CS 181 B&C EXAM #1 NAME. You have 90 minutes to complete this exam. You may assume without proof any statement proved in class.
|
|
- Katherine Hodges
- 5 years ago
- Views:
Transcription
1 CS 8 B&C EXAM # NAME SPRING 204 UCLA ID You have 90 minutes to complete this exam. You may assume without proof any statement proved in class. Give a simple verbal description of the language recognized by the following DFA Draw NFAs for the following languages, taking full advantage of nondeterminism: a. strings over alphabet f0; ; : : : ; 9g where the final digit has not appeared before; b. binary strings that begin or end with 00 or.
2 3 Prove that the following languages over the binary alphabet are regular: a. strings in which every is immediately followed by 00; b. strings that contain both 00 and 0 as substrings; c. strings that end with 00.
3 4 Let L and L 2 be languages that can be recognized by NFAs with n and n 2 states, respectively. Prove that L \ L 2 can be recognized by a DFA with at most 2 n Cn 2 states. 5 Prove that every language L f0; g can be expressed as a countable union L D S for some regular languages R ;R 2 ;R 3 ;:::. id R i
4 6 For a language L, define delete.l/ Dfuv W u v 2 L for some 2 g: Thus, delete.l/ is the set of all strings obtained by taking a nonempty string in L and deleting a single character from it. Prove that if L is regular, so is delete.l/. 7 For a language L; define suffix.l/ Dfv W uv 2 L for some ug: Thus, suffix.l/ is the set of all suffixes of strings in L. Show how to transform a DFA for any given regular language L into an NFA for suffix.l/:
5 SOLUTIONS
6 CS 8 B&C EXAM # NAME SPRING 204 UCLA ID You have 90 minutes to complete this exam. You may assume without proof any statement proved in class. Give a simple verbal description of the language recognized by the following DFA Solution. All binary strings that end with Draw NFAs for the following languages, taking full advantage of nondeterminism: a. strings over alphabet f0; ; : : : ; 9g where the final digit has not appeared before; b. binary strings that begin or end with 00 or. Solution. a. b.
7 3 Prove that the following languages over the binary alphabet are regular: a. strings in which every is immediately followed by 00; b. strings that contain both 00 and 0 as substrings; c. strings that end with 00. Solution. a. The language is recognized by the following NFA: b. The language of strings containing 00 is recognized by Analogously, the language of strings containing 0 is recognized by Since regular languages are closed under intersection, the language in the problem statement is regular. c. The language is recognized by the following NFA: New Section Page 2 New Section Page 2 New Section Page 2 New Section Page 2
8 4 Let L and L 2 be languages that can be recognized by NFAs with n and n 2 states, respectively. Prove that L \ L 2 can be recognized by a DFA with at most 2 n Cn 2 states. Solution. Using the method discussed in class, transform the NFAs for L and L 2 to DFAs with at most 2 n and 2 n 2 states, respectively. Then combine these DFAs to obtain a DFA for L \L 2 with at most 2 n 2 n 2 D 2 n Cn 2 states, using the Cartesian-product construction from class. 5 Prove that every language L f0; g can be expressed as a countable union L D S for some regular languages R ;R 2 ;R 3 ;:::. id R i Solution. For any string w 2f0; g ; the language fwg is regular because it is recognized by the NFA Now define R i to be the language whose only string is the ith string in L, in lexicographic order (with the understanding that R i D if L has fewer than i strings). Then where each R i is regular by above. L D [ R i ; id
9 6 For a language L, define delete.l/ Dfuv W u v 2 L for some 2 g: Thus, delete.l/ is the set of all strings obtained by taking a nonempty string in L and deleting a single character from it. Prove that if L is regular, so is delete.l/. Solution: DFA for L NFA for delete(l) q! same as original DFA, but make all states reject ε add this arrow for every q and σ δ(q, σ)! same as original DFA 7 For a language L; define suffix.l/ Dfv W uv 2 L for some ug: Thus, suffix.l/ is the set of all suffixes of strings in L. Show how to transform a DFA for any given regular language L into an NFA for suffix.l/: Solution. Add "-transitions from the initial state q 0 to every state reachable from q 0.
