Abstract: The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial intelligence. In the intervening years, the idea of cognition as computation has emerged as a fundamental tenet of Artificial Intelligence (AI) and cognitive science. But what kind of computation is cognition? We describe a computational formalism centered around a probabilistic Turing machine called QUERY, which captures the operation of probabilistic conditioning via conditional simulation. Through several examples and analyses, we demonstrate how the QUERY abstraction can be used to cast common-sense reasoning as probabilistic inference in a statistical model of our observations and the uncertain structure of the world that generated that experience. This formulation is a recent synthesis of several research programs in AI and cognitive science, but it also represents a surprising convergence of several of Turing's pioneering insights in AI, the foundations of computation, and statistics.

Abstract: We study the parameterized complexity of domination-type problems (sigma,rho)-domination is a general and unifying framework introduced by Telle: a set D of vertices of a graph G is (sigma,rho)-dominating if for any v in D, |N(v)\cap D| in sigma and for any $v otin D, |N(v)\cap D| in rho We mainly show that for any sigma and rho the problem of (sigma,rho)-domination is W[2] when parameterized by the size of the dominating set This general statement is optimal in the sense that several particular instances of (sigma,rho)-domination are W[2]-complete (eg Dominating Set) We also prove that (sigma,rho)-domination is W[2] for the dual parameterization, ie when parameterized by the size of the dominated set We extend this result to a class of domination-type problems which do not fall into the (sigma,rho)-domination framework, including Connected Dominating Set We also consider problems of coding theory which are related to domination-type problems with parity constraints In particular, we prove that the problem of the minimal distance of a linear code over Fq is W[2] for both standard and dual parameterizations, and W[1]-hard for the dual parameterization To prove W[2]-membership of the domination-type problems we extend the Turing-way to parameterized complexity by introducing a new kind of non deterministic Turing machine with the ability to perform `blind' transitions, ie transitions which do not depend on the content of the tapes We prove that the corresponding problem Short Blind Multi-Tape Non-Deterministic Turing Machine is W[2]-complete We believe that this new machine can be used to prove W[2]-membership of other problems, not necessarily related to domination

Abstract: We present a type system for an extension of lambda calculus with a conditional construction, named STAB, that characterizes the PSPACE class. This system is obtained by extending STA, a type assignment for lambda-calculus inspired by Lafont’s Soft Linear Logic and characterizing the PTIME class. We extend STA by means of a ground type and terms for Booleans and conditional. The key issue in the design of the type system is to manage the contexts in the rule for conditional in an additive way. Thanks to this rule, we are able to program polynomial time Alternating Turing Machines. From the well-known result APTIME = PSPACE, it follows that STAB is complete for PSPACE.Conversely, inspired by the simulation of Alternating Turing machines by means of Deterministic Turing machine, we introduce a call-by-name evaluation machine with two memory devices in order to evaluate programs in polynomial space. As far as we know, this is the first characterization of PSPACE that is based on lambda calculus and light logics.

Abstract: The original TuringTest is modified in order to take into account the age&gender of a Judge who evaluates the machine and the age&gender of a Human with whom the machine is compared during evaluation. This yields a basic taxonomy of TuringTest-consistent scenarios which is subsequently extended by taking into account the type of intelligence being evaluated. Consistently with the Theory of Multiple Intelligences, nine basic intelligence types are proposed, and an example of a possible scenario for evaluation of emotional intelligence in early stages of development is given. It is suggested that specific intelligence types can be subsequently grouped into hierarchy at the top of which is seated an Artificial Intelligence labelled as “meta-modular”. Finally, it is proposed that such a meta-modular AI should be defined as an Artificial Autonomous Agent and should be given all the rights and responsibilities according to age of human counterparts in comparison with whom an AI under question has passed the TuringTest. 1 BASIC TURINGTEST TAXONOMY Primo [1] , we present a labelling schema for a set of diverse artificial intelligence tests inspired by a procedure initially proposed by Alan Mathison Turing [2], in order to standardize attribution and evaluation of the legal status of Artificial Agents (AAs), be it robot, chat-bot or any other non-organic verbally

Abstract: The Church-Turing thesis has stood the test of time, capturing computation models Turing could not have conceived of, including digital computation, probabilistic, parallel and quantum computers and the Internet. The thesis has become accepted doctrine in computer science and the ACM has named its highest honor after Turing. Many now view computation as a fundamental part of nature, like atoms or the integers.

