Ubiquity symposium 'What is computation?'

Alan Turing's machine model of the universal machine model laid the theory and foundation of current computers, and layers can be regarded as an essence of computer science of current generation computers, averting the ubiquity of the universal computing; however, gradually, against Moore’s law and stepping into higher speed-computing needs, betraying the shortcomings of Turing’s model, are come up a new structure paradigm, namely specific domain architectures. Domain architecture is a style of software development which can extracts the complex business logic and build it out as a pure ‘domain model’, one that is independent of technical solutions. It is a bit like preparing an exact business blueprint of a software system: the software code may truly reflect business concepts and business rules. By defining clear boundaries and responsibilities, the domain architecture makes the system highly understandable, maintainable and capable of dynamically responding to changes in frequent business requirements. This article argues that people are entering a "post-Turing era", and people gradually turn from the pursuit of universality to pursuit of efficiency and accuracy. And that success of domain-specific architectures is no mere technology nor is it a new form rather than Turing’s form as represented by GPUs. Moreover, the future of computing will, sooner or later, be a heterogeneous era dominated by this new form.

Almost all of the progress of artificial intelligence in the last 50 years has been based on the Turing model and Von Neumann architecture. Researchers have always tried to put the human intelligence into machines by the ways of algorithms, codes or symbols that could be understood and executed by machines, thus, we may be bounded to Turing model too tightly. In Internet and World Wide Web and developing cloud computing, network has changed the role from a single huge Turing machine or sum of some Turing machines to the collective intelligence, where the inputs or outputs of nodes in network are happening not only among computers, but also among people, such that Internet has been beyond Turing machine. Users in Internet who own similar interests may cluster naturally into scalable and boundless communities with uncertainty, where online interaction avoids the difficulty of common sense representation in traditional artificial intelligence. Furthermore, collective intelligence may emerge from the crowds interaction. Those would become the new research frontiers in intelligence science.

The Panopticon (which means “watcher of everything”) is a well-known prison structure of continuous surveillance and discipline studied by Bentham in 1785. Today, where persistent, massive scale, surveillance is immensely facilitated by new technologies, the term Panopticon vaguely characterizes institutions with a power to acquire and process, undetectably, personal information. In this paper we propose a theoretical framework for studying Panopticons and their detectability status. We show, based on the Theory of Computation, that detecting Panopticons, modelled either as a simple Turing Machine or as an Oracle Turing Machine, is an undecidable problem. Furthermore, we show that for each sufficiently expressive formal system, we can effectively construct a Turing Machine for which it is impossible to prove, within the formal system, its Panopticon status. Finally, we discuss how Panopticons can be physically detected by the heat they dissipate each time they acquire, effortlessly, information in the form of an oracle and we investigate their detectability status with respect to a more powerful computational model than classical Turing Machines, the Infinite Time Turing Machines (ITTMs).

Artificial Intelligence (AI) was the inspiration that shaped computing as we know it today. In this article, I explore why and how AI would continue to inspire computing and reinvent it when Moore's Law is running out of steam. At the dawn of computing, Alan Turing proposed that instead of comprising many different specific machines, the computing machinery for AI should be a Universal Digital Computer, modeled after human computers, which carry out calculations with pencil on paper. Based on the belief that a digital computer would be significantly faster, more diligent and patient than a human, he anticipated that AI would be advanced as software. In modern terminology, a universal computer would be designed to understand a language known as an Instruction Set Architecture (ISA), and software would be translated into the ISA. Since then, universal computers have become exponentially faster and more energy efficient through Moore's Law, while software has grown more sophisticated. Even though software has not yet made a machine think, it has been changing how we live fundamentally. The computing revolution started when the software was decoupled from the computing machinery. Since the slowdown of Moore's Law in 2005, the universal computer is no longer improving exponentially in terms of speed and energy efficiency. It has to carry ISA legacy, and cannot be aggressively modified to save energy. Turing's proposition of AI as software is challenged, and the temptation of making many domain-specific AI machines emerges. Thanks to Deep Learning, software can stay decoupled from the computing machinery in the language of linear algebra, which it has in common with supercomputing. A new universal computer for AI understands such language natively to then become a Native Supercomputer. AI has been and will still be the inspiration for computing. The quest to make machines think continues amid the slowdown of Moore's Law. AI might not only maximize the remaining benefits of Moore's Law, but also revive Moore's Law beyond current technology.

The Turing machine convincingly formalized the concepts of “algorithm,” “computation,” and “computable.” It convinced researchers by its simplicity, generality, mechanical operation, and resemblance to human activity when solving computational problems, and by Turing’s reasoning and analysis of “computable” functions and his argumentation that partial “computable” functions are exactly Turing computable functions. Turing considered several variants that are generalizations of the basic model of his machine. But he also proved that they add nothing to the computational power of the basic model. This strengthened the belief in the Turing machine as an appropriate model of computation. Turing machines can be encoded and consequently enumerated. This enabled the construction of the universal Turing machine that is capable of computing anything that can be computed by any other Turing machine. This seminal discovery laid the theoretical grounds for several all important practical consequences, the general-purpose computer and the operating system being the most notable. The Turing machine is a versatile model of computation: it can be used to compute values of a function, or to generate elements of a set, or to decide about the membership of an object in a set. The last led to the notions of decidable and semi-decidable sets that would later prove to be very important in solving general computational problems.

Medium access control and in particular resource allocation is one of the most important tasks when designing wireless communication systems as it determines the overall performance of a system. For the particular allocation of the available resources it is of crucial importance to know whether or not a channel supports a certain quality-of-service (QoS) requirement. This paper develops a decision framework based on Turing machines and studies the algorithmic decidability of whether or not a QoS requirement is met. Turing machines have no limitations on computational complexity, computing capacity, and storage. They can simulate any given algorithm and therewith characterize the fundamental performance limits for today’s digital computers. In this paper, secure communication and identification systems are considered both under channel uncertainty and adversarial attacks. While for perfect channel state information, the question is decidable since the corresponding capacity function is computable, it is shown that the corresponding questions become semidecidable in the case of channel uncertainty and adversarial attacks. This means there exist Turing machines that stop and output the correct answer if and only if a channel supports the given QoS requirement. Interestingly, the opposite question of whether a channel capacity is below a certain threshold is not semidecidable.

This introductory chapter discusses the development of Alan Turing's ‘universal computing machine’, better known as the universal Turing Machine. The earliest large-scale electronic digital computers, the British Colossus (1943) and American ENIAC (1945), did not store programmes in memory. In 1936, Turing came up with an idea for a machine with limitless memory, in which both data and instructions were to be stored. By 1945, groups in Britain and the US began developing hardware for a universal Turing machine. Turing headed a group at the National Physical Laboratory in London that designed the Automatic Computing Engine (ACE), the first relatively complete specification of an electronic stored-programme digital computer.

We discuss combining physical experiments with machine computations and introduce a form of analogue–digital (AD) Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of AD machine are studied, in which physical parameters can be set exactly and approximately. Using non-uniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines.

According to the interactive view of computation, communication happens during the computation, not before or after it. This approach, distinct from concurrency theory and the theory of computation, represents a paradigm shift that changes our understanding of what is computation and how it is modeled. Interaction machines extend Turing machines with interaction to capture the behavior of concurrent systems, promising to bridge these two fields. This promise is hindered by the widespread belief, incorrectly known as the Church-Turing thesis, that no model of computation more expressive than Turing machines can exist. Yet Turing's original thesis only refers to the computation of functions and explicitly excludes other computational paradigms such as interaction. In this paper, we identify and analyze the historical reasons for this widespread belief. Only by accepting that it is false can we begin to properly investigate formal models of interaction machines. We conclude the paper by presenting one such model, Persistent Turing Machines (PTMs). PTMs capture sequential interaction, which is a limited form of concurrency; they allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of Turing machines and of the Church-Turing thesis.

t is remarkable that today's computers, after the tremendous development during the last 50 years, are still essentially described by the mathematical model formulated by AIan Turing in the 1930's. Turing's model describes computers which operate according to the laws ofclassical physics. What would happen ifa computer was operating according to the quantum laws? Physi­ cists and computer scientists have been interested in this question since the early 1980's, but research in quantum computation real­ ly started to flourish after 1994 when Peter Shor discovered a quantum algorithm to find prime factors oflarge integers effi­ ciently, a problem which is intrinsically hard for any classical computer (see (1) for an introduction into quantum computa­ tion). The lack ofan algorithm for efficient factoring on a classical machine is actually the basis ofthe widely used RSA encryption scheme. Phase coherence needs to be maintained for a sufficient­ ly long time in the memory of a quantum computer. This may sound like a harmless requirement, but in fact it is the main rea­ son why the physical implementation of quantum computation is so difficult. Usually, a quantum memory is thought of as a set oftwo-level systems, named quantum bits, or qubits for short. In analogy to the classical bit, two orthogonal computational basis states 10) and 11) are defined. The textbook example of a quan­ tum two-level system is the 1/2 of, say, an electron, where one can identify the spin up state with 10) and the spin down state with \1). While several other two-level systems have been proposed for quantum computing, we will devote the majority of our discussion to the potential use ofelectron spins in nanostruc­ tures (such as quantum dots) as qubits. Shor's fadoring algorithm We return to Shor's algorithm, since it allows us to explain many important concepts. At the heart of it lies the quantum Fourier transform (QFT). Given n qubits with an orthonormal basis 10), ...,12-1), the QFT is a unitary2x2 matrix UQFTsuch that

Indirect addressing and the time relationships of some models of sequential computation

Luciano Floridi’s Information Ethics (IE) is a new theoretical foundation of Ethics. According to Floridi, ICT with all informational structures and processes generates our new informational habitat, the Infosphere. For IE, moral action is an information processing pattern. IE addresses the fundamentally informational character of our interaction with the world, including interactions with other agents. Information Ethics is macro-ethics as it focuses on systems/networks of agents and their behavior. The IE’s capacity to study ethical phenomena on the basic level of underlying information patterns and processes makes it unique among ethical theories in providing a conceptual framework for fundamental level analysis of present globalised ICT-based world. It allows computational modeling – a powerful tool for study which increases our understanding of informational mechanisms of ethics. Computational models help capturing behaviors invisible to unaided mind which relies exclusively on shared intuitions. The article presents an analysis of the application of IE as interpreted within the framework of Info-Computationalism. The focus is on responsibility/accountability distribution and similar phenomena of information communication in networks of agents. Agent-based modeling enables studying the increasing complexity of behavior in multi-agent systems when agents (actors) are ranging from cellular automata to softbots, robots and humans. Autonomous, learning artificial intelligent systems technologies are developing rapidly, resulting in a new division of tasks between humans and robots/softbots. The biggest present-day concern about autonomous intelligent systems is the fear of human loss of control and robots acting inappropriately and causing harm. Among inappropriate kinds of behavior is the ethically unacceptable one. In order to assure ethically adequate behavior of autonomous intelligent systems, artifactual ethical responsibility/accountability should be one of the built-in features of intelligent artifacts. Adding the requirement for artifactual ethical behavior to a robot/softbot does not by any means take responsibility from humans designing, producing and controlling autonomous intelligent systems. On the contrary, it will make explicit the necessity for all involved with such intelligent technology to assure its ethical conduct. Today’s robots are used mainly as complex electromechanical tools and do not have any capability of taking moral responsibility. But technology progress is remarkable; robots are quickly improving their sensory and motor competencies, and the development of artifactual (synthetic) emotions adds new dimensions to robotics. Artifactual reasoning and other information processing skills are advancing – all of which is causing significant progress in the field of Social Robotics. We have thus strong reasons to try to analyze future technological development where robots/softbots are so intelligent and responsive that they possess artifactual morality alongside with artifactual intelligence. Technological artifacts are always part of a broader socio-technological system with distributed responsibilities. The development of autonomous, learning, morally responsible intelligent agents relies consequently on several responsibility feedback loops; the awareness and preparedness for handling risks on the side of designers, producers, implementers, users and maintenance personnel as well as the support of the society at large which will provide a response on the consequences of the use of technology. This complex system of shared responsibilities should secure a safe functioning of hybrid systems of humans and intelligent machines. Information Ethics provides a conceptual framework for computational modeling of such socio-technological systems. Apart from examples of specific applications of IE, interpretation of several widely debated questions, such as the role of Levels of Abstraction, naturalism and complexity/diversity in Information Ethics, is offered through Info-Computationalist analysis.

In this chapter, we introduce the definitions of automata Turing machines. We present different flavors of Turing machines including deterministic, probabilistic, and multi-tape machines. We present several complexity classes, i.e. collections of problems that can be solved by a machine with similar resources, including the P and NP classes. We present the Church-Turing thesis, which states that if a problem can be solved by a physical machine, then it can also be solved by any deterministic Turing machine. In the last part of the chapter, we introduce quantum Turing machines and the quantum circuit model. We study the complexity class BQP. This is the class of problems that can be solved by a quantum computer with polynomial resources and a small error probability. Finally, we introduce QMA, the quantum version of the complexity class NP. We present the k-LOCAL problem, and we show that this problem is in QMA

The theory of computer science is based around universal Turing machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of classical UTMs. For the most important class of problem in computer science, non-deterministic polynomial complete problems, non-deterministic UTMs (NUTMs) are theoretically exponentially faster than both classical UTMs and quantum mechanical UTMs (QUTMs). However, no attempt has previously been made to build an NUTM, and their construction has been regarded as impossible. Here, we demonstrate the first physical design of an NUTM. This design is based on Thue string rewriting systems, and thereby avoids the limitations of most previous DNA computing schemes: all the computation is local (simple edits to strings) so there is no need for communication, and there is no need to order operations. The design exploits DNA's ability to replicate to execute an exponential number of computational paths in P time. Each Thue rewriting step is embodied in a DNA edit implemented using a novel combination of polymerase chain reactions and site-directed mutagenesis. We demonstrate that the design works using both computational modelling and in vitro molecular biology experimentation: the design is thermodynamically favourable, microprogramming can be used to encode arbitrary Thue rules, all classes of Thue rule can be implemented, and non-deterministic rule implementation. In an NUTM, the resource limitation is space, which contrasts with classical UTMs and QUTMs where it is time. This fundamental difference enables an NUTM to trade space for time, which is significant for both theoretical computer science and physics. It is also of practical importance, for to quote Richard Feynman ‘there's plenty of room at the bottom’. This means that a desktop DNA NUTM could potentially utilize more processors than all the electronic computers in the world combined, and thereby outperform the world's current fastest supercomputer, while consuming a tiny fraction of its energy.

Turing's present-day and all-time relevance arises from the timelessness of the issues he tackled, and the innovative light he shed upon them. Turing first defined the algorithmic limits of computability, when determined via effective mechanism, and showed the generality of his definition by proving its equivalence to other general, but less algorithmic, non-mechanical, more abstract formulations of computability. In truth, his originality much impressed Gödel, for the simplicity of the mechanism invoked—what we nowadays call a Turing Machine (or program)—and for the proof of existence of a Universal Turing Machine (what we call digital computer)—which can demonstrably mimic any other Turing Machine, i.e. execute any program. Indeed, Turing Machines simply rely on having a finite-state automaton (like a vending machine), and an unbound paper tape made of discrete squares (like a paper roll), with at most one rewritable symbol on each square. Turing also first implicitly introduced the perspective of ‘functionalism'—though he did not use the word, it was introduced later by Putnam, inspired by Turing's work—by showing that what counts is the realizability of functions, independently of the hardware that embodies them. And that realizability is afforded by the very simplicity of his devised mechanism, what he then called A-machines (but now bear his name), which rely solely on the manipulation of symbols—as discrete as the fingers of one hand—wherein both data and instructions are represented with symbols, both being subject to manipulation. The twain, data as well as instructions, are stored in memory, where instructions double as data and as rules for acting—the stored program idea. No one to this day has invented a computational mechanical process with such general properties, which cannot be theoretically approximated with arbitrary precision by some Turing Machine, wherein interactions are to be captured by Turing's innovative concept of oracle. In these days of discrete-time quantization, computational biological processes, and proof of ever expanding universe—the automata and the tape—the Turing Machine reigns supreme. Moreover, universal functionalism—another Turing essence—is what enables the inevitable bringing together of the ghosts in the several embodied machines (silicon-based, biological, extra-terrestrial or otherwise) to promote their symbiotic epistemic co-evolution, since they partake of the same theoretic functionalism. Turing is truly and forever among us.