Practical Intractability: A Critique of the Hypercomputation Movement

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more mathematically concrete challenge to hypercomputability, and will show that one is immediately led into physical impossibilities, thereby demonstrating the infeasibility of hypercomputers more generally. This gives impetus to propose and justify a more plausible starting point for an extension to the classical paradigm that is physically possible, at least in principle. Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, one should focus on extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine. I present the first steps toward this goal by considering contemporary computational problems dealing with intractability and issues surrounding cyber-physical systems, and argue that a reasonable extension to the classical paradigm should focus on these issues in order to be practically viable.     

Minimality considerations for ordinal computers modeling constructibility

We describe a simple model of ordinal computation which can compute truth in the constructible universe. We try to use well-structured programs and direct limits of states at limit times whenever possible. This may make it easier to define a model of ordinal computation within other systems of hypercomputation, especially systems inspired by physical models.     

Language Is Physical

Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication or thinking would be possible. Efficient implementability for creating and reading language expressions is discussed and illustrated with a quantum mechanical model. The reason for interest in language is that language expressions can have meaning, either as an informal language or as a formal language associated with mathematical or physical theories. It is noted that any universally applicable physical theory, or coherent theory of physics and mathematics together, includes in its domain physical models of expressions for both the informal language used to discuss the theory and the expressions of the theory itself. It follows that there must be some formulas in the formal theory that express some of their own physical properties. The inclusion of intelligent systems in the domain of the theory means that the theory, e.g., quantum mechanics, must describe, in some sense, its own validation. Maps of language expressions into physical states are discussed. A spin projection example is discussed as are conditions under which such a map is a Gödel map. The possibility that language is also mathematical is very briefly discussed. PACS: 03.67–a; 03.65.Ta; 03.67.Lx     

A model-theoretic interpretation of environment-induced superselection

The question of what constitutes a ‘system’ is foundational to quantum measurement theory. Environment-induced superselection or ‘einselection’ has been proposed as an observer-independent mechanism by which apparently classical systems ‘emerge’ from physical interactions between degrees of freedom described completely quantum mechanically. It is shown here that einselection can only generate classical systems if the ‘environment’ is assumed a priori to be classical; einselection therefore does not provide an observer-independent mechanism by which classicality can emerge from quantum dynamics. Einselection is then reformulated in terms of positive operator-valued measures acting on a global quantum state. It is shown that this reformulation enables a natural interpretation of apparently classical systems as virtual machines that requires no assumptions beyond those of classical computer science.     

A methodological approach for user interface development of collaborative applications: A case study

In the last few years, the production of systems which support learning and group work has been high. However, the design and development of these types of systems are difficult, mainly due to the multidisciplinarity involved. Furthermore, the Graphic User Interface (GUI) of an application is receiving greater attention, since it can be decisive in determining if the application is accepted or rejected by users. Model-based design is a widespread technique in the user interface development process. While reviewing approaches that deal with the modeling and design of user interfaces supporting collaborative tasks, we have detected that there is no proposal that links interactive and collaborative issues. We have introduced a methodological approach to solve this shortcoming. This approach is called CIAM (Collaborative Interactive Application Methodology) and it is composed of several stages in which conceptual models are created using CIAN (Collaborative Interactive Application Notation). These models start by modeling the organization in which the application will be used, as well as the tasks that must be supported. In the initial stages, the organization and the collaborative tasks are modeled using high-level specifications. In the following stages, the level of detail increases and, finally, the interaction between the individual users and the application is modeled using ConcurTaskTrees (CTT) notation. The interaction model acts as a bridge between the design and the implementation of the Graphic User Interface. In this paper we present our methodological approach and an example of applying this method for user interface design of collaborative and interactive applications.     

A no-summoning theorem in relativistic quantum theory

Alice gives Bob an unknown localized physical state at some point P. At some point Q in the causal future of P, Alice will ask Bob for the state back. Bob knows this, but does not know at which point Q until the request is made. Bob can satisfy Alice’s summons, with arbitrarily short delay, for a quantum state in Galilean space-time or a classical state in Minkowski space-time. However, given an unknown quantum state in Minkowski space-time, he cannot generally fulfil her summons. This no-summoning theorem is a fundamental feature of, and intrinsic to, relativistic quantum theory. It follows from the no-signalling principle and the no-cloning theorem, but not from either alone.     

Entanglement mean field theory: Lipkin–Meshkov–Glick Model

Entanglement mean field theory is an approximate method for dealing with many-body systems, especially for the prediction of the onset of phase transitions. While previous studies have concentrated mainly on applications of the theory on short-range interaction models, we show here that it can be efficiently applied also to systems with long-range interaction Hamiltonians. We consider the (quantum) Lipkin–Meshkov–Glick spin model, and derive the entanglement mean field theory reduced Hamiltonian. A similar recipe can be applied to obtain entanglement mean field theory reduced Hamiltonians corresponding to other long-range interaction systems. We show, in particular, that the zero temperature quantum phase transition present in the Lipkin–Meshkov–Glick model can be accurately predicted by the theory.     

