational) graphs of finite out-degree (which include unnormed pushdown processes). The question of decidability of bisimilarity for a more general class of so called Type -1 systems (generated by prefix rewrite rules of the form where is a regular language) was left open; this was repeatedly indicated by both Stirling and Sénizergues. Here we answer the question negatively, i.e., we show undecidability of bisimilarity on Type -1 systems, even in the normed case. We complete the picture by considering classes of systems that use rewrite rules of the form and and show when they yield low undecidability (Π-completeness) and when high undecidability (Σ-completeness), all with and without the assumption of normedness.

We extend the propositional dynamic logic PDL of Fischer and Ladner with a restricted kind of recursive programs using the formalism of visibly pushdown automata (Alur, Madhusudan 2004). We show that the satisfiability problem for this extension remains decidable, generalising known decidability results for extensions of PDL by non-regular programs.