PPT-Chapter 1 INTRODUCTION TO THE THEORY OF COMPUTATION

Learning Objectives At the conclusion of the chapter the student will be able to Define the three basic concepts in the theory of computation automaton formal language and grammar Solve exercises using mathematical techniques and notation learned in previous courses. Mike Stannett, University of Sheffield (m.stannett@dcs.shef.ac.uk). New Worlds of Computation, LIFO, . Orléans. , 23 May 2011. Outline of talk. Cosmological computation (what is it?). First-order relativity theories (Andréka et al.). π. . by Archimedes. Bill McKeeman. Dartmouth College. 2012.02.15. Abstract. It is famously known that Archimedes approximated . π.  by computing the perimeters of . many-sided . regular polygons, one polygon inside the circle and one outside. This presentation recapitulates . Theory of Computation Lecture 4: Programs and Computable Functions II. 1. Computable Functions. What does it exactly mean when we say that a program computes a function?. Theory of Computation Lecture 16: A Universal Program VII. 1. Recursively Enumerable Sets. Definition:. The set B  N is called . recursively enumerable. Theory of Computation Lecture 12: A Universal Program IV. 1. The Halting Problem. Let us define the predicate . HALT(x, y).. For a given number y, let . P. be the program such that #(. 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.. 1. Topics ahead. Computation in general. Hilbert’s Program: Is mathematics. c. omplete,. c. onsistent and. decidable? (. Entscheidungsproblem. ). Answers. Goedel’s. theorem. Turing’s machine. Chapter 4: Computation. Fall 2017. http://cseweb.ucsd.edu/. classes/fa17/cse105-a/. Today's learning goals . Sipser Ch 4.1, 4.2. Trace high-level descriptions of algorithms for computational problems.. Use counting arguments to prove the existence of unrecognizable (undecidable) languages.. Ranjit . Kumaresan. (MIT). Based on joint works with . Iddo. . Bentov. (. Technion. ), Tal Moran (IDC), Guy . Zyskind. (MIT). x. f. . (. x,y. ). y. f. . (. x,y. ). Secure Computation. Most general problem in cryptography. What is possible to compute?. We can prove that there are some problems computers cannot solve. There are some problems computers can theoretically solve, but are intractable (would take too long to compute to be practical). What is possible to compute?. We can prove that there are some problems computers cannot solve. There are some problems computers can theoretically solve, but are intractable (would take too long to compute to be practical). Fall . 2017. http://cseweb.ucsd.edu/classes/fa17/cse105-a/. Learning goals. Introductions. Clickers. When did you take CSE 20?. Winter 2017. Fall 2016. Spring 2016. Winter 2016. PETER 108: AC. To change your remote frequency. 1. Computation. In general, a . partial function. f on a set S. m. is a function whose domain is a subset of S. m. .. If a partial function on S. m. has the domain S. m. , then it is called . total. Charly Collin – . Sumanta. . Pattanaik. – Patrick . LiKamWa. Kadi Bouatouch. Painted materials. Painted materials. Painted materials. Painted materials. Our goal. Base layer. Binder thickness.