## shows a graphical structure of the thesis.

### 그리고 extended Church-Turing thesis 에 의하면

A the beginning of the lesson, we promised that we could link up these two chains and use the transitivity of reductions to show that Vertex Cover and Independent Set were NP-complete. We now turn to the last link in this chain and will reduce 3CNF-SAT to Independent Set. As we’ve already argued these problems are in NP, so that will complete the proofs.

### The Church Turing Thesis: Turing Machine = Max Logical Power

Alan Turing and the Unsolvable Problem To Halt or Not to Halt That Is the Question Cristian S. Calude 26 April 2012 Alan Turing Alan Mathison Turing was born in a nursing home in Paddington, London, now

This bold claim, that any computer is essentially equivalent to aTuring machine grew out of contemporaneous work by Alonzo Church andAlan Turing, and is variously referred to as Church's Thesis, theChurch-Turing Thesis, the Turing-Church thesis, the Church-Turingconjecture, and Turing's thesis. There are several equivalentformulations of the thesis stated at different times and to differentdegrees of rigor, but the central idea is that:

The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world can be translated into an equivalent computation involving a . In Church's original formulation (Church 1935, 1936), the thesis says that real-world calculation can be done using the , which is equivalent to using .There are conflicting points of view about the Church-Turing thesis. One says that it can be proven, and the other says that it serves as a definition for computation. There has never been a proof, but the evidence for its validity comes from the fact that every realistic model of computation, yet discovered, has been shown to be equivalent. If there were a device which could answer questions beyond those that a can answer, then it would be called an .The Church-Turing thesis encompasses more kinds of than those originally envisioned, such as those involving , , , and . It also applies to other kinds of computations found in theoretical computer science such as quantum computing and probabilistic computing.The Church-Turing thesis has been extended to a proposition about the processes in the natural world by Stephen Wolfram in his (Wolfram 2002), which also claims that there are only a small number of intermediate levels of computing power before a system is and that most natural systems are universal.Some computational models are more efficient, in terms of and memory, for different tasks. For example, it is suspected that quantum computers can perform many common tasks with lower , compared to modern computers, in the sense that for large enough versions of these problems, a quantum computer would solve the problem faster than an ordinary computer. In contrast, there exist questions, such as the , which an ordinary computer cannot answer, and according to the Church-Turing thesis, no other computational device can answer such a question.There are various extensions of the Church-Turing thesis that addressthe relative efficiency of different models of computation, such asthe **Complexity-Theoretic Church-Turing Thesis** states that:The Church Turing thesis is perhaps best understood as a**definition** of the types of functions that are calculable inthe real world - not as a theorem to be proven. As evidence for thesuitability of this as a definition, multiple (indeed every oneconsidered to far) distinct models of computation have been shown tobe equivalent to the Turing model with regard to what functions theycan compute.Why engineer systems simulating living creatures and their societies? Well, it helps usunderstand better those living creatures and their societies. But in the process, weobtain artificial creatures with the same capabilities as the ones *simulated* fromthe living creatures. So we have a benefit, both for engineering and biology (Maes, 1991). Invitation to Computer Science, C++ Version, Third Edition 2 Objectives In this chapter, you will learn about: A model of a computing agent A model of an algorithm Turing machine examples The Church–Turing thesis Unsolvable problems

Contents Foreword By Douglas Hofstadter Preface IX XV Part I. Turing's Life and Thoughts Alan Turing: an Introductory Biography 3 Andrew Hodges References 8 Alan's Apple: Hacking the Turing Test 9 Valeria Patera 1 The Author's View 9 2 Turing and the Apple By Giulio Giorello 10 3 The Play 12 References 40 What Would Alan Turing Have Done After 1954? 43 Andrew Hodges 1 A Survey of Turing's Legacy in Church's Thesis and Copeland's Thesis 47 3 Computability and Quantum Physics 53 References 56 From Turing to the Information Society 59 Daniela Cerqui 1 The So-called "Information Society" 59 2 An Anthropological Analysis 60 3 First Tendency: the Disappearing Body? 61 4 Second Tendency: Reproducing Every Bodily Element 65 5 Information as the Lowest Common Denominator 66 6 Turing, Wiener and Cybernetics 67 7 Intelligence, Rationality and Humankind 68 8 From Unorganized to Organized Machines 69