CS 181 EXAM #1 NAME. You have 90 minutes to complete this exam. You may state without proof any fact taught in class or assigned as homework.
CS 8 EXAM # NAME FALL 206 UCLA ID You have 90 minutes to complete this exam. You may state without proof any fact taught in class or assigned as homework. Give a simple verbal description of the language
More information1. (10 points) Draw the state diagram of the DFA that recognizes the language over Σ = {0, 1}
CSE 5 Homework 2 Due: Monday October 6, 27 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
More informationMidterm Exam II CIS 341: Foundations of Computer Science II Spring 2006, day section Prof. Marvin K. Nakayama
Midterm Exam II CIS 341: Foundations of Computer Science II Spring 2006, day section Prof. Marvin K. Nakayama Print family (or last) name: Print given (or first) name: I have read and understand all of
More information6 NFA and Regular Expressions
Formal Language and Automata Theory: CS21004 6 NFA and Regular Expressions 6.1 Nondeterministic Finite Automata A nondeterministic finite automata (NFA) is a 5-tuple where 1. is a finite set of states
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Today's learning goals Sipser Ch 1.2, 1.3 Design NFA recognizing a given language Convert an NFA (with or without
More informationTheory of Computation Dr. Weiss Extra Practice Exam Solutions
Name: of 7 Theory of Computation Dr. Weiss Extra Practice Exam Solutions Directions: Answer the questions as well as you can. Partial credit will be given, so show your work where appropriate. Try to be
More informationLast lecture CMSC330. This lecture. Finite Automata: States. Finite Automata. Implementing Regular Expressions. Languages. Regular expressions
Last lecture CMSC330 Finite Automata Languages Sets of strings Operations on languages Regular expressions Constants Operators Precedence 1 2 Finite automata States Transitions Examples Types This lecture
More information14.1 Encoding for different models of computation
Lecture 14 Decidable languages In the previous lecture we discussed some examples of encoding schemes, through which various objects can be represented by strings over a given alphabet. We will begin this
More informationNFAs and Myhill-Nerode. CS154 Chris Pollett Feb. 22, 2006.
NFAs and Myhill-Nerode CS154 Chris Pollett Feb. 22, 2006. Outline Bonus Questions Equivalence with Finite Automata Myhill-Nerode Theorem. Bonus Questions These questions are open to anybody. I will only
More informationI have read and understand all of the instructions below, and I will obey the Academic Honor Code.
Midterm Exam CS 341-451: Foundations of Computer Science II Fall 2014, elearning section Prof. Marvin K. Nakayama Print family (or last) name: Print given (or first) name: I have read and understand all
More informationHKN CS 374 Midterm 1 Review. Tim Klem Noah Mathes Mahir Morshed
HKN CS 374 Midterm 1 Review Tim Klem Noah Mathes Mahir Morshed Midterm topics It s all about recognizing sets of strings! 1. String Induction 2. Regular languages a. DFA b. NFA c. Regular expressions 3.
More informationContext Free Grammars. CS154 Chris Pollett Mar 1, 2006.
Context Free Grammars CS154 Chris Pollett Mar 1, 2006. Outline Formal Definition Ambiguity Chomsky Normal Form Formal Definitions A context free grammar is a 4-tuple (V, Σ, R, S) where 1. V is a finite
More informationlec3:nondeterministic finite state automata
lec3:nondeterministic finite state automata 1 1.introduction Nondeterminism is a useful concept that has great impact on the theory of computation. When the machine is in a given state and reads the next
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Today's learning goals Sipser Ch 1.2, 1.3 Decide whether or not a string is described by a given regular expression
More informationCS/ECE 374 Fall Homework 1. Due Tuesday, September 6, 2016 at 8pm
CSECE 374 Fall 2016 Homework 1 Due Tuesday, September 6, 2016 at 8pm Starting with this homework, groups of up to three people can submit joint solutions. Each problem should be submitted by exactly one
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 3.2, 3.3 Define variants of TMs Enumerators Multi-tape TMs Nondeterministic TMs
More informationCS154 Midterm Examination. May 4, 2010, 2:15-3:30PM
CS154 Midterm Examination May 4, 2010, 2:15-3:30PM Directions: Answer all 7 questions on this paper. The exam is open book and open notes. Any materials may be used. Name: I acknowledge and accept the
More informationRegular Languages and Regular Expressions
Regular Languages and Regular Expressions According to our definition, a language is regular if there exists a finite state automaton that accepts it. Therefore every regular language can be described
More informationFront End: Lexical Analysis. The Structure of a Compiler
Front End: Lexical Analysis The Structure of a Compiler Constructing a Lexical Analyser By hand: Identify lexemes in input and return tokens Automatically: Lexical-Analyser generator We will learn about
More informationTheory of Computations Spring 2016 Practice Final Exam Solutions
1 of 8 Theory of Computations Spring 2016 Practice Final Exam Solutions Name: Directions: Answer the questions as well as you can. Partial credit will be given, so show your work where appropriate. Try
More informationMidterm I (Solutions) CS164, Spring 2002
Midterm I (Solutions) CS164, Spring 2002 February 28, 2002 Please read all instructions (including these) carefully. There are 9 pages in this exam and 5 questions, each with multiple parts. Some questions
More informationCS 310: State Transition Diagrams
CS 30: State Transition Diagrams Stefan D. Bruda Winter 207 STATE TRANSITION DIAGRAMS Finite directed graph Edges (transitions) labeled with symbols from an alphabet Nodes (states) labeled only for convenience
More informationECS 120 Lesson 16 Turing Machines, Pt. 2
ECS 120 Lesson 16 Turing Machines, Pt. 2 Oliver Kreylos Friday, May 4th, 2001 In the last lesson, we looked at Turing Machines, their differences to finite state machines and pushdown automata, and their
More informationHomework 1 Due Tuesday, January 30, 2018 at 8pm
CSECE 374 A Spring 2018 Homework 1 Due Tuesday, January 30, 2018 at 8pm Starting with this homework, groups of up to three people can submit joint solutions. Each problem should be submitted by exactly
More informationCS 125 Section #10 Midterm 2 Review 11/5/14
CS 125 Section #10 Midterm 2 Review 11/5/14 1 Topics Covered This midterm covers up through NP-completeness; countability, decidability, and recognizability will not appear on this midterm. Disclaimer:
More informationFinite Automata Part Three
Finite Automata Part Three Recap from Last Time A language L is called a regular language if there exists a DFA D such that L( D) = L. NFAs An NFA is a Nondeterministic Finite Automaton Can have missing
More informationClosure Properties of CFLs; Introducing TMs. CS154 Chris Pollett Apr 9, 2007.
Closure Properties of CFLs; Introducing TMs CS154 Chris Pollett Apr 9, 2007. Outline Closure Properties of Context Free Languages Algorithms for CFLs Introducing Turing Machines Closure Properties of CFL
More informationAutomating Construction of Lexers
Automating Construction of Lexers Regular Expression to Programs Not all regular expressions are simple. How can we write a lexer for (a*b aaa)? Tokenizing aaaab Vs aaaaaa Regular Expression Finite state
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Today's learning goals Sipser Ch 2, 3.1 State and use the Church-Turing thesis. Describe several variants of Turing
More informationDVA337 HT17 - LECTURE 4. Languages and regular expressions
DVA337 HT17 - LECTURE 4 Languages and regular expressions 1 SO FAR 2 TODAY Formal definition of languages in terms of strings Operations on strings and languages Definition of regular expressions Meaning
More informationCS103 Handout 42 Spring 2017 May 31, 2017 Practice Final Exam 1
CS103 Handout 42 Spring 2017 May 31, 2017 Practice Final Exam 1 We strongly recommend that you work through this exam under realistic conditions rather than just flipping through the problems and seeing
More informationCMPSCI 250: Introduction to Computation. Lecture 20: Deterministic and Nondeterministic Finite Automata David Mix Barrington 16 April 2013
CMPSCI 250: Introduction to Computation Lecture 20: Deterministic and Nondeterministic Finite Automata David Mix Barrington 16 April 2013 Deterministic and Nondeterministic Finite Automata Deterministic
More informationCS402 Theory of Automata Solved Subjective From Midterm Papers. MIDTERM SPRING 2012 CS402 Theory of Automata
Solved Subjective From Midterm Papers Dec 07,2012 MC100401285 Moaaz.pk@gmail.com Mc100401285@gmail.com PSMD01 MIDTERM SPRING 2012 Q. Point of Kleen Theory. Answer:- (Page 25) 1. If a language can be accepted
More informationCS 441 Discrete Mathematics for CS Lecture 24. Relations IV. CS 441 Discrete mathematics for CS. Equivalence relation
CS 441 Discrete Mathematics for CS Lecture 24 Relations IV Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Equivalence relation Definition: A relation R on a set A is called an equivalence relation
More informationFinite automata. We have looked at using Lex to build a scanner on the basis of regular expressions.
Finite automata We have looked at using Lex to build a scanner on the basis of regular expressions. Now we begin to consider the results from automata theory that make Lex possible. Recall: An alphabet
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Fall 2016 http://cseweb.ucsd.edu/classes/fa16/cse105-abc/ Today's learning goals Sipser sec 3.2 Describe several variants of Turing machines and informally explain why they
More informationCOMP-421 Compiler Design. Presented by Dr Ioanna Dionysiou
COMP-421 Compiler Design Presented by Dr Ioanna Dionysiou Administrative! [ALSU03] Chapter 3 - Lexical Analysis Sections 3.1-3.4, 3.6-3.7! Reading for next time [ALSU03] Chapter 3 Copyright (c) 2010 Ioanna
More informationt!1; R 0! 1; R q HALT
CS 181 FINA EXAM SPRING 2014 NAME UCA ID You have 3 hours to complete this exam. You may assume without proof any statement proved in class. (2 pts) 1 Give a simple verbal description of the function f
More informationFinite Automata. Dr. Nadeem Akhtar. Assistant Professor Department of Computer Science & IT The Islamia University of Bahawalpur
Finite Automata Dr. Nadeem Akhtar Assistant Professor Department of Computer Science & IT The Islamia University of Bahawalpur PhD Laboratory IRISA-UBS University of South Brittany European University
More informationMIT Specifying Languages with Regular Expressions and Context-Free Grammars
MIT 6.035 Specifying Languages with Regular essions and Context-Free Grammars Martin Rinard Laboratory for Computer Science Massachusetts Institute of Technology Language Definition Problem How to precisely
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 2.2 Define push-down automata informally and formally Trace the computation
More informationCOMP 330 Autumn 2018 McGill University
COMP 330 Autumn 2018 McGill University Assignment 4 Solutions and Grading Guide Remarks for the graders appear in sans serif font. Question 1[25 points] A sequence of parentheses is a sequence of ( and
More informationUniversity of Waterloo Midterm Examination
University of Waterloo Midterm Examination 1 Fall 2008 Student Name: UW Student ID Number: UW Userid: Course Abbreviation and Number: CS 241 Course Title: Foundations of Sequential Programs Section(s):
More informationTheory Bridge Exam Example Questions Version of June 6, 2008
Theory Bridge Exam Example Questions Version of June 6, 2008 This is a collection of sample theory bridge exam questions. This is just to get some idea of the format of the bridge exam and the level of
More informationTheory of Computations Spring 2016 Practice Final
1 of 6 Theory of Computations Spring 2016 Practice Final 1. True/False questions: For each part, circle either True or False. (23 points: 1 points each) a. A TM can compute anything a desktop PC can, although
More informationCS 432 Fall Mike Lam, Professor. Finite Automata Conversions and Lexing
CS 432 Fall 2017 Mike Lam, Professor Finite Automata Conversions and Lexing Finite Automata Key result: all of the following have the same expressive power (i.e., they all describe regular languages):
More informationJNTUWORLD. Code No: R
Code No: R09220504 R09 SET-1 B.Tech II Year - II Semester Examinations, April-May, 2012 FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science and Engineering) Time: 3 hours Max. Marks: 75 Answer any five
More informationVALLIAMMAI ENGNIEERING COLLEGE SRM Nagar, Kattankulathur 603203. DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING Year & Semester : III Year, V Semester Section : CSE - 1 & 2 Subject Code : CS6503 Subject
More informationCSE450. Translation of Programming Languages. Lecture 20: Automata and Regular Expressions
CSE45 Translation of Programming Languages Lecture 2: Automata and Regular Expressions Finite Automata Regular Expression = Specification Finite Automata = Implementation A finite automaton consists of:
More informationLexical Analysis. Implementation: Finite Automata
Lexical Analysis Implementation: Finite Automata Outline Specifying lexical structure using regular expressions Finite automata Deterministic Finite Automata (DFAs) Non-deterministic Finite Automata (NFAs)
More informationImplementation of Lexical Analysis
Implementation of Lexical Analysis Outline Specifying lexical structure using regular expressions Finite automata Deterministic Finite Automata (DFAs) Non-deterministic Finite Automata (NFAs) Implementation
More informationDefinition 2.8: A CFG is in Chomsky normal form if every rule. only appear on the left-hand side, we allow the rule S ǫ.
CS533 Class 02b: 1 c P. Heeman, 2017 CNF Pushdown Automata Definition Equivalence Overview CS533 Class 02b: 2 c P. Heeman, 2017 Chomsky Normal Form Definition 2.8: A CFG is in Chomsky normal form if every
More informationImplementation of Lexical Analysis
Implementation of Lexical Analysis Outline Specifying lexical structure using regular expressions Finite automata Deterministic Finite Automata (DFAs) Non-deterministic Finite Automata (NFAs) Implementation
More informationCSE 431S Scanning. Washington University Spring 2013
CSE 431S Scanning Washington University Spring 2013 Regular Languages Three ways to describe regular languages FSA Right-linear grammars Regular expressions Regular Expressions A regular expression is
More informationCS2 Language Processing note 3
CS2 Language Processing note 3 CS2Ah 5..4 CS2 Language Processing note 3 Nondeterministic finite automata In this lecture we look at nondeterministic finite automata and prove the Conversion Theorem, which
More informationConverting a DFA to a Regular Expression JP
Converting a DFA to a Regular Expression JP Prerequisite knowledge: Regular Languages Deterministic Finite Automata Nondeterministic Finite Automata Regular Expressions Conversion of Regular Expression
More informationMultiple Choice Questions
Techno India Batanagar Computer Science and Engineering Model Questions Subject Name: Formal Language and Automata Theory Subject Code: CS 402 Multiple Choice Questions 1. The basic limitation of an FSM
More informationCSCE 5400 ASSIGNMENT #1 SOLUTION
CSCE 5400 ASSIGNMENT #1 SOLUTION 1. Design deterministic finite automata to recognize the languages below. Test your DFA s using Prolog on the indicated strings in the language, as well as some strings
More informationMIT Specifying Languages with Regular Expressions and Context-Free Grammars. Martin Rinard Massachusetts Institute of Technology
MIT 6.035 Specifying Languages with Regular essions and Context-Free Grammars Martin Rinard Massachusetts Institute of Technology Language Definition Problem How to precisely define language Layered structure
More informationLexical Analysis. Prof. James L. Frankel Harvard University
Lexical Analysis Prof. James L. Frankel Harvard University Version of 5:37 PM 30-Jan-2018 Copyright 2018, 2016, 2015 James L. Frankel. All rights reserved. Regular Expression Notation We will develop a
More informationLecture 2 Finite Automata
Lecture 2 Finite Automata August 31, 2007 This lecture is intended as a kind of road map to Chapter 1 of the text just the informal examples that I ll present to motivate the ideas. 1 Expressions without
More informationLimits of Computation p.1/?? Limits of Computation p.2/??
Context-Free Grammars (CFG) There are languages, such as {0 n 1 n n 0} that cannot be described (specified) by finite automata or regular expressions. Context-free grammars provide a more powerful mechanism
More informationVariants of Turing Machines
November 4, 2013 Robustness Robustness Robustness of a mathematical object (such as proof, definition, algorithm, method, etc.) is measured by its invariance to certain changes Robustness Robustness of
More informationAmbiguous Grammars and Compactification
Ambiguous Grammars and Compactification Mridul Aanjaneya Stanford University July 17, 2012 Mridul Aanjaneya Automata Theory 1/ 44 Midterm Review Mathematical Induction and Pigeonhole Principle Finite Automata
More informationProