Homework. Staff. Happy and fruitful New Year. Welcome to CS105. (Happy New Year) שנה טובה. Meeting Times.
|
|
- Dinah Day
- 6 years ago
- Views:
Transcription
1 Welcome to CS5 and Happy and fruitful ew Year שנה טובה (Happy ew Year) Meeting Times Lectures: Tue Thu 3:3p -4:5p WLH ote: Thu Oct 9 Lecture is canceled there may be a make-up lecture by quarter s end. Sections: Mon :p -:5p WLH 9 Scott Tue 3:p -3:5p WLH 9 Amos ote: Students should come to both sections. Mid-term: Thu Oct 3 3:3p WLH Final: Tue Dec 9 :3a -:p TBA 3 Staff Instructor: Amos Israeli room -6. Office Hours: Fri - or by arrangement Tel#: aisraeli at cs.ucsd.edu TA: Scott Yilek room B-4a Office Hours: Mon 4-5:3 syilek at cs.ucsd.edu Web Page: Homework There will be 5-6 assignments. Assignments will be given on Monday s section and must be returned by the Thu lecture one week later. First assignment will be given next Monday and must be returned on Wed Oct 8 or in Scott s mailbox on Thu Oct 9 th. 4
2 Academic Integrity You are encouraged to discuss the assignments problems among yourselves. Each student must hand in her/his own solution. You must Adhere to all rules of Academic Integrity of CS Dept. UCSD and others. (Meaning: no cheating or copying from any source) 5 Grading A: (85-) B: (7-84) C: (55-69) D: (4-54) F: (-39) 7 Grading Assignments: % Midterm: 3% -% (students are allowed to drop it) open book open notes. Final: 5% -8% open book open notes. 6 Bibliography Required: Michael Sipser: Introduction to the Theory of Computation Second Edition Thomson. 8
3 Introduction to Computability Theory Lecture: Finite Automata and Regular Languages Prof. Amos Israeli (פרופ' עמוס ישראלי) 9 Introduction Computability Theory deals with the profound mathematical basis for Computer Science yet it has some interesting practical ramifications that I will try to point out sometimes. The question we will try to answer in this course is: What can be computed? What Cannot be computed and where is the line between the two? Introduction Computer Science stems from two starting points: Mathematics: What can be computed? And what cannot be computed? Electrical Engineering:How can we build computers? ot in this course. Computational Models A Computational Model is a mathematical object (Defined on paper) that enables us to reason about computation and to study the properties and limitations of computing. We will deal with Three principal computational models in increasing order of Computational Power.
4 Computational Models We will deal with three principal models of computations:. Finite Automaton (in short FA). recognizes Regular Languages.. Stack Automaton. recognizes Context Free Languages. 3. Turing Machines (in short TM). recognizes Computable Languages. 3 Finite Automata - A Short Example The control of a washing machine is a very simple example of a finite automaton. The most simple washing machine accepts quarters and operation does not start until at least 3 quarters were inserted. Alan Turing -A Short Detour Dr. Alan Turing is one of the founders of Computer Science (he was an English Mathematician). Important facts:. Invented Turing machines.. Invented the Turing Test. 3. Broke the German submarine transmission coding machine Enigma. 4. Was arraigned for being gay and committed suicide soon after. 4 Thanks: Vadim Lyubasehvsky ow on PostDoc in Tel-Aviv
5 Finite Automata - A Short Example The control of a washing machine is a very simple example of a finite automaton. The most simple washing machine accepts quarters and operation does not start until at least 3 quarters were inserted. The second washing machine accepts 5 cents coins as well. Finite Automata - A Short Example The control of a washing machine is a very simple example of a finite automaton. The most simple washing machine accepts quarters and operation does not start until at least 3 quarters were inserted. The second washing machine accepts 5 cents coins as well. The most complex washing machine accepts $ coins too.
