Search 250 million research papers

Machine humour: examples from Turing test experiments

Shah, H., Warwick, K. · Coventry University Open Collections (Coventry university) · 2016

Cited by 0

§ Turing Machines Defined § How a Turing Machine Works § Turing Machine “Addition ” Example § The Halting Problem Defined § Examples of Halting Problem § Oracle Turing Machines Defined § Applications History

Sadika Amreen, Reazul Hoque, Alan Mathison Turing · 2016

mathematician, was influential in the development of computer science. §Turing first described the Turing machine in his 1936 article ”On Computable Numbers, with an Application to the Entscheidungsproblem.” §The Turing machine plays a significant role in the creation of the modern computer. Turing Machines §A Turing machine is a hypothetical machine. §Despite its simplicity, the machine can simulate ANY computer algorithm, no matter how complicated it is! Turing Machines §For simplicity, we assume that this machine can only process 0, 1 and Blank §The machine has a head which is positioned over one of the squares on the tape §The head can perform the following three basic operations: • Read the symbol on the square under the head • Edit the symbol by writing a new symbol or erasing it • Move the tape left or right by one square so that the machine can read and edit the symbol on a neighboring square Turing Machines §A very simple representation of a Turing Machine would consist of a infinitely long tape (memory) §Each square on the tape is Blank at the start and symbols can be written over it How a Turing Machine Works We will try to print symbols “1 1 0 ” on an initially blank tape 1 We write a “1 ” on the square under the head Next, we move the tape left by one square 1 Now, write “1 ” on the square under the head

Cited by 0

Defining a Halting Decidability Decider

Olcott, Pete · PhilPapers (PhilPapers Foundation)

In this paper we show how to define a halting decidability decider that rejects all finite string Turing machine descriptions that would otherwise make halting undecidable. All of the conventional halting problem proof counter-examples would be rejected on the basis that they specify an infinitely recursive evaluation sequence thus are malformed expressions of the language of Turing Machine descriptions. \n

Cited by 0

On real-time Turing machines

Hanák, Jan · Czech Digital Mathematics Library (Institute of Mathematics CAS) · 1966

Generalizing Rabin's idea of the "bottleneck square" we give certain sufficient conditions for the non-recognition by one-tape one-head real time Turing machines.The use of our result (Theorem 2) is illustrated in examples, especially there is constructed a set not recognizable by the above mentioned Turing machines but recognized by a one-twodimensional tape one-head real-time Turing machine and by a two-(onedimensional) tape one-head real-time Turing machine, too.1. BASIC CONCEPTS *) By a segment we mean a nonempty set of squares (of the tape) which with every two squares contains also all the squares lying between them.

Cited by 0Open access

Classically-controlled Quantum Computation

Simon Perdrix, Philippe Jorrand · Electronic Notes in Theoretical Computer Science · 2006

It is reasonable to assume that quantum computations take place under the control of the classical world. For modeling this standard situation, we introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing machine with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In CQTM, unitary transformations and quantum measurements are allowed. We show that any classical Turing machine is simulated by a CQTM without loss of efficiency. Furthermore, we show that any k-tape CQTM is simulated by a 2-tape CQTM with a quadratic loss of efficiency. The gap between classical and quantum computations which was already pointed out in the framework of measurement-based quantum computation (see [ 13]) is confirmed in the general case of classically-controlled quantum computation. In order to appreciate the similarity between programming classical Turing machines and programming CQTM, some examples of CQTM are given. Keywords: Classically-Controlled Quantum Computation, Quantum Turing Machine 1.

Cited by 11Open access

ON THE NECESSITY OF FORMAL MODELS FOR REAL-TIME PARALLEL COMPUTATIONS

Stefan D. Bruda, Selim G. Akl · Parallel Processing Letters · 2001

We assume the multitape real-time Turing machine as a formal model for parallel real-time computation. Then, we show that, for any positive integer k, there is at least one language L k which is accepted by a k-tape real-Turing machine, but cannot be accepted by a (k - 1)-tape real-time Turing machine. It follows therefore that the languages accepted by real-time Turing machines form an infinite hierarchy with respect to the number of tapes used. Although this result was previously obtained elsewhere, our proof is considerably shorter, and explicitly builds the languages L k . The ability of the real-time Turing machine to model practical real-time and/or parallel computations is open to debate. Nevertheless, our result shows how a complexity theory based on a formal model can draw interesting results that are of more general nature than those derived from examples. Thus, we hope to offer a motivation for looking into realistic parallel real-time models of computation.