Quantum knots and mosaics

In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the “quantum embodiment” of a closed knotted physical piece of rope. A quantum knot, as a state of this system, represents the state of such a knotted closed piece of rope, i.e., the particular spatial configuration of the knot tied in the rope. Associated with a quantum knot system is a group of unitary transformations, called the ambient group, which represents all possible ways of moving the rope around (without cutting the rope, and without letting the rope pass through itself.) Of course, unlike a classical closed piece of rope, a quantum knot can exhibit non-classical behavior, such as quantum superposition and quantum entanglement. This raises some interesting and puzzling questions about the relation between topological and quantum entanglement. The knot type of a quantum knot is simply the orbit of the quantum knot under the action of the ambient group. We investigate quantum observables which are invariants of quantum knot type. We also study the Hamiltonians associated with the generators of the ambient group, and briefly look at the quantum tunneling of overcrossings into undercrossings. A basic building block in this paper is a mosaic system which is a formal (rewriting) system of symbol strings. We conjecture that this formal system fully captures in an axiomatic way all of the properties of tame knot theory.     

Establishing the equivalence between Szegedy’s and coined quantum walks using the staggered model

Coined quantum walks (QWs) are being used in many contexts with the goal of understanding quantum systems and building quantum algorithms for quantum computers. Alternative models such as Szegedy’s and continuous-time QWs were proposed taking advantage of the fact that quantum theory seems to allow different quantized versions based on the same classical model, in this case the classical random walk. In this work, we show the conditions upon which coined QWs are equivalent to Szegedy’s QWs. Those QW models have in common a large class of instances, in the sense that the evolution operators are equal when we convert the graph on which the coined QW takes place into a bipartite graph on which Szegedy’s QW takes place, and vice versa. We also show that the abstract search algorithm using the coined QW model can be cast into Szegedy’s searching framework using bipartite graphs with sinks.     

On the Possibility of Quantum Informational Structural Realism

In The Philosophy of Information, Luciano Floridi presents an ontological theory of Being qua Being, which he calls “Informational Structural Realism”, a theory which applies, he says, to every possible world. He identifies primordial information (“dedomena”) as the foundation of any structure in any possible world. The present essay examines Floridi’s defense of that theory, as well as his refutation of “Digital Ontology” (which some people might confuse with his own). Then, using Floridi’s ontology as a starting point, the present essay adds quantum features to dedomena, yielding an ontological theory for our own universe, Quantum Informational Structural Realism, which provides a metaphysical interpretation of key quantum phenomena, and diminishes the “weirdness” or “spookiness” of quantum mechanics.     

Formal verification of a pervasive messaging system

As ubiquitous computing becomes a reality, its applications are increasingly being used in business-critical, mission-critical and even in safety-critical, areas. Such systems must demonstrate an assured level of correctness. One approach to the exhaustive analysis of the behaviour of systems is formal verification, whereby each important requirement is logically assessed against all possible system behaviours. While formal verification is often used in safety analysis, it has rarely been used in the analysis of deployed pervasive applications. Without such formality it is difficult to establish that the system will exhibit the correct behaviours in response to its inputs and environment. In this paper, we show how model-checking techniques can be applied to analyse the probabilistic behaviour of pervasive systems. As a case study we apply this technique to an existing pervasive message-forwarding system, Scatterbox. Scatterbox incorporates many typical characteristics of pervasive systems, such as dependence on sensor reliability and dependence on context. We assess the dynamic temporal behaviour of the system, including the analysis of probabilistic elements, allowing us to verify formal requirements even in the presence of uncertainty in sensors. We also draw some tentative conclusions concerning the use of formal verification for pervasive computing in general.     

Robust H∞ controller design for a class of linear quantum systems with time delay

Time delay is frequently encountered in practical quantum feedback control systems with long transmission lines and measurement process. This paper is concerned with measurement‐based feedback H^∞ control for quantum systems with time delays appearing in the feedback loops. A physical model is presented for the quantum time‐delay system described by complex quantum stochastic differential equations. Quantum versions of some fundamental properties, such as dissipativity and stability, are discussed for this model. A numerical procedure is proposed for H^∞ controller synthesis, which can deal with a non‐convex optimization problem arising in the design processes. Copyright © 2016 John Wiley & Sons, Ltd.     

A predictive model of impurity diffusion coefficients in face-centered-cubic metallic systems based on machine-learning

This paper develops models for diffusion coefficient prediction to provide parameters for atomic mobility databases and to assist material design in a multi-scale simulation framework for face-centered-cubic (fcc) alloys. Models of impurity-diffusion activation energy (Q_I) and self-diffusion activation energy (Q_s) are trained using machine-learning with experimental diffusion data and basic physical properties. The values of Q_s in body-centered cubic (bcc), fcc and hexagonal close-packed (hcp) can be well-predicted using melting temperature, electronic configuration, atomic properties and elasticity parameters. Estimates of Q_I in fcc metallic systems calculated using a model with six features agreed well with experimental data. Compared with previous models of Q_s and Q_I, the newly developed models exhibit higher coefficients of determination (R²) and significantly lower mean absolute errors. The self- and impurity-diffusion coefficients in fcc metallic systems can be simulated by these models. The models are also successfully applied during the assessment process of the Ni–Ti binary atomic mobility database. Thus, the developed models provide an easy and reliable method for estimating the self- or impurity-diffusion coefficients of fcc alloys when they are unavailable.     

On the automated translational execution of the action language for foundational UML

To manage the rapidly growing complexity of software development, abstraction and automation have been recognised as powerful means. Among the techniques pushing for them, model-driven engineering has gained increasing attention from industry for, among others, the possibility to automatically generate code from models. To generate fully executable code, models should describe complex behaviours. While pragmatically this is achieved by employing programming languages for defining actions within models, the abstraction gap between modelling and programming languages can undermine consistency between models and code as well as analysability and reusability of models. In light of this, model-aware action languages should be preferred. This is the case of the Action Language for Foundational UML (ALF). In this paper, we provide a solution for the fully automated translational execution of ALF towards C++. Additionally, we give an insight on how to simplify the transition from the use of programming languages for modelling fine-grained behaviours to model-aware action languages in industrial MDE. The solution presented in this paper has been assessed on industrial applications to verify its applicability to complex systems as well as its scalability.     

To boldly go: an occam-π mission to engineer emergence

Future systems will be too complex to design and implement explicitly. Instead, we will have to learn to engineer complex behaviours indirectly: through the discovery and application of local rules of behaviour, applied to simple process components, from which desired behaviours predictably emerge through dynamic interactions between massive numbers of instances. This paper describes a process-oriented architecture for fine-grained concurrent systems that enables experiments with such indirect engineering. Examples are presented showing the differing complex behaviours that can arise from minor (non-linear) adjustments to low-level parameters, the difficulties in suppressing the emergence of unwanted (bad) behaviour, the unexpected relationships between apparently unrelated physical phenomena (shown up by their separate emergence from the same primordial process swamp) and the ability to explore and engineer completely new physics (such as force fields) by their emergence from low-level process interactions whose mechanisms can only be imagined, but not built, at the current time.     

The CGMV method for quantum walks

We review the main aspects of a recent approach to quantum walks, the CGMV method. This method proceeds by reducing the unitary evolution to canonical form, given by the so-called CMV matrices, which act as a link to the theory of orthogonal polynomials on the unit circle. This connection allows one to obtain results for quantum walks which are hard to tackle with other methods. Behind the above connections lies the discovery of a new quantum dynamical interpretation for well known mathematical tools in complex analysis. Among the standard examples which will illustrate the CGMV method are the famous Hadamard and Grover models, but we will go further showing that CGMV can deal even with non-translation invariant quantum walks. CGMV is not only a useful technique to study quantum walks, but also a method to construct quantum walks à la carte. Following this idea, a few more examples illustrate the versatility of the method. In particular, a quantum walk based on a construction of a measure on the unit circle due to F. Riesz will point out possible non-standard behaviours in quantum walks.     

Investigating user switching intention for mobile instant messaging application: Taking WeChat as an example

Post adoptive IT use is an important research topic in information systems field, mainly including sustained behaviours and switching behaviours. While there are a great number of studies on users’ continuance intentions for diversified IT, users’ IT switching behaviours are less studied. This research attempts to identify the features of users IT switching behaviours. We introduce a migration theory from social network perspective to explore the intrinsic and extrinsic factors influencing users’ switching intention in the context of mobile instant messaging (MIM) application. In particular, we develop a model that examines the role of networks, deprivations and trusts on MIM users’ switching intentions to WeChat in China. A survey research method is utilized to test this model and hypotheses. We found that functional deprivation, monetary deprivation and personal innovativeness could positively influence users’ switching intentions. Networks of obligation was found to have no significantly direct influence on switching intentions, but fully mediated by functional and monetary deprivations. However, trust transferred from MIMs provider has no significant effect on switching intentions. The findings are believed to theoretically contribute to further understand users’ IT switching behaviours and yield some practical implications for designers and managers in MIM providers and their products propaganda.