PPT-1 Turing Machines Reading: Chapter 8

2 Turing Machines are Very powerful abstract machines that could simulate any modern day computer although very very slowly Why design such a machine If a problem cannot be solved. They provide a precise formal de64257nition of what it means for a function to be computable Many other de64257nitions of computation have been proposed over the years for example one could try to formalize precisely what it means to run a program A Turing machine is a primitive yet general computer with an in64257nite tape In each cycle the control unit reads the current tape symbol writes a symbol on the tape moves one position to the left or right and switches to the next state The last th They provide a precise formal de64257nition of what it means for a function to be computable Many other de64257nitions of computation have been proposed over the years for example one could try to formalize precisely what it means to run a program 14. th. September, 2012. Turing and Ordinal Logic. (Or “To Infinity and Beyond …”). James Harland. School of Computer Science & IT, RMIT University. james.harland@rmit.edu.au. Turing at Princeton. Lecture 1: . Introduction & Review. David Steurer. August 23, 2012. What is complexity theory?. problems. resources. 3SAT. ={. satisfiable. 3CNF formulas}. LP. ={feasible linear programs}. How do resource limitations impact. Announcements. Read: Searle “Minds Brains and Programs”. I will be holding extra office hours on Wednesday after lecture.. The big question. Before proceeding to look at an instance of a computational theory of mind (CTM), we need to address an important question: could a machine ever think?. Lecture 1: . Intro; Turing machines; . Class P and NP . . . Indian Institute of Science. About the course. Computational complexity attempts . to classify computational . problems. Lecture 1: . Intro; Turing machines; . Class P and NP . . . Indian Institute of Science. About the course. Computational complexity attempts . to classify computational . problems. the Halting Problem. This work is licensed under the Creative Commons Attribution-. NonCommercial. -. ShareAlike. 3.0 . Unported. License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.. Theory of Computation Lecture 24: Turing Machines III. 1. Turing Machines. Actually, Turing’s original model of a computer was different from the Post-Turing language.. Decidability Concept 4.1. The Halting Problem 4.2. P vs. NP 7.2 and 7.3. NP-completeness & . Cook-Levin Theorem 7.4. Review: Turing Machines in a nutshell. Church-Turing Thesis. Turing Machine . Curriculum Leaders. Theoretical Computers: Fun With Finite State Machines. Computing Without Computers . Insert any specific notes. Start / End time. Toilets. Fire Drill / Exits. Theoretical Computers: Fun With Finite State Machines. Reading: Chapter 8. 2. Turing Machines are…. Very powerful (abstract) machines that could simulate any modern day computer (although very, very slowly!). Why design such a machine?. If a problem cannot be “. The Turing Test Minds & Machines Alan Turing British mathematician known for: Turing Machines (1936) Breaking German Enigma (WWII) Turing Test (1950) ? “I propose to consider the question, 'Can machines think?' This should begin with definitions of the meaning of the terms 'machine 'and 'think'. … [But] Instead of attempting such a definition I shall replace the question by another... The new form of the problem can be described in terms of a game which we call the 'imitation game'.“