Computational Models - Introduction 1 Handout Mode Instructors: Prof. Iftach Haitner iftach.haitner at cs.tau.ac.il Teaching Assistants: Noam Mazor [email protected]Mark Roznov markroza at post.tau.ac.il Tel Aviv University. Fall Semester, 2017-2018. Mondays, 13–16 October 23, 2017 1 Based on slides by Benny Chor, Tel Aviv University, modifying slides by Maurice Herlihy, Brown University. Iftach Haitner (TAU) Computational Models - Introduction October 23, 2017 1 / 28
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Computational Models - Introduction1
Handout Mode
Instructors:Prof. Iftach Haitner iftach.haitner at cs.tau.ac.il
I Midterm, covering first 6 lectures (up to computability). We will discuss itwhen we get closer.
I Midterm (magen) is scheduled to Friday, December 1, 2017.
I Final exam, covering all course material.
I You must pass the final exam to get a passing course grade.
I Final Grade: 0.75 · Exam + 0.15 ·max{Midterm,Exam}+ 0.10 · HW .
I Prerequisites (formally): Extended introduction to computer scienceI But most importantly is “mathematical maturity”.I Students from other disciplines with mathematical background
encouraged to contact the instructor.
I Textbook: Sipser — Introduction to the theory of computation, first orsecond editions.
I Other (excelent) book: Hopcroft, Motwani, and Ullman —Introduction to Automata Theory, Languages, and Computation.
I Related to controllers and hardware design.I Useful in text processing and finding patterns in strings.I Probabilistic (Markov) versions useful in modeling various natural
phenomena (e.g. speech recognition).
I Push down automata.
I Tightly related to a family of languages known as context freelanguages.
I Play important role in compilers, design of programming languages,and studies of natural languages.
In the first half of the 20th century, mathematicians such as Kurt Göedel, AlanTuring, and Alonzo Church discovered that some fundamental problemscannot be solved by computers.
I Proof verification of statements can be automated.
I It is natural to expect that determining validity can also be done by acomputer.
I Theorem: A computer cannot determine if mathematical statement trueor false.
I Results needed theoretical models for computers.
I These theoretical models helped lead to the construction of realcomputers.
Base step: A single-cow set is definitely the same color.Induction Step: Assume all sets of i cows are the same color.Divide the set {1, . . . , i + 1} into U = {1, . . . , i}, and V = {2, . . . , i + 1}.
All cows in U are the same color by the induction hypothesis.All cows in V are the same color by the induction hypothesis.All cows in U ∩ V are the same color by the induction hypothesis.
Hence, all cows are the same color.Quod Erat Demonstrandum (QED).