Distributed population protocols: naturally!

Edited by Michael Köhler-Bussmeier, Ekkart Kindler, Heiko RölkeClassical population protocols manage a fix size population of agents that are created by the input population: one agent exactly per unit of the input. As a consequence, complex protocols that have to perform several independent tasks find here a clear bottleneck that drastically reduces the parallelism in the execution of those tasks. To solve this problem, I propose to manage distributed population protocols, that simply generalize the classical ones by generating a (fix, finite) set of agents per each unit of the input. A surprising fact is that these protocols are not really new, if instead of considering only the classical protocols with an input alphabet we consider the alternative simpler one that states as input mechanism a given subset of the set of states. Distributed population protocols are not only interesting because they allow more parallel and faster executions, but specially because the distribution of both code and data will allow much simpler protocols, inspired by the distribution of both places and transitions in Petri nets.Sección Deptal. de Sistemas Informáticos y ComputaciónFac. de Ciencias MatemáticasTRUEpu

Decision Problems for Petri Nets with Names

We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition Systems. In particular, we obtain decidability of coverability and termination, so that the expressive power of Turing machines is not reached. Moreover, they are strictly Well Structured, so that the boundedness problem is also decidable. We consider two properties, width-boundedness and depth-boundedness, that factorize boundedness. Width-boundedness has already been proven to be decidable. We prove here undecidability of depth-boundedness. Finally, we obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure

Proving Continuity of Coinductive Global Bisimulation Distances: A Never Ending Story

We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the cost of transformations: how much we need to modify one of the compared processes to obtain the other. Our original definition only covered finite processes, but a coinductive approach allows us to extend it to cover infinite but finitary trees. After having shown many interesting properties of our distance, it was our intention to prove continuity with respect to projections, but unfortunately the issue remains open. Nonetheless, we have obtained several partial results that are presented in this paper.Comment: In Proceedings PROLE 2015, arXiv:1512.0617

Alan Turing: Una aproximación personal a su obra

Con ocasión del centenario del nacimiento de Alan Turing, y la celebración a nivel internacional de «The Alan Turing Year», con el que se conmemora el mismo a nivel internacional, presentamos una visión personal de su obra, exponiendo de manera divulgativa sus principales resultados e incidiendo fundamentalmente en las ideas que los guiaron. Nos centramos en especial en los temas que hoy en día catalogamos como fronterizos entre la Matemática y la Informática, destacando sus contribuciones seminales a la Teoría de la Computabilidad y a la Inteligencia Artificial, las actividades relacionadas con la Criptografía durante la Segunda Guerra Mundial, y finalmente sus aportaciones absolutamente visionarias a temas tan actuales como la Vida Artificial, la Morfogénesis y los Algoritmos Genéticos

Extending the Petri box calculus with time

PBC (Petri Box Calculus) is a process algebra where real parallelism of concurrent systems can be naturally expressed. One of its main features is the definition of a denotational semantics based on Petri nets, which emphasizes the structural aspects of the modelled systems. However, this formal model does not include temporal aspects of processes, which are necessary when considering real-time systems. The aim of this paper is to extend the existing calculus with those temporal aspects. We consider that actions are not instantaneous, that is, their execution takes time. We present an operational semantics and a denotational semantics based on timed Petri nets. Finally, we discuss the introduction of other new features such as time-outs and delays. Throughout the paper we assume that the reader is familiar with both Petri nets and PBC

Denotational semantics for timed testing

In this paper we present a denotational semantics for a timed process algebra, which is fully abstract with respect to the must testing semantics previously developed [Lla96,LdFN96]. The domain of semantic processes is made up of consistent sets of barbs, which generalize the notion of acceptance sets, in such a way that the actions that are offered but not taken in each state are also recorded. the main difficulty when defining this denotational semantics has been that the natural ordering between semantic processes cannot be proved to be complete. So an alternative stronger complete ordering has to be considered, which is proved to be consistent with the original one, in the sense that lubs of chains with respect to the new ordering are also lubs with respect to the original one

Equational Characterization of Covariant-Contravariant Simulation and Conformance Simulation Semantics

Covariant-contravariant simulation and conformance simulation generalize plain simulation and try to capture the fact that it is not always the case that "the larger the number of behaviors, the better". We have previously studied their logical characterizations and in this paper we present the axiomatizations of the preorders defined by the new simulation relations and their induced equivalences. The interest of our results lies in the fact that the axiomatizations help us to know the new simulations better, understanding in particular the role of the contravariant characteristics and their interplay with the covariant ones; moreover, the axiomatizations provide us with a powerful tool to (algebraically) prove results of the corresponding semantics. But we also consider our results interesting from a metatheoretical point of view: the fact that the covariant-contravariant simulation equivalence is indeed ground axiomatizable when there is no action that exhibits both a covariant and a contravariant behaviour, but becomes non-axiomatizable whenever we have together actions of that kind and either covariant or contravariant actions, offers us a new subtle example of the narrow border separating axiomatizable and non-axiomatizable semantics. We expect that by studying these examples we will be able to develop a general theory separating axiomatizable and non-axiomatizable semantics.Comment: In Proceedings SOS 2010, arXiv:1008.190

A sound and complete proof system for probabilistic processes

n this paper we present a process algebra model of probabilistic communicating processes based on classical CSP. To define our model we have replaced internal non-determinism by generative probabilistic choices, and external non-determinism by reactive probabilistic choices, with the purpose of maintaining the meaning of the classical CSP operators, once generalized in a probabilistic way. Thus we try to keep valid, as far as possible, the laws of CSP. This combination of both internal and external choice makes strongly difficult the definition of a probabilistic version of CSP. In fact, we can find in the current literature quite a number of papers on probabilistic processes, but only in a few of them internal and external choices are combined, trying to preserve their original meaning. Starting with a denotational semantics where the corresponding domain is a set of probabilistic trees with two kinds of nodes, representing the internal and external choices, we define a sound and complete proof system, with very similar laws to those of the corresponding CSP

Mobile Synchronizing Petri Nets: A Choreographic Approach for Coordination in Ubiquitous Systems

AbstractThe term Ubiquitous Computing was coined by Mark Weiser almost two decades ago. Despite all the time that has passed since Weiser's vision, ubiquitous computing still has a long way ahead to become a pervasive reality. One of the reasons for this may be the lack of widely accepted formal models capable of capturing and analyzing the complexity of the new paradigm. We propose a simple Petri Net based model to study some of its main characteristics. We model both devices and software components as a special kind of coloured Petri Nets, located in locations, that can move to other locations and synchronize with other co-located nets, offering and requesting services. We obtain an amenable model for ubiquitous computing, due to its graphical representation. We present our proposal in a progressive way, first presenting a basic model where coordination is formalized by the synchronized firing of pairs of compatible transitions that offer and request a specific service, and ad hoc networks are modeled by constraining mobility by the dynamic acquisition of locality names. Next, we introduce a mechanism for the treatment of robust security properties, namely the generation of fresh private names, to be used for authentication properties