Abstract: We present a practical implementation of a variation of the Turing Test for realistic computer graphics. The test determines whether virtual representations of objects appear as real as genuine objects. Two experiments were conducted wherein a real object and a similar virtual object is presented to test subjects under specific restrictions. A criterion for passing the test is presented based on the probability for the subjects to be unable to recognise a computer generated object as virtual. The experiments show that the specific setup can be used to determine the quality of virtual reality graphics. Based on the results from these experiments, future versions of the Graphics Turing Test could ease the restrictions currently necessary in order to test object telepresence under more general conditions. Furthermore, the test could be used to determine the minimum requirements to achieve object telepresence.

Abstract: Practical application of the Turing Test throws up all sorts of questions regarding the nature of intelligence in both machines and humans. For example - Can machines tell original jokes? What would this mean to a machine if it did so? It has been found that acting as an interrogator even top philosophers can be fooled into thinking a machine is human and/or a human is a machine - why is this? Is it that the machine is performing well or is it that the philosopher is performing badly? All these questions, and more, will be considered. Just what does the Turing test tell us about machines and humans? Actual transcripts will be considered with startling results.

Abstract: In one of the many and fundamental side-remarks made by Turing in his 1950 paper (The Imitation Game paper), an analogy is made between Mechanism and Writing. Turing is aware that his Machine is a writing/re-writing mechanism, but he doesn't go deeper into the comparison. Striding along the history of writing, we shall hint here at the nature and the role of alphabetic writing in the invention of Turing's (and today's) notion of computability. We shall stress that computing is a matter of alphabetic sequence checking and replacement, far away from the physical world, yet related to it once the role of physical measurement is taken into account. Turing Morphogenesis paper, 1952, provides the guidelines for the modern analysis of "continuous dynamics" at the core Turing's late and innovative approach to bio-physical processes.

Abstract: We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity of ultrametric automata can differ very much.

Abstract: 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 Godel, 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.

Abstract: In his first major publication, ‘On computable numbers, with an application to the Entscheidungsproblem’ (1936), Turing introduced his abstract Turing machines.1 (Turing referred to these simply as ‘computing machines’— the American logician Alonzo Church dubbed them ‘Turing machines’.2) ‘On Computable Numbers’ pioneered the idea essential to the modern computer—the concept of controlling a computing machine’s operations by means of a program of coded instructions stored in the machine’s memory. This work had a profound influence on the development in the 1940s of the electronic stored-program digital computer—an influence often neglected or denied by historians of the computer. A Turing machine is an abstract conceptual model. It consists of a scanner and a limitless memory-tape. The tape is divided into squares, each of which may be blank or may bear a single symbol (‘0’ or ‘1’, for example, or some other symbol taken from a finite alphabet). The scanner moves back and forth through the memory, examining one square at a time (the ‘scanned square’). It reads the symbols on the tape and writes further symbols. The tape is both the memory and the vehicle for input and output. The tape may also contain a program of instructions. (Although the tape itself is limitless—Turing’s aim was to show that there are tasks that Turing machines cannot perform, even given unlimited working memory and unlimited time—any input inscribed on the tape must consist of a finite number of symbols.) A Turing machine has a small repertoire of basic operations: move left one square, move right one square, print, and change state. Movement is always by one square at a time. The scanner can print a symbol on the scanned square (after erasing any existing symbol). By changing its state the machine can (as Turing put it) ‘remember some of the symbols which it has “seen”