6 Finite Automaton -An Example q s q q States: Q = { q q q s Initial State: s Final State: q q } Finite Automaton Formal Definition ( F ) A finite automaton is a 5-tupple Q Σδ q where:. Q is a finite set called the states.. Σ is a finite set called the alphabet. 3. δ : Q Σ Q is the transition function. 4. q Q is the start state and 5. F Q is the set of accept states. 3 Finite Automaton An Example q s q q Transition Function: δ ( q s ) = q δ ( q s ) = q δ ( q ) =δ ( q ) = q δ ( q ) =δ ( q ) = q Alphabet: { }. ote: Each state has all transitions. Accepted words:... Observations. Each state has a single transition for each symbol in the alphabet.. Every FA has a computation for every finite string over the alphabet. 4
7 Examples. accepts all words (strings) ending with. M The language recognized by called L ( ) M M ( ) { } satisfies: L M ends with. = w w 5 The automaton Correctness Argument: The FA s states encode the last input bit and q is the only accepting state. The transition function preserves the states encoding. How to do it. Find some simple examples (short accepted and rejected words). Think what should each state remember (represent). 3. Draw the states with a proper name. 4. Draw transitions that preserve the states memory. 5. Validate or correct. 6. Write a correctness argument. Examples. accepts all words (strings) ending with. M ( ) { ends with } L M = w w. accepts all words ending with. M 3. accepts all words ending with and M 4 ε the empty word. This is the Complement Automaton of.. M 8
8 Examples M. accepts all words (strings) ending with. ( ) { ends with } L M = w w.. accepts all words ending with. M 3 M { ab } 3. accepts all strings over alphabet 4 that start and end with the samesymbol. 9 Languages Definition:A language is a set of strings over some alphabet. Examples: L = L L 3 { } m n { n are positive integers } = m = bit strings whose binary value is a multiple of 4 3 Examples (cont) n m M 5 4. accepts all words of the form mn m n > where are integers and. 5. accepts all words in. M 6 { } 3 Languages A language of an FA M L M is the set of M ( ) words (strings) that M accepts. ( M ) If we say that recognizes. La = L M La If La is recognized by some finite A La automaton is a Regular Language. 3
9 Some Questions Q: How do you prove that a language La is regular? M ( ) A: By presenting an FA satisfying La= L M. Q: How do you prove that a language La is not regular? A: Hard! to be answered on Week3 of the course. Q3: Why is it important? A3: Recognition of a regular language requires a controller with bounded Memory. 33 The Regular Operations given a language one can verify it is regular by presenting an FA that accept the language. Regular Operations give us a systematic way of constructing languages that are apriority regular. (That is: o verification is required). 35 The Regular Operations Let A and B be regular languages above the same alphabet. We define the 3 Regular Operations: Σ { } { } { x x x k and x A } Union: A B = x x A or x B. Concatenation: A o B = xy x A and y B. * Star: A =.... k k 34 The Regular Operations - Examples A = { good bad } A o B = goodgirl goodboy badgirl. B = { girl boy } { good bad girl boy } { badboy } A B = * ε good bad goodgood goodbad A =. goodgoodgoodbad badbadgood bad... 36
10 Theorem The class of Regular languages above the same alphabet is closedunder the union operation. Meaning: The union of two regular languages is Regular.. 37 Proof idea If A and A are regular each has its own recognizing automaton and respectively. In order to prove that the language A A is regular we have to construct an FA that accepts exactly the words in A A. ote:cannot apply followed by. 39 Example { } { } Consider L starts with and = w w L = w ends with. w The union set is the set of all bit strings that either start with or end with. Each of these sets can be recognized by an FA with 3 states. Can you construct an FA that recognizes the union set? Proof idea We construct an FA that simulates the computations of and simultaneously. Each state of the simulating FA represents a pair of states of and of respectively. Can you define the transition function and the final state(s) of the simulating FA? 4
11 Wrap up In this talk we:. Motivated the course.. Defined Finite Automata (Latin Pl. form of automaton). 3. Learned how to deal with construction of automata and how to come up with a correctness argument. A 4
Homework. Staff. Happy and fruitful New Year. Welcome to CSE105. (Happy New Year) שנה טובה. and. Meeting Times
Welcome to CSE5 and Happy and fruitful New Year שנה טובה (Happy New Year) Meeting Times Lectures: Tue Thu :p -3:p Cognitive Science Building Sections: Mon :p -:5p Pepper Canyon Hall Will Tue :p -:5p WLH
More informationComputational Models - Lecture 1 1
Computational Models - Lecture 1 1 Handout Mode Ronitt Rubinfeld and Iftach Haitner. Tel Aviv University. February 29/ March 02, 2016 1 Based on frames by Benny Chor, Tel Aviv University, modifying frames
More informationCritical CS Questions