Cited by 6

The Future of Human-machine communication: The Turing test

Kevin Warwick, Huma Shah · Pure (Coventry University) · 2017

The Turing test is regarded as the ultimate milestone for machine communication abilities. It involves distinguishing between a human and a computer in their responses to unrestricted questions. Here we investigate the nature of the<br/>communications, including behaviors and interaction in real Turing test scenarios to assess the state of play. In particular we consider the effects of lying, misunderstanding, humor, and lack of knowledge, giving actual examples of each. We look at specific cases of machines performing well and consider transcripts taken from the 2014 Royal Society experiment when a machine first passed the Turing test.

Cited by 0Open access

Topological entropy of Turing complete dynamics (with an appendix by Ville Salo)

Renzo Bruera, Robert Cardona, Eva Miranda et al. · arXiv (Cornell University) · 2024

We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "regular Turing machines" (which includes most of the examples of universal Turing machines) has positive topological entropy. We deduce that any Turing complete dynamics with a continuous encoding that simulates a universal machine in this class is chaotic. This applies to our previous constructions of Turing complete area-preserving diffeomorphisms of the disk and 3D stationary Euler flows. The article concludes with an appendix written by Ville Salo that introduces a method to construct universal Turing machines that are not regular and have zero topological entropy.

Cited by 0Open access

A Comparative Study on Quantum Pushdown Automata, Turing Machine and Quantum Turing Machine

Tanistha Nayak, Tirtharaj Dash · 2012

Abstract — An automaton is a simple model of computer. There are various automata each with its formal definition. Generally an automaton has some form of input, some form of output, internal states may or may not have some from of storage, hardwired not programmable. In this paper we have discussed about Quantum Pushdown Automata, Turing Machine and Quantum Turing Machine and compared the power among these and by taking some interesting examples. Our main objective is to study about these three machines.

Cited by 0

Physical Hypercomputation and the Church–Turing

2008

Abstract. We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy’s thesis. Key words: Church–Turing thesis, effective computation, Gandy’s thesis, physical hypercomputation, supertasks A hypercomputer is a physical or an abstract system that computes functions that cannot be computed by a universal Turing machine. Turing (1939) was perhaps the first to introduce hypercomputers. He called them o-machines, for machines with oracles. Other examples of hypercomputers are described in Copeland and Sylvan (1999). In what follows we describe a possible physical device that computes a non-Turing computable function. This physical hypercomputer is a version of the devices introduced by Pitowsky (1990) and Hogarth (1992, 1994). We consider

Cited by 0

The definition of formal languages in the meta language of normal forms of knowledge

A.F. Kurgaev, S.M. Grygoryev · PROBLEMS IN PROGRAMMING · 2017

The expressive means of the metalanguage of normal forms of knowledge in relation to different level formal languages are investigated. The formal descriptions of a multitude of linguistic examples are given. The graphic metadescription equivalent to the given text description of the interpreter of the universal Turing machine is developed. The description provided of the universal Turing machine interpreter can be applied to solving the task of modelling the behavior of any T-machine (which performs the task of data conversion on its memory tape). The formal definition of the translator of the determined Turing machine is given. The ability to describe in the metalanguage of normal forms of knowledge the interpreting-translating and the translating-translating processes of formulating and solving of a given task, for which a solution exists is substantiated and defined. Problems in programming 2017; 4: 037-050

Cited by 1Open access

KEYWORDS: accelerating Turing machine, asynchronous computation, Church&amp;apos;s thesis,

B. Jack Copel, Oron Shagrir · 2008

What are the limits of physical computation? In his &amp;apos;Church&amp;apos;s Thesis and Principles for Mechanisms&amp;apos;, Turing&amp;apos;s student Robin Gandy proved that any machine satisfying four idealised physical &amp;apos;principles &amp;apos; is equivalent to some Turing machine. Gandy&amp;apos;s four principles in effect define a class of computing machines (&amp;apos;Gandy machines&amp;apos;). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We will point to interesting examples of (ideal) physical machines that fall outside the class of Gandy machines and compute functions that are not Turing-machine computable. 1.

Cited by 0

Translation of Quantum Circuits into Quantum Turing Machines for Deutsch and Deutsch-Jozsa Problems

Corrente, Giuseppe · arXiv (Cornell University) · 2021

We want in this article to show the usefulness of Quantum Turing Machine (QTM) in a high-level didactic context as well as in theoretical studies. We use QTM to show its equivalence with quantum circuit model for Deutsch and Deutsch-Jozsa algorithms. Further we introduce a strategy of translation from Quantum Circuit to Quantum Turing models by these examples. Moreover we illustrate some features of Quantum Computing such as superposition from a QTM point of view and starting with few simple examples very known in Quantum Circuit form.

Cited by 0Open access

Turing Computability

George Boolos, John P. Burgess, Richard C. Jeffrey · Cambridge University Press eBooks · 2002

A function is effectively computable if there are definite, explicit rules by following which one could in principle compute its value for any given arguments. This notion will be further explained below, but even after further explanation it remains an intuitive notion. In this chapter we pursue the analysis of computability by introducing a rigorously defined notion of a Turing-computable function. It will be obvious from the definition that Turing-computable functions are effectively computable. The hypothesis that, conversely, every effectively computable function is Turing computable is known as Turing's thesis. This thesis is not obvious, nor can it be rigorously proved (since the notion of effective computability is an intuitive and not a rigorously defined one), but an enormous amount of evidence has been accumulated for it. A small part of that evidence will be presented in this chapter, with more in chapters to come. We first introduce the notion of Turing machine, give examples, and then present the official definition of what it is for a function to be computable by a Turing machine, or Turing computable.

Cited by 0

Classically controlled quantum computation

SIMON PERDRIX, PHILIPPE JORRAND · Mathematical Structures in Computer Science · 2006

It is reasonable to assume that quantum computations take place under the control of the classical world. For modelling this standard situation, we introduce a Classically controlled Quantum Turing Machine (CQTM), which is a Turing machine with a quantum tape for acting on quantum data, and a classical transition function for formalised classical control. In a CQTM, unitary transformations and quantum measurements are allowed. We show that any classical Turing machine can be simulated by a CQTM without loss of efficiency. Furthermore, we show that any -tape CQTM can be simulated by a 2-tape CQTM with a quadratic loss of efficiency. In order to compare CQTMs with existing models of quantum computation, we prove that any uniform family of quantum circuits (Yao 1993) is efficiently approximated by a CQTM. Moreover, we prove that any semi-uniform family of quantum circuits (Nishimura and Ozawa 2002), and any measurement calculus pattern (Danos et al. 2004) are efficiently simulated by a CQTM. Finally, we introduce a Measurement-based Quantum Turing Machine (MQTM), which is a restriction of CQTMs in which only projective measurements are allowed. We prove that any CQTM is efficiently simulated by a MQTM. In order to appreciate the similarity between programming classical Turing machines and programming CQTMs, some examples of CQTMs are given.

Cited by 10

An Introductory Survey of Artificial Intelligence: Concepts and Key Models

Shanglin Wu · Advances in Engineering Technology Research · 2025

Artificial intelligence（AI） is an emerging subfield of computer science. A hundred years ago, it was unimaginable for people to conceive of a machine that could study as a human. At an early stage of artificial intelligence, the father of artificial intelligence, Alan Turing, designed an advanced test named the Turing test, which inspires people to believe that a machine is capable of imitating humans. Following his step, a lot of scientists made significant contributions to artificial intelligence development. Nowadays, AI is a complex field, encompassing machine learning and deep learning as two key examples. Both of these two examples are inspired by the human’ thinking process. Machine learning focuses on learning and analyzing data to produce a reliable output, while deep learning can simulate the structure of human’ brain and address the problem by using neural networks. Knowing the development of artificial intelligence and how these algorithms work is crucial for understanding this interesting new branch of computer science.

Cited by 0Open access

Towards a molecular logic machine

F. Remacle, R. D. Levine · The Journal of Chemical Physics · 2001

Finite state logic machines can be realized by pump–probe spectroscopic experiments on an isolated molecule. The most elaborate setup, a Turing machine, can be programmed to carry out a specific computation. We argue that a molecule can be similarly programmed, and provide examples using two photon spectroscopies. The states of the molecule serve as the possible states of the head of the Turing machine and the physics of the problem determines the possible instructions of the program. The tape is written in an alphabet that allows the listing of the different pump and probe signals that are applied in a given experiment. Different experiments using the same set of molecular levels correspond to different tapes that can be read and processed by the same head and program. The analogy to a Turing machine is not a mechanical one and is not completely molecular because the tape is not part of the molecular machine. We therefore also discuss molecular finite state machines, such as sequential devices, for which the tape is not part of the machine. Nonmolecular tapes allow for quite long input sequences with a rich alphabet (at the level of 7 bits) and laser pulse shaping experiments provide concrete examples. Single molecule spectroscopies show that a single molecule can be repeatedly cycled through a logical operation.

Cited by 45

TURING GAMES: A STUDY OF EQUIVALENCE BETWEEN GAMES AND COMPUTATION

Devang Thakkar · 2008

Abstract. In this paper I try to explore the equivalence of Turing Machines and games. The main idea I am trying to achieve is that every computation is a game and vice versa. Now the basic model that computer science proposes for computation is the model of a Turing machine where in the machine has a state transition function which is a set of rules that define what state you should be in and an input tape which consists of symbols based on which future decisions are made. The model that I propose tries to achieve a smooth transition between a game and a Turing Machine and hence allows application of mathematical techniques of either field to be applied to the other. I provide the basis and examples of two transforms; one that converts a Turing machine into a game and second that converts a game to a Turing machine. The main question that might be arising in your mind right now is what purpose does this serve? The reasoning here is if I am able to generalize my transforms and make these reductions possible then I can use the relation between language strings and paths to equilibrium that I prove in this paper to provide useful reductions from hard problems arising in the fields of both computational complexity and game theory to simpler ones in the other field. Finally I provide various open questions for future work in this area and also some applications of the results proposed here.

Cited by 0

Lecture 5

Jonathan Katz · 2009

We show two lower bounds that are proved using related ideas. The results are not necessarily so interesting in their own right, but the proofs are interesting as rare examples in complexity theory when we can prove a direct lower bound on the power of a (uniform) complexity class! 1.1 One-Tape Turing Machines We first show a language L requiring quadratic time to decide on a one-tape Turing machine. Besides being interesting in its own right, it separates the power of one-tape and two-tape machines (since L can be decided in linear time on a two-tape Turing machine). For a finite string x over any alphabet, let ¯x be the reverse of x. Taking Σ = {0,1,#}, define the language of palindromes as: L def = {x¯x | x ∈ Σ ∗}. Theorem 1 Deciding L requires time Ω(n 2) on a one-tape Turing machine. Proof Let M be a one-tape Turing machine deciding L. For each n which is a multiple of four, consider the following subset of L: Ln def = {x # n 2 ¯x | x ∈ {0,1} n 4}. For any x ∈ Ln and position i ∈ {1,...,n} on the tape of M, let Ci(x), the crossing sequence on x at position i, denote the ordered sequence of states that M is in as the head of M crosses over the line between the ith and (i + 1)th cells (in either direction). Define C(x) def

Cited by 0

Random numbers as probabilities of machine behaviour

George Barmpalias, Douglas Cenzer, Christopher P. Porter · arXiv (Cornell University) · 2016

A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary codes. For example, Chaitin's Omega is a well known Martin-Loef random number that is obtained by considering the halting probability of a universal prefix-free machine. In the last decade, similar examples have been obtained for higher forms of randomness, i.e. randomness relative to strong oracles. In this work we obtain characterizations of the algorithmically random reals in higher randomness classes, as probabilities of certain events that can happen when an oracle universal machine runs probabilistically on a random oracle. Moreover we apply our analysis to different machine models, including oracle Turing machines, prefix-free machines, and models for infinite online computation. We find that in many cases the arithmetical complexity of a property is directly reflected in the strength of the algorithmic randomness of the probability with which it occurs, on any given universal machine. On the other hand, we point to many examples where this does not happen and the probability is a number whose algorithmic randomness is not the maximum possible (with respect to its arithmetical complexity). Finally we find that, unlike the halting probability of a universal machine, the probabilities of more complex properties like totality, cofinality, computability or completeness do not necessarily have the same Turing degree when they are defined with respect to different universal machines.

Cited by 0Open access