Abstract: One of the most innovative areas in contemporary research is the study of the deep conceptual connection between physics, information and the “counting” of information, i.e. a search for a computation model for physical systems. Any physical system can be considered as an information processor in dialogue with the external environment. The initial values are transformed into the final ones by the system’s internal dynamics. The Church–Turing Thesis (CTT), in its strong form, states that any processing of syntactic information can be described by means of a suitable Turing Machine (TM). The analogy between a quantum of action and a bit seems very natural (minimum action necessary to cause an observable change in a physical system), and so the CTT, as it is maintained — quite imprecisely — is considered a “statement on the physical world”. Here we ask the question: Is this statement really valid? Is the CT thesis so naturally and obviously applicable to physics? In recent years the critical debate on the limit of application of recursive functions in physics has grown and, in this direction, the two most important research areas are hypercomputation and quantum information theory. Some classical works have strengthened the idea that the behaviour of a mechanical discrete system evolving according to local laws is recursive. Such works have shown the relations between the classical computation theory and the physical deterministic systems. In particular, it can be noted a strong analogy between a TM’s asymptotic unpredictable behaviours and deterministic chaos; in both cases the local rules do not imply a long-term predictable behaviour, indeed [28, 10, 27, 15]. Different strategies have been proposed to apply such computational scheme to the continuous language of differential equations [22]. The general reasons taken into consideration to justify the use of TM in physics can be summarised as follows: Beyond Turing: Hypercomputation and Quantum Morphogenesis

Abstract: Recent cyberattacks have demonstrated that current approaches to the malware problem (e.g., detection) are inadequate. This is not surprising as virus detection is Turing undecidable. 1 Further, some recent malware implementations use NP problems to encrypt and hide the malware. 2 Two goals guide an alternative approach: (a) Program execution should hide computational steps in order to hinder “reverse engineering” efforts by malware hackers; (b) New computational models should be explored that make it more difficult to hijack the purpose of program execution. The methods explained here pertain to (a) implemented with a new computational model, called the active element machine (AEM). 3 An AEM is composed of computational primitives called active elements that simultaneously transmit and receive pulses to and from other active elements. Each pulse has an amplitude and a width, representing how long the pulse amplitude lasts as input to the active element receiving the pulse. If active element Ei simultaneously receives pulses with amplitudes summing to a value greater than Ei’s threshold and Ei’s refractory period has expired, then Ei fires. When Ei fires, it sends pulses to other active elements. If Ei fires at time t, a pulse reaches element Ek at time t+ τik where τik is the transmission time from Ei to Ek. The AEM language uses five commands – Element, Connection, Fire, Program and Meta – to write AEM programs, where time is explicitly specified and multiple commands may simultaneously execute. An Element command creates, at the time specified in the command, an active element with a threshold value, a refractory period and a most recent firing time. A Connection command sets, at the time specified in the command, a pulse amplitude, a pulse width and a transmission time from element Ei to element Ek. The Fire command fires an input element at a particular time. The Program command defines the execution of multiple commands with a single command. Element and Connection commands establish the AEM architecture and firing activity. The Meta command can change the AEM architecture during AEM program execution. This model uses quantum random input to generate random firing patterns that deterministically execute a universal Turing machine (UTM) program η. Random firing interpretations are constructed with dynamic level sets on boolean functions that compute η. The quantum randomness is an essential component for building the random firing patterns that are Turing incomputable. 4 It is assumed that the following are all kept perfectly secret: the state and tape of the UTM, represented by the active elements and connections; the quantum random bits determining how η is computed for each computational step; and the dynamic connections in the AEM. Formally, let f1j , f2j , . . . fmj represent the random firing pattern computing η during the jth computational step and assume an adversary can eavesdrop on f1j , f2j , . . . fmj . Let q denote the current state of the UTM, ak a UTM alphabet symbol and qk a UTM state. Perfect secrecy means that probabilities P (q = qk|f1j = b1 . . . fmj = bm) = P (q = qk) and P (Tk = ak|f1j = b1 . . . fmj = bm) = P (Tk = ak) for each bi ∈ {0, 1} and each Tk which is the contents of the kth tape square. If these secrecy conditions hold, then there doesn’t exist a “reverse engineer” Turing machine that can map the random firing patterns back to an unbounded sequence of UTM instructions. For an unbounded number of computational steps, define function g : N→ {0, 1} where g((j − 1)m+ r) = f(r+1)j and 0 ≤ r < m. Then g is incomputable. Proposed methods of hypercomputation currently have no physical realization. 5 The methods described here can be physically realized using an off-the-shelf quantum random generator device with a USB plug connected to a laptop computer executing a finite AEM program.