Slides modified by Benny Chor, based on original slides by Maurice Herlihy, Brown University. p. 1 Critical CS Questions What is a computer? And What is a Computation? real computers too complex for any
More informationCPS 220 Theory of Computation REGULAR LANGUAGES
CPS 22 Theory of Computation REGULAR LANGUAGES Introduction Model (def) a miniature representation of a thing; sometimes a facsimile Iraq village mockup for the Marines Scientific modelling - the process
More informationComputational Models #1
Computational Models #1 Handout Mode Nachum Dershowitz & Yishay Mansour March 13-15, 2017 Nachum Dershowitz & Yishay Mansour Computational Models #1 March 13-15, 2017 1 / 41 Lecture Outline I Motivation
More informationCISC 4090: Theory of Computation Chapter 1 Regular Languages. Section 1.1: Finite Automata. What is a computer? Finite automata
CISC 4090: Theory of Computation Chapter Regular Languages Xiaolan Zhang, adapted from slides by Prof. Werschulz Section.: Finite Automata Fordham University Department of Computer and Information Sciences
More informationCS 154 Introduction to Automata and Complexity Theory
CS 154 Introduction to Automata and Complexity Theory cs154.stanford.edu 1 INSTRUCTORS & TAs Ryan Williams Cody Murray Lera Nikolaenko Sunny Rajan 2 Textbook 3 Homework / Problem Sets Homework will be
More informationComputational Models: Class 1
Computational Models: Class 1 Benny Chor School of Computer Science Tel Aviv University October 19, 2015 Based on slides by Maurice Herlihy, Brown University, and modifications by Iftach Haitner and Yishay
More informationCHAPTER 1 Regular Languages. Contents
Finite Automata (FA or DFA) CHAPTER Regular Languages Contents definitions, examples, designing, regular operations Non-deterministic Finite Automata (NFA) definitions, euivalence of NFAs and DFAs, closure
More informationCOM364 Automata Theory Lecture Note 2 - Nondeterminism
COM364 Automata Theory Lecture Note 2 - Nondeterminism Kurtuluş Küllü March 2018 The FA we saw until now were deterministic FA (DFA) in the sense that for each state and input symbol there was exactly
More informationCS 154, Lecture 2: Finite Automata, Closure Properties Nondeterminism,
CS 54, Lecture 2: Finite Automata, Closure Properties Nondeterminism, Why so Many Models? Streaming Algorithms 0 42 Deterministic Finite Automata Anatomy of Deterministic Finite Automata transition: for
More informationTime Magazine (1984)
Time Magazine (1984) Put the right kind of software into a computer, and it will do whatever you want it to. There may be limits on what you can do with the machines themselves, but there are no limits
More informationFORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY
5-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY NON-DETERMINISM and REGULAR OPERATIONS THURSDAY JAN 6 UNION THEOREM The union of two regular languages is also a regular language Regular Languages Are
More informationCS:4330 Theory of Computation Spring Regular Languages. Finite Automata and Regular Expressions. Haniel Barbosa
CS:4330 Theory of Computation Spring 2018 Regular Languages Finite Automata and Regular Expressions Haniel Barbosa Readings for this lecture Chapter 1 of [Sipser 1996], 3rd edition. Sections 1.1 and 1.3.
More informationNon-Deterministic Finite Automata
Slides modified Yishay Mansour on modification by Benny Chor, based on original slides by Maurice Herlihy, Brown University. p. 8 Non-Deterministic Finite Automata 0,1 0,1 0 0,ε q q 1 q 2 3 1 q 4 an NFA
More informationAnnouncements. Problem Set 6 due next Monday, February 25, at 12:50PM. Midterm graded, will be returned at end of lecture.
Turing Machines Hello Hello Condensed Slide Slide Readers! Readers! This This lecture lecture is is almost almost entirely entirely animations that that show show how how each each Turing Turing machine
More informationUNIT-III REGULAR LANGUAGES
Syllabus R9 Regulation REGULAR EXPRESSIONS UNIT-III REGULAR LANGUAGES Regular expressions are useful for representing certain sets of strings in an algebraic fashion. In arithmetic we can use the operations
More informationComputability Theory
CS:4330 Theory of Computation Spring 2018 Computability Theory Decidable Languages Haniel Barbosa Readings for this lecture Chapter 4 of [Sipser 1996], 3rd edition. Section 4.1. Decidable Languages We
More informationTheory of Computation Lecture 1. Dr. Nahla Belal
Theory of Computation Lecture 1 Dr. Nahla Belal Book The primary textbook is: Introduction to the Theory of Computation by Michael Sipser. Grading 10%: Weekly Homework. 30%: Two quizzes and one exam. 20%:
More informationFORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY
5-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY 5-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY YOU NEED TO PICK UP THE SYLLABUS, THE COURSE SCHEDULE, THE PROJECT INFO SHEET, TODAY S CLASS NOTES
More informationCSE 105 Homework 1 Due: Monday October 9, Instructions. should be on each page of the submission.
