A Logic for True Concurrency

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. We believe that this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201

Revisiting logical semantics for processes and their distances

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Informática, Departamento de Sistemas Informáticos y Computación, leída el 2-02-2016Esta tesis se enmarca en el amplio campo de la teoría de la concurrencia. Más específicamente, nos centramos en el estudio de las relaciones de similitud entre procesos concurrentes. Comenzamos estudiando la bisimulación, considerada la más importante de estas relaciones, y vemos después cómo podemos extender nuestros resultados al resto de las semánticas de procesos estudiadas durante las últimas décadas. En particular, nuestra contribución a la comunidad científica, se centra en dos puntos principales: – El desarrollo de una caracterización lógica uniforme de las semánticas de procesos: proponemos un esquema lógico común (enmarcado en la conocida lógica modal de Hennessy-Milner) e incluimos las diferentes semánticas en este esquema, enfatizando las diferencias y similitudes entre ellas, que se presentan del modo más claro posible. – La presentación de una nueva noción de distancia, tanto entre procesos finitos como infinitos: la misma se diferencia de las anteriormente propuestas en su carácter global, que acumula las diferencias que aportan los distintos cómputos, en lugar de quedarnos con la máxima de ellas...This thesis can be included in the broad field of concurrency theory. More specifically, we focus on the study of the similarities between concurrent processes. We start from bisimulation, the main of these relations, and then we see how we can extend the obtained results to the rest of the semantics developed along the last years. In particular, our main contributions can be roughly described by the following two items: – The development of a unified logical characterization of process semantics: we propose a common logical scheme (within the framework of the well known Hennessy-Milner Logic) and we set the different semantics in this scheme by emphasizing, in the clearest possible way, the (dis)similarities between them. – We present a new notion of distance for both finite and infinite processes. This novel notion differs from the previously available ones in its global character: instead of taking the maximum disagreement between the two compared processes, it adds all the differences provided by their whole sets of computations...Depto. de Sistemas Informáticos y ComputaciónFac. de InformáticaTRUEunpu

Structural operational semantics for non-deterministic processes with quantitative aspects

General frameworks have been recently proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format and a corresponding notion of bisimulation for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function GSOS (WF-GSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness and completeness of the WF-GSOS specification format, and that bisimilarities induced by these specifications are always congruences.Comment: Extended version of arXiv:1406.206