Abstract: The Turing Test checks for human intelligence, rather than any putative general intelligence. It involves repeated interaction requiring learning in the form of adaption to the human conversation partner. It is a macro-level post-hoc test in contrast to the definition of a Turing machine, which is a prior micro-level definition. This raises the question of whether learning is just another computational process, i.e., can be implemented as a Turing machine. Here we argue that learning or adaption is fundamentally different from computation, though it does involve processes that can be seen as computations. To illustrate this difference we compare (a) designing a Turing machine and (b) learning a Turing machine, defining them for the purpose of the argument. We show that there is a well-defined sequence of problems which are not effectively designable but are learnable, in the form of the bounded halting problem. Some characteristics of human intelligence are reviewed including it's: interactive nature, learning abilities, imitative tendencies, linguistic ability and context-dependency. A story that explains some of these is the Social Intelligence Hypothesis. If this is broadly correct, this points to the necessity of a considerable period of acculturation (social learning in context) if an artificial intelligence is to pass the Turing Test. Whilst it is always possible to ‘compile' the results of learning into a Turing machine, this would not be a designed Turing machine and would not be able to continually adapt (pass future Turing Tests). We conclude three things, namely that: a purely "designed" Turing machine will never pass the Turing Test; that there is no such thing as a general intelligence since it necessarily involves learning; and that learning/adaption and computation should be clearly distinguished.

Abstract: The parameterized problem $p\textsc{-Halt}$ takes as input a nondeterministic Turing machine $\mathbb{M}$ and a natural number n, the size of $\mathbb{M}$ being the parameter It asks whether every accepting run of $\mathbb{M}$ on empty input tape takes more than n steps This problem is in the class XPuni , the class "uniform XP," if there is an algorithm deciding it, which for fixed machine $\mathbb{M}$ runs in time polynomial in n It turns out that various open problems of different areas of theoretical computer science are related or even equivalent to $p{\rm \textsc{-Halt}\in{XP}_{uni}}$ Thus this statement forms a bridge which allows to derive equivalences between statements of different areas (proof theory, complexity theory, descriptive complexity, …) which at first glance seem to be unrelated As our presentation shows, various of these equivalences may be obtained by the same method

Abstract: Various methods exists in the litearture for denoting the configuration of a Turing Machine. A key difference is whether the head position is indicated by some integer (mathematical representation) or is specified by writing the machine state next to the scanned tape symbol (intrinsic representation). From a mathematical perspective this will make no difference. However, since Turing Machines are primarily used for proving undecidability and/or hardness results these representations do matter. Based on a number of applications we show that the intrinsic representation should be preferred.

Abstract: In this paper we describe how we tried to make the well-known JFLAP Turing machine simulator accessible to blind students taking a theoretical computer science course. Software accessibility is an important topic for both legal and ethical reasons: in our case, however, we also wanted to make the accessible software usable by blind students in cooperation with the other students, in order to encourage the integration of the blind students within the rest of the class. For this reason, the accessible version of the JFLAP Turing machine simulator that we developed is as much similar as possible to and fully compatible with the original one. In the paper, we also report some very satisfactory preliminary validation results that indicate how the new software can really make Turing machines accessible to blind students.

Abstract: We define the main factor of intelligence as the ability to comprehend, for- malising this ability with the help of new constructs based on descriptional complexity. The result is a comprehension test, or C-test, exclusively defined in terms of univer- sal descriptional machines (e.g universal Turing machines). Despite the absolute and non-anthropomorphic character of the test it is equally applicable to both humans and machines. Moreover, it correlates with classical psychometric tests, thus establishing the first firm connection between information theoretic notions and traditional IQ tests. The Turing Test is compared with the C-test and their joint combination is discussed. As a result, the idea of the Turing Test as a practical test of intelligence should be left behind, and substituted by computational and factorial tests of different cognitive abilities, a much more useful approach for artificial intelligence progress and for many other intriguing questions that are presented beyond the Turing Test.

Abstract: We prove that neat and natural fragments of the higher order programming language, PCF, capture complexity classes defined by imposing resource bounds on Turing machines. Moreover, we survey some related research on on Godel’s T, and discuss the relationship between fragments of Godel’s T and fragments of PCF. Our proofs are based on denotational semantics and domain theory.

Abstract: Based upon the principles of Turing incomputability, connectedness and novel properties of the Active Element Machine, a malware-resistant computing machine is constructed. Using randomness, the active element machine can deterministically execute a universal Turing machine (universal digital computer program) with active element firing patterns that are Turing incomputable. In some embodiments, if the state and tape (or other memory) contents of the universal Turing machine and the random bits generated from the quantum source are all kept perfectly secret and no information is leaked about the dynamic connections between the active elements, then it is Turing incomputable to construct a translator Turing machine (translator digital computer program) that maps the random firing interpretations back to the sequence of instructions executed by the universal Turing machine. A more powerful computational procedure is created than Turing's computational procedure (digital computer procedure).

Abstract: In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic Turing machines (EDTMs). We discuss different E-valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recognition is equal to or less than depth-first recognition in general. The equivalence requires an underlying E value lattice to degenerate into an MV algebra. We also study variants of ENTMs. ENTMs with a classical initial state and ENTMs with a classical final state have the same power as ENTMs with quantum initial and final states. In particular, the latter can be simulated by ENTMs with classical transitions under a certain condition. Using these findings, we prove that ENTMs are not equivalent to EDTMs and that ENTMs are more powerful than EDTMs. This is a notable difference from the classical Turing machines.

Abstract: Turing machines are an important concept in theoretical computer science. Several simple languages have been developed till date for modeling and simulation of Turing machines, often for pedagogical purposes. The Turing Machine Description Language (TMDL) is one such language and it is best known for its textbook style descriptive representation of Turing machines. This paper reports the development of a two-pass optimizing compiler for the language. In an experiment, it was observed that the optimizing compiler produces object programs that are up to 1.784 times shorter and 1.032 times faster than those produced by an existing compiler that does not employ code optimization.

Abstract: Alan Mathison Turing is revered among computer scientists for laying down the foundations of theoretical computer science via the introduction of the Turing machine, an abstract model of computation upon which, an elegant notion of cost and a theory of complexity can be developed In this paper we argue that the contribution of Turing to "the other side of computer science", namely the domain of numerical computations as pioneered by Newton, Gauss, &c, and carried out today in the name of numerical analysis, is of an equally foundational nature

Abstract: 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.

Abstract: MyTuringTable is a Turing Machine simulator designed to help students read and understand Turing's seminal 1937 paper on computability. We discuss our reasons for developing the tool, and report on its use in a "Great Ideas in Computer Science" course for the Air Force Academy Cadet Scholars program.

Abstract: We address the view about using the Turing Machine model and the real number model for solving continuous scientific problems. Furthermore we will argue that the Turing Machine is the wrong model of computation for the continuous problems of science.