CSE 5 Homework Due: Monday October 9, 7 Instructions Upload a single file to Gradescope for each group. should be on each page of the submission. All group members names and PIDs Your assignments in this
More informationTheory of Computation (I) Yijia Chen Fudan University
Theory of Computation (I) Yijia Chen Fudan University Instructor Yijia Chen Homepage: http://basics.sjtu.edu.cn/~chen Email: yijiachen@fudan.edu.cn Textbook Introduction to the Theory of Computation Michael
More informationCSE 2001: Introduction to Theory of Computation Fall Suprakash Datta
CSE 2001: Introduction to Theory of Computation Fall 2012 Suprakash Datta datta@cse.yorku.ca Office: CSEB 3043 Phone: 416-736-2100 ext 77875 Course page: http://www.cs.yorku.ca/course/2001 9/6/2012 CSE
More informationCS 154, Lecture 3: DFA NFA, Regular Expressions
CS 154, Lecture 3: DFA NFA, Regular Expressions Homework 1 is coming out Deterministic Finite Automata Computation with finite memory Non-Deterministic Finite Automata Computation with finite memory and
More informationCS 208: Automata Theory and Logic
CS 208: Automata Theory and Logic b a a start A x(la(x) y.(x < y) L b (y)) B b Department of Computer Science and Engineering, Indian Institute of Technology Bombay. 1 of 19 Logistics Course Web-page:
More informationAutomata Theory. Lecture on Discussion Course of CS120. Runzhe SJTU ACM CLASS
Automata Theory Lecture on Discussion Course of CS2 This Lecture is about Mathematical Models of Computation. Why Should I Care? - Ways of thinking. - Theory can drive practice. - Don t be an Instrumentalist.
More informationDecidability. Human-aware Robotics. 2017/10/31 Chapter 4.1 in Sipser Ø Announcement:
Decidability 2017/10/31 Chapter 4.1 in Sipser Ø Announcement: q q q Slides for this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse355/lectures/decidability.pdf Happy Hollaween! Delayed
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION "Winter" 2018 http://cseweb.ucsd.edu/classes/wi18/cse105-ab/ Today's learning goals Sipser Section 1.4 Explain the limits of the class of regular languages Justify why the
More informationProofs, Strings, and Finite Automata. CS154 Chris Pollett Feb 5, 2007.
Proofs, Strings, and Finite Automata CS154 Chris Pollett Feb 5, 2007. Outline Proofs and Proof Strategies Strings Finding proofs Example: For every graph G, the sum of the degrees of all the nodes in G
More informationCS 154. Finite Automata, Nondeterminism, Regular Expressions
CS 54 Finite Automata, Nondeterminism, Regular Expressions Read string left to right The DFA accepts a string if the process ends in a double circle A DFA is a 5-tuple M = (Q, Σ, δ, q, F) Q is the set
More informationA Note on Turing Machine Design
CS103 Handout 17 Fall 2013 November 11, 2013 Problem Set 7 This problem explores Turing machines, nondeterministic computation, properties of the RE and R languages, and the limits of RE and R languages.
