PPT-1 Introduction to Computability Theory

Lecture14 The Halting Problem Prof Amos Israeli In this lecture we present an undecidable language The language that we prove to be undecidable is a very natural language namely the language consisting of pairs of the form where . 045J18400J utomata Computability and Complexity Prof Nanc ynch Recitation 4 Distinguishable strings and indices ebruary 29 2007 Elena Grigor escu Pr oblem Quiz Questions Pr oblem Recall quiz question Ar gue t Lecture5: Context . Free Languages. Prof. Amos Israeli. On the last lecture we completed our study of regular languages. (There is still a lot to learn but our time is limited…).. Introduction and Motivation. J Paul Gibson. TSP: . Mathematical. . Foundations. MAT7003/. L7-. Computability. .. 1. MAT 7003 : Mathematical Foundations. (for Software Engineering). J . Paul. Gibson, A207. paul.gibson@it-sudparis.eu. Lecture2: Non Deterministic Finite . Automata (cont.). Prof. Amos Israeli. Roadmap for Lecture. In this lecture we:. Prove that NFA-s and DFA-s are . equivalent. . . Present . the three regular operations.. Lecture14: Recap. Prof. Amos Israeli. Regular languages – Finite automata.. Context free languages – Stack automata.. Decidable languages – Turing machines.. Undecidability.. Reductions.. Subjects. Lecture7: . PushDown . Automata (Part 1). Prof. Amos Israeli. In this lecture we introduce . Pushdown Automata. , a computational model equivalent to context free languages.. A pushdown automata is an NFA . Lecture10: . Turing Machines. Prof. Amos Israeli. In this lecture we introduce . Turing Machines . and discuss some of their properties.. Introduction and Motivation. . 2. A . Turing Machine . is a finite state machine augmented with an infinite tape.. Lecture4: Non Regular Languages. Prof. Amos Israeli. Motivate the Pumping Lemma. . Present and demonstrate the . pumping. concept.. Present and prove the . Pumping Lemma. .. Use the pumping lemma to . Lecture11: . Variants of Turing Machines. Prof. Amos Israeli. There are many alternative definitions of Turing machines. Those are called . variants . of the original Turing machine. Among the variants are machines with many tapes and non deterministic machines. . An Approach to Smoking Cessation using Acupuncture, Herbs, and Lifestyle Management. World Health Organization. Tobacco Dependence. “Diseases, symptoms or conditions for which the therapeutic effect of acupuncture has been shown but for which further proof is needed”. Lecture9: Variants of Turing Machines. Prof. Amos Israeli. There are many alternative definitions of Turing machines. Those are called . variants . of the original Turing machine. Among the variants are machines with many tapes and non deterministic machines. . Social and Political Philosophy. Our subject matter this semester has traditionally been associated with practical philosophy.. There are clearly theoretical elements involved (the nature of power, the sources of authority) but the aim of inquiring into these matters is ultimately to make choices about our life together.. In this topic, we will:. Ask what is computable. Describe a Turing machine. Define Turing completeness. Computability. How do we define what is and what is not computable?. Is it possible to write a C++ function which cannot be written using Pascal, Java, or C#, or vice versa?. Turing\'s World is a self-contained introduction to Turing machines, one of the fundamental notions of logic and computer science. The text and accompanying diskette allow the user to design, debug, and run sophisticated Turing machines in a graphical environment on the Macintosh. Turning\'s World introduces users to the key concpets in computability theory through a sequence of over 100 exercises and projects. Within minutes, users learn to build simple Turing machines using a convenient package of graphical functions. Exercises then progress through a significant portion of elementary computability theory, covering such topics as the Halting problem, the Busy Beaver function, recursive functions, and undecidability. Version 3.0 is an extensive revision and enhancement of earlier releases of the program, allowing the construction of one-way and two-way finite state machines (finite automata), as well as nondeterministic Turing and finite-state machines. Special exercises allow users to explore these alternative machines.