PPT-1 Introduction to Computability Theory

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 . This conviction of the solvability of every mathematical problem is a powerful incentive to the worker We hear within us the perpetual call There is the problem Seek its solution You can 64257nd it by pure reason for in mathematics these is no ign elseviercomlocatetcs The concept of computability Carol E Cleland Department of Philosophy Institute for Cognitive Science University of Colorado Boulder CO 8009 USA Received August 2003 received in revised form November 2003 Abstract explore the con More precisely we can explain what it means for a partial arith metic function to be computable Since we can code any 64257nite discrete object as a natural number in a natural way we also have a notion of computability on these obj ects We can use . Nachum Dershowitz and Yuri Gurevich. 1. Some basic definition. The functions which can be built up from the initial functions using composition, primitive recursion and inversion are called the . Sanjit A. SeshiaEECS, UC BerkeleyAcknowledgments: L.vonAhn, L. Blum, M. Blum S. A. SeshiaWhat we Lecture14: Recap. Prof. Amos Israeli. Regular languages – Finite automata.. Context free languages – Stack automata.. Decidable languages – Turing machines.. Undecidability.. Reductions.. Subjects. 15-453. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. MINIMIZING . DFAs. THURSDAY Jan . 24. IS THIS . MINIMAL?. 1. 1. 1. 1. 0. 0. 0. 0. NO. IS THIS . MINIMAL?. 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 . 12 computability problemiscomputableifitcanbesolvedbysomealgorithm;aproblemthatisnoncomputablecannotbesolvedbyanyalgorithm.Section12.1considers instructional . design. Prepared by:. Soo. . Pei . Zhi. P-QM0033/10. QIM 501 Instructional Design and Delivery . by. David. Paul . Ausubel. Biography. Biography. Introduction. During meaningful learning, the person “subsumes,” or organizes or incorporates, new knowledge into old knowledge.. 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. . Sigmund Freud is the father of psychoanalysis. He based many . of his theories on the idea of . the social archetype which causes archetypal theory to have similarities with Psychological Criticism (which we will look at later this semester. . Theoretical Traditions. Macro and Micro Level Theories . 1. Neoclassical Criminology . The Classical School Rebirth. Deterrence Theory. Rational Choice Theory . 2. 3. Before the . Classical School of Criminology . 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.