More informationAutomata Theory, Computability and Complexity
Automata Theory, Computability and Complexity Mridul Aanjaneya Stanford University June 26, 22 Mridul Aanjaneya Automata Theory / 64 Course Staff Instructor: Mridul Aanjaneya Office Hours: 2:PM - 4:PM,
More informationMapping Reducibility. Human-aware Robotics. 2017/11/16 Chapter 5.3 in Sipser Ø Announcement:
Mapping Reducibility 2017/11/16 Chapter 5.3 in Sipser Ø Announcement: q Slides for this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse355/lectures/mapping.pdf 1 Last time Reducibility
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2016 http://cseweb.ucsd.edu/classes/sp16/cse105-ab/ Today's learning goals Sipser Ch 2 Design a PDA and a CFG for a given language Give informal description for a PDA,
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION "Winter" 2018 http://cseweb.ucsd.edu/classes/wi18/cse105-ab/ Today's learning goals Sipser Section 1.1 Design an automaton that recognizes a given language. Specify each of
More informationCSE 2001: Introduction to Theory of Computation Fall Suprakash Datta
CSE 2001: Introduction to Theory of Computation Fall 2013 Suprakash Datta datta@cse.yorku.ca Office: CSEB 3043 Phone: 416-736-2100 ext 77875 Course page: http://www.eecs.yorku.ca/course/2001 9/10/2013
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION "Winter" 2018 http://cseweb.ucsd.edu/classes/wi18/cse105-ab/ Today's learning goals Sipser Section 1.1 Construct finite automata using algorithms from closure arguments Determine
More informationComputational Models
Slides modified by Benny Chor, based on original slides by Maurice Herlihy, Brown University. p. 1 Computational Models Inroduction to the Theory of Computing Instructor: Prof. Benny Chor (benny at cs
More informationTHEORY OF COMPUTATION
SHARIF UNIVERSITY OF TECHNOLOGY THEORY OF COMPUTATION FIRST WEEK February 13, 2016 1 COURSE DESCRIPTION Session 1 1 Course Description Welcome to "Theory of Computation" course. In this course we will
More informationIntroduction to the Theory of Computation. Automata 1VO + 1PS. Lecturer: Dr. Ana Sokolova.
Introduction to the Theory of Computation Automata 1VO + 1PS Lecturer: Dr. Ana Sokolova http://cs.uni-salzburg.at/~anas/ Setup and Dates Lectures and Instructions 23.10. 3.11. 17.11. 24.11. 1.12. 11.12.
More informationacs-04: Regular Languages Regular Languages Andreas Karwath & Malte Helmert Informatik Theorie II (A) WS2009/10
Regular Languages Andreas Karwath & Malte Helmert 1 Overview Deterministic finite automata Regular languages Nondeterministic finite automata Closure operations Regular expressions Nonregular languages
More informationComputability and Complexity
Computability and Complexity Lecture 5 Reductions Undecidable problems from language theory Linear bounded automata given by Jiri Srba Lecture 5 Computability and Complexity 1/14 Reduction Informal Definition
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2016 http://cseweb.ucsd.edu/classes/sp16/cse105-ab/ Today's learning goals Sipser Ch 3.3, 4.1 State and use the Church-Turing thesis. Give examples of decidable problems.
More informationI have read and understand all of the instructions below, and I will obey the University Code on Academic Integrity.
Midterm Exam CS 341-451: Foundations of Computer Science II Fall 2016, elearning section Prof. Marvin K. Nakayama Print family (or last) name: Print given (or first) name: I have read and understand all
More informationCS21 Decidability and Tractability
CS21 Decidability and Tractability Lecture 2 January 5, 2018 January 5, 2018 CS21 Lecture 2 1 Outline Finite Automata Nondeterministic Finite Automata Closure under regular operations NFA, FA equivalence
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION "Winter" 2018 http://cseweb.ucsd.edu/classes/wi18/cse105-ab/ Today's learning goals Sipser Section 1.1 Determine if a language is regular Apply closure properties to conclude
More informationIntroduction to the Theory of Computation. Automata 1VO + 1PS. Lecturer: Dr. Ana Sokolova.
Introduction to the Theory of Computation Automata 1VO + 1PS Lecturer: Dr. Ana Sokolova http://cs.uni-salzburg.at/~anas/ Setup and Dates Lectures Tuesday 10:45 pm - 12:15 pm Instructions Tuesday 12:30
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION "Winter" 2018 http://cseweb.ucsd.edu/classes/wi18/cse105-ab/ Today's learning goals Sipser Ch 4.1 Explain what it means for a problem to be decidable. Justify the use of encoding.
More informationFORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY
15-453 FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY REVIEW for MIDTERM 1 THURSDAY Feb 6 Midterm 1 will cover everything we have seen so far The PROBLEMS will be from Sipser, Chapters 1, 2, 3 It will be
More informationIntroduction to Languages and Computation
Introduction to Languages and Computation George Voutsadakis 1 1 Mathematics and Computer Science Lake Superior State University LSSU Math 400 George Voutsadakis (LSSU) Languages and Computation July 2014
More informationAnnouncements. Problem Set Four due Thursday at 7:00PM (right before the midterm).
