On the Equivalence of Cellular Automata and the Tile Assembly Model

In this paper, we explore relationships between two models of systems which are governed by only the local interactions of large collections of simple components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM). While sharing several similarities, the models have fundamental differences, most notably the dynamic nature of CA (in which every cell location is allowed to change state an infinite number of times) versus the static nature of the aTAM (in which tiles are static components that can never change or be removed once they attach to a growing assembly). We work with 2-dimensional systems in both models, and for our results we first define what it means for CA systems to simulate aTAM systems, and then for aTAM systems to simulate CA systems. We use notions of simulate which are similar to those used in the study of intrinsic universality since they are in some sense strict, but also intuitively natural notions of simulation. We then demonstrate a particular nondeterministic CA which can be configured so that it can simulate any arbitrary aTAM system, and finally an aTAM tile set which can be configured so that it can be used to simulate any arbitrary nondeterministic CA system which begins with a finite initial configuration.Comment: In Proceedings MCU 2013, arXiv:1309.104

Formal modelling and analysis of dynamic reconfiguration of dependable systems

PhD ThesisThe contribution of this thesis is a novel way of formally modelling and analyzing dynamic process reconfiguration in dependable systems. Modern dependable systems are required to be flexible, reliable, available and highly predictable. One way of achieving flexibility, reliability and availability is through dynamic reconfiguration. That is, by changing at runtime the structure of a system – consisting of its components and their communication links – or the hardware location of its software components. However, predicting the system’s behaviour during its dynamic reconfiguration is a challenge, and this motivates our research. Formal methods can determine whether or not a system’s design is correct, and design correctness is a key factor in ensuring the system will behave predictably and reliably at runtime. Therefore, our approach is formal. Existing research on software reconfiguration has focused on planned reconfiguration and link mobility. The focus of this thesis is on unplanned process reconfiguration. That is, the creation, deletion and replacement of processes that is not designed into a system when it is manufactured. We describe a process algebra (CCSdp) which is CCS extended with a new type of process (termed a fraction process) in order to model process reconfiguration. We have deliberately not introduced a new operator in CCSdp in order to model unplanned reconfiguration. Instead, we define a bisimulation ( o f ) that is used to identify a process for reconfiguration by behavioural matching. The use of behavioural matching based on o f (rather than syntactic or structural congruence-based matching) helps to make models simple and terse. However, o f is too weak to be a congruence. Therefore, we strengthen the conditions defining o f to obtain another bisimulation ( dp) which is a congruence, and (therefore) can be used for equational reasoning. Our notion of fraction process is recursive to enable fractions to be themselves reconfigured. We bound the depth of recursion of a fraction and its successors in order to ensure that o f and dp are decidable. Furthermore, we restrict the set of states in a model of a system to be finite, which also supports decidability of the two bisimulations and helps model checking. We evaluate CCSdp in two ways. First, with respect to requirements used to evaluate other formalisms. Second, through a simple case study, in which the reconfiguration of an o ce workflow is modelled using CCSdp.EPSRC fundin

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

Twin‐engined diagnosis of discrete‐event systems

Diagnosis of discrete-event systems (DESs) is computationally complex. This is why a variety of knowledge compilation techniques have been proposed, the most notable of them rely on a diagnoser. However, the construction of a diagnoser requires the generation of the whole system space, thereby making the approach impractical even for DESs of moderate size. To avoid total knowledge compilation while preserving efficiency, a twin-engined diagnosis technique is proposed in this paper, which is inspired by the two operational modes of the human mind. If the symptom of the DES is part of the knowledge or experience of the diagnosis engine, then Engine 1 allows for efficient diagnosis. If, instead, the symptom is unknown, then Engine 2 comes into play, which is far less efficient than Engine 1. Still, the experience acquired by Engine 2 is then integrated into the symptom dictionary of the DES. This way, if the same diagnosis problem arises anew, then it will be solved by Engine 1 in linear time. The symptom dic- tionary can also be extended by specialized knowledge coming from scenarios, which are the most critical/probable behavioral patterns of the DES, which need to be diagnosed quickly

Bounded reordering in the distributed test architecture

In the distributed test architecture, the system under test (SUT) interacts with its environment at multiple physically distributed ports and the local testers at these ports do not synchronize their actions. This presents many challenges and, in particular, apparently incorrect behaviors can be the consequence of an erroneous assumption about the exact order in which actions were performed at different ports. In previous work, we defined a conformance relation for the distributed test architecture. Essentially, the SUT is faulty if we observe a trace σ such that no admissible reordering of the actions in σ could have been produced by the specification. However, this notion can be weak if the compared traces might be too different. This paper introduces conformance relations where, for a given metric, a reordering is only considered if the distance between the two traces is at most a certain bound k . We introduce two different metrics and provide algorithms to construct finite automata accepting these close , with respect to each metric, sequences. We also study the computational complexity of the two main problems associated with the new framework: deciding whether a trace is accepted by the new automaton and deciding whether one system conforms to a specification with respect to the new conformance relation

PLACES'10: The 3rd Workshop on Programmng Language Approaches to concurrency and Communication-Centric Software

Paphos, Cyprus. March 201

Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.Siirretty Doriast