Optimal Conclusive Discrimination of Two Non-orthogonal Pure Product Multipartite States Locally

We consider one copy of a quantum system prepared in one of two non-orthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols which obtain optimal probability in the sense of conclusive discrimination by means of local operations and classical communications(LOCC) as good as by global operations. Also, we show a protocol which minimezes the average number of local operations. Our result implies that two product pure multipartite states might not have the non-local property though more than two can have.Comment: revtex, 3 pages, no figur

Global state predicates in rough real-time

Distributed systems are characterized by the fact that the constituent processes have neither common memory nor a common system clock. These processes communicate solely via message passing. While providing a number of benefits such as increased reliability, increased computational power, and geographic dispersion, this architecture significantly complicates many of the tasks of software development and verification, including evaluation of the program state. In the case of distributed systems, the program state is comprised of the local states of the constituent processes, as well as the state of the channels between processes, and is called the global state.;With no common system clock, many distributed system protocols rely on the global ordering of local process events imposed by the message passing that occurs between processes. This leads to a partial global ordering of local process events, which can then be used to determine which process states could (or could not) have occurred simultaneously.;Traditional predicate evaluation protocols evaluate predicates on the global state of a distributed computation using consistent global states. This evaluation is complicated by the fact that the event ordering imposed by message passing is only partial. A complete history of the global states that occurred during an execution cannot always be constructed. This introduces inefficiency into predicate detection protocols and prohibits detection of certain predicates.;This dissertation explores the use of this rough global time base for global state predicate evaluation within distributed systems. By structuring the evaluation on the assumption that a global time base exists, we can develop simple and efficient protocols for both stable and unstable predicate evaluation. Further, we can evaluate certain predicates which are not easily evaluated using consistent global states. We demonstrate these advantages by developing protocols for detection of distributed termination, distributed deadlock detection, and detection of certain unstable predicates as they occur. as the global time base is rough, we can only detect unstable predicates which remain true for a sufficient duration. We additionally develop several formalizations which assist the protocol developer in dealing with the fact that the global time base is not perfect. We demonstrate the application of these formalizations within the protocols that we develop

Optimisation in ‘Self-modelling’ Complex Adaptive Systems

When a dynamical system with multiple point attractors is released from an arbitrary initial condition it will relax into a configuration that locally resolves the constraints or opposing forces between interdependent state variables. However, when there are many conflicting interdependencies between variables, finding a configuration that globally optimises these constraints by this method is unlikely, or may take many attempts. Here we show that a simple distributed mechanism can incrementally alter a dynamical system such that it finds lower energy configurations, more reliably and more quickly. Specifically, when Hebbian learning is applied to the connections of a simple dynamical system undergoing repeated relaxation, the system will develop an associative memory that amplifies a subset of its own attractor states. This modifies the dynamics of the system such that its ability to find configurations that minimise total system energy, and globally resolve conflicts between interdependent variables, is enhanced. Moreover, we show that the system is not merely ‘recalling’ low energy states that have been previously visited but ‘predicting’ their location by generalising over local attractor states that have already been visited. This ‘self-modelling’ framework, i.e. a system that augments its behaviour with an associative memory of its own attractors, helps us better-understand the conditions under which a simple locally-mediated mechanism of self-organisation can promote significantly enhanced global resolution of conflicts between the components of a complex adaptive system. We illustrate this process in random and modular network constraint problems equivalent to graph colouring and distributed task allocation problems

A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics

In multiagent dynamical systems, privacy protection corresponds to avoid disclosing the initial states of the agents while accomplishing a distributed task. The system-theoretic framework described in this paper for this scope, denoted dynamical privacy, relies on introducing output maps which act as masks, rendering the internal states of an agent indiscernible by the other agents as well as by external agents monitoring all communications. Our output masks are local (i.e., decided independently by each agent), time-varying functions asymptotically converging to the true states. The resulting masked system is also time-varying, and has the original unmasked system as its limit system. When the unmasked system has a globally exponentially stable equilibrium point, it is shown in the paper that the masked system has the same point as a global attractor. It is also shown that existence of equilibrium points in the masked system is not compatible with dynamical privacy. Application of dynamical privacy to popular examples of multiagent dynamics, such as models of social opinions, average consensus and synchronization, is investigated in detail.Comment: 38 pages, 4 figures, extended version of arXiv preprint arXiv:1808.0808

Verifying and comparing finite state machines for systems that have distributed interfaces

This paper concerns state-based systems that interact with their environment at physically distributed interfaces, called ports. When such a system is used a projection of the global trace, a local trace, is observed at each port. As a result the environment has reduced observational power: the set of local traces observed need not define the global trace that occurred. We consider the previously defined implementation relation ⊆s and prove that it is undecidable whether N ⊆s M and so it is also undecidable whether testing can distinguishing two states or FSMs. We also prove that a form of model-checking is undecidable when we have distributed observations and give conditions under which N ⊆s M is decidable. We then consider implementation relation ⊆sk that concerns input sequences of length κ or less. If we place bounds on κ and the number of ports then we can decide N ⊆sk M in polynomial time but otherwise this problem is NP-hard

Dynamic Load Balancing Based on Applications Global States Monitoring

8 pages à paraîtreInternational audienceThe paper presents how to use a special novel distributed program design framework with evolved global control mechanisms to assure processor load balancing during execution of application programs. The new framework supports a programmer with an API and GUI for automated graphical design of program execution control based on global application states monitoring. The framework provides highlevel distributed control primitives at process level and a special control infrastructure for global asynchronous execution control at thread level. Both kinds of control assume observations of current multicore processor performance and communication throughput enabled in the executive distributed system. Methods for designing processor load balancing control based on a system of program and system properties metrics and computational data migration between application executive processes is presented and assessed by experiments with execution of graph representations of distributed programs

Distributed controller design for a class of sparse singular systems with privacy constraints

In the current research on distributed control of interconnected large-scale dynamical systems an often neglected issue is the desire to ensure privacy of subsystems. This gives motivation for the presented distributed controller design method which requires communication and the exchange of model data only with direct neighbors. Thus, no global system knowledge is required. An important property of many large-scale systems is the presence of algebraic conservation constraints, for example in terms of energy or mass flow. Therefore, the presented controller design takes these constraints explicitly into account while preserving the sparsity structure of the distributed system necessary for a distributed design. The computation is based on the simulation of the system states and of adjoint states. The control objective is represented by the finite horizon linear quadratic cost functional