Finite Automata Announcements Problem Set Four due Thursday at 7:PM (right before the midterm). Stop by OH with questions! Email cs3@cs.stanford.edu with questions! Review session tonight, 7PM until whenever
More informationAutomata: a short introduction
ILIAS, University of Luxembourg Discrete Mathematics II May 2012 What is a computer? Real computers are complicated; We abstract up to an essential model of computation; We begin with the simplest possible
More informationClarifications from last time. This Lecture. Last Lecture. CMSC 330: Organization of Programming Languages. Finite Automata.
CMSC 330: Organization of Programming Languages Last Lecture Languages Sets of strings Operations on languages Finite Automata Regular expressions Constants Operators Precedence CMSC 330 2 Clarifications
More informationCS 581: Introduction to the Theory of Computation! Lecture 1!
CS 581: Introduction to the Theory of Computation! Lecture 1! James Hook! Portland State University! hook@cs.pdx.edu! http://www.cs.pdx.edu/~hook/cs581f10/! Welcome!! Contact Information! Jim Hook! Office:
More informationPart I: Definitions and Properties
Turing Machines Part I: Definitions and Properties Finite State Automata Deterministic Automata (DFSA) M = {Q, Σ, δ, q 0, F} -- Σ = Symbols -- Q = States -- q 0 = Initial State -- F = Accepting States
More informationCS 121, Section 2. Week of September 16, 2013
CS 121, Section 2 Week of September 16, 2013 1 Concept Review 1.1 Overview In the past weeks, we have examined the finite automaton, a simple computational model with limited memory. We proved that DFAs,
More informationPumping Lemma for CFLs
Pumping Lemma for CFLs v y s Here we go again! Intuition: If L is CF, then some CFG G produces strings in L If some string in L is very long, it will have a very tall parse tree If a parse tree is taller
More informationCSC173 Workshop: 13 Sept. Notes
CSC173 Workshop: 13 Sept. Notes Frank Ferraro Department of Computer Science University of Rochester September 14, 2010 1 Regular Languages and Equivalent Forms A language can be thought of a set L of
More informationINF Introduction and Regular Languages. Daniel Lupp. 18th January University of Oslo. Department of Informatics. Universitetet i Oslo
INF28 1. Introduction and Regular Languages Daniel Lupp Universitetet i Oslo 18th January 218 Department of Informatics University of Oslo INF28 Lecture :: 18th January 1 / 33 Details on the Course consists
More informationCS 530: Theory of Computation Based on Sipser (second edition): Notes on regular languages(version 1.1)
CS 530: Theory of Computation Based on Sipser (second edition): Notes on regular languages(version 1.1) Definition 1 (Alphabet) A alphabet is a finite set of objects called symbols. Definition 2 (String)
More informationTuring Machines Part III
Turing Machines Part III Announcements Problem Set 6 due now. Problem Set 7 out, due Monday, March 4. Play around with Turing machines, their powers, and their limits. Some problems require Wednesday's
More informationCSCI 2670 Introduction to Theory of Computing
CSCI 267 Introduction to Theory of Computing Agenda Last class Reviewed syllabus Reviewed material in Chapter of Sipser Assigned pages Chapter of Sipser Questions? This class Begin Chapter Goal for the
More informationCSE 105 Theory of Computation
CSE 105 Theory of Computation http://www.jflap.org/jflaptmp/ Professor Jeanne Ferrante 1 Today s Agenda Quick Review of CFG s and PDA s Introduction to Turing Machines and their Languages Reminders and
More informationCISC4090: Theory of Computation
CISC4090: Theory of Computation Chapter 2 Context-Free Languages Courtesy of Prof. Arthur G. Werschulz Fordham University Department of Computer and Information Sciences Spring, 2014 Overview In Chapter
More informationContext-Free Languages
CS:4330 Theory of Computation Spring 2018 Context-Free Languages Pushdown Automata Haniel Barbosa Readings for this lecture Chapter 2 of [Sipser 1996], 3rd edition. Section 2.2. Finite automaton 1 / 13
More informationHomework Assignment 6 Answers
Homework Assignment 6 Answers CSCI 2670 Introduction to Theory of Computing, Fall 2016 December 2, 2016 This homework assignment is about Turing machines, decidable languages, Turing recognizable languages,
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2018 http://cseweb.ucsd.edu/classes/sp18/cse105-ab/ Today's learning goals Sipser Section 1.1 Prove closure properties of the class of regular languages Apply closure
More informationTAKE-HOME: OUT 02/21 NOON, DUE 02/25 NOON
CSE 555 MIDTERM EXAMINATION SOLUTIONS TAKE-HOME: OUT 02/21 NOON, DUE 02/25 NOON The completed test is to be submitted electronically to colbourn@asu.edu before the deadline, or time-stamped by the main
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Review of CFG, CFL, ambiguity What is the language generated by the CFG below: G 1 = ({S,T 1,T 2 }, {0,1,2}, { S
More informationFinite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018
Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018 Lecture 15 Ana Bove May 17th 2018 Recap: Context-free Languages Chomsky hierarchy: Regular languages are also context-free; Pumping lemma
More informationFinite Automata and Languages
CS62, IIT BOMBAY Finite Automata and Languages Ashutosh Trivedi Department of Computer Science and Engineering, IIT Bombay CS62: New Trends in IT: Modeling and Verification of Cyber-Physical Systems (2
More informationCS5371 Theory of Computation. Lecture 7: Automata Theory V (CFG, CFL, CNF)
CS5371 Theory of Computation Lecture 7: Automata Theory V (CFG, CFL, CNF) Announcement Homework 2 will be given soon (before Tue) Due date: Oct 31 (Tue), before class Midterm: Nov 3, (Fri), first hour
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2018 http://cseweb.ucsd.edu/classes/sp18/cse105-ab/ Today's learning goals Sipser Ch 4.1 Explain what it means for a problem to be decidable. Justify the use of encoding.
More informationHarvard CS 121 and CSCI E-207 Lecture 4: NFAs vs. DFAs, Closure Properties
Harvard CS 121 and CSCI E-207 Lecture 4: NFAs vs. DFAs, Closure Properties Salil Vadhan September 13, 2012 Reading: Sipser, 1.2. How to simulate NFAs? NFA accepts w if there is at least one accepting computational
More informationProving languages to be nonregular
Proving languages to be nonregular We already know that there exist languages A Σ that are nonregular, for any choice of an alphabet Σ. This is because there are uncountably many languages in total and
More informationCISC 4090 Theory of Computation
9/2/28 Stereotypical computer CISC 49 Theory of Computation Finite state machines & Regular languages Professor Daniel Leeds dleeds@fordham.edu JMH 332 Central processing unit (CPU) performs all the instructions
More informationComputer Sciences Department
1 Reference Book: INTRODUCTION TO THE THEORY OF COMPUTATION, SECOND EDITION, by: MICHAEL SIPSER 3 objectives Finite automaton Infinite automaton Formal definition State diagram Regular and Non-regular
More informationCS 154. Finite Automata vs Regular Expressions, Non-Regular Languages
CS 154 Finite Automata vs Regular Expressions, Non-Regular Languages Deterministic Finite Automata Computation with finite memory Non-Deterministic Finite Automata Computation with finite memory and guessing
More informationCS 301. Lecture 18 Decidable languages. Stephen Checkoway. April 2, 2018
CS 301 Lecture 18 Decidable languages Stephen Checkoway April 2, 2018 1 / 26 Decidable language Recall, a language A is decidable if there is some TM M that 1 recognizes A (i.e., L(M) = A), and 2 halts
More informationcse303 ELEMENTS OF THE THEORY OF COMPUTATION Professor Anita Wasilewska
cse303 ELEMENTS OF THE THEORY OF COMPUTATION Professor Anita Wasilewska LECTURE 1 Course Web Page www3.cs.stonybrook.edu/ cse303 The webpage contains: lectures notes slides; very detailed solutions to
More information2017/08/31 Chapter 1.2 & 1.3 in Sipser Ø Announcement:
Regular Expressions Human-aware and Robo.cs Operations 2017/08/31 Chapter 1.2 & 1.3 in Sipser Ø Announcement: q q q q Many thanks to students who have responded so far! There is still time to respond to
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2016 http://cseweb.ucsd.edu/classes/sp16/cse105-ab/ Today's learning goals Sipser Ch 2 Define push down automata Trace the computation of a push down automaton Design
More informationFooling Sets and. Lecture 5
Fooling Sets and Introduction to Nondeterministic Finite Automata Lecture 5 Proving that a language is not regular Given a language, we saw how to prove it is regular (union, intersection, concatenation,
More informationThe Pumping Lemma and Closure Properties
The Pumping Lemma and Closure Properties Mridul Aanjaneya Stanford University July 5, 2012 Mridul Aanjaneya Automata Theory 1/ 27 Tentative Schedule HW #1: Out (07/03), Due (07/11) HW #2: Out (07/10),
More informationFinite Automata Part Two
Finite Automata Part Two DFAs A DFA is a Deterministic Finite Automaton A DFA is defined relative to some alphabet Σ. For each state in the DFA, there must be exactly one transition defined for each symbol
More informationIntroduction to Automata
Introduction to Automata Seungjin Choi Department of Computer Science and Engineering Pohang University of Science and Technology 77 Cheongam-ro, Nam-gu, Pohang 37673, Korea seungjin@postech.ac.kr 1 /
More informationIntroduction to Theoretical Computer Science. Motivation. Automata = abstract computing devices
Introduction to Theoretical Computer Science Motivation Automata = abstract computing devices Turing studied Turing Machines (= computers) before there were any real computers We will also look at simpler
More informationNon-emptiness Testing for TMs
180 5. Reducibility The proof of unsolvability of the halting problem is an example of a reduction: a way of converting problem A to problem B in such a way that a solution to problem B can be used to
More informationME 025 Mechanics of Materials
ME 025 Mechanics of Materials General Information: Term: 2019 Summer Session Instructor: Staff Language of Instruction: English Classroom: TBA Office Hours: TBA Class Sessions Per Week: 5 Total Weeks:
More informationMath/EECS 1028M: Discrete Mathematics for Engineers Winter Suprakash Datta
Math/EECS 1028M: Discrete Mathematics for Engineers Winter 2017 Suprakash Datta datta@cse.yorku.ca Office: CSEB 3043 Phone: 416-736-2100 ext 77875 Course page: http://www.eecs.yorku.ca/course/1028 Administrivia
More informationFormal Definition of a Finite Automaton. August 26, 2013
August 26, 2013 Why a formal definition? A formal definition is precise: - It resolves any uncertainties about what is allowed in a finite automaton such as the number of accept states and number of transitions
More informationComputational Models - Lecture 4
Computational Models - Lecture 4 Regular languages: The Myhill-Nerode Theorem Context-free Grammars Chomsky Normal Form Pumping Lemma for context free languages Non context-free languages: Examples Push
More informationThe Church-Turing Thesis
The Church-Turing Thesis Huan Long Shanghai Jiao Tong University Acknowledgements Part of the slides comes from a similar course in Fudan University given by Prof. Yijia Chen. http://basics.sjtu.edu.cn/
More informationCS5371 Theory of Computation. Lecture 5: Automata Theory III (Non-regular Language, Pumping Lemma, Regular Expression)
CS5371 Theory of Computation Lecture 5: Automata Theory III (Non-regular Language, Pumping Lemma, Regular Expression) Objectives Prove the Pumping Lemma, and use it to show that there are non-regular languages
More informationRegular Languages and Finite Automata
Regular Languages and Finite Automata Theorem: Every regular language is accepted by some finite automaton. Proof: We proceed by induction on the (length of/structure of) the description of the regular
More informationCSCI 2200 Foundations of Computer Science Spring 2018 Quiz 3 (May 2, 2018) SOLUTIONS
CSCI 2200 Foundations of Computer Science Spring 2018 Quiz 3 (May 2, 2018) SOLUTIONS 1. [6 POINTS] For language L 1 = {0 n 1 m n, m 1, m n}, which string is in L 1? ANSWER: 0001111 is in L 1 (with n =
More informationV Honors Theory of Computation
V22.0453-001 Honors Theory of Computation Problem Set 3 Solutions Problem 1 Solution: The class of languages recognized by these machines is the exactly the class of regular languages, thus this TM variant
More informationPS2 - Comments. University of Virginia - cs3102: Theory of Computation Spring 2010
University of Virginia - cs3102: Theory of Computation Spring 2010 PS2 - Comments Average: 77.4 (full credit for each question is 100 points) Distribution (of 54 submissions): 90, 12; 80 89, 11; 70-79,
More informationCSCE 551: Chin-Tser Huang. University of South Carolina
CSCE 551: Theory of Computation Chin-Tser Huang huangct@cse.sc.edu University of South Carolina Church-Turing Thesis The definition of the algorithm came in the 1936 papers of Alonzo Church h and Alan
More informationDecidability and Undecidability
Decidability and Undecidability Major Ideas from Last Time Every TM can be converted into a string representation of itself. The encoding of M is denoted M. The universal Turing machine U TM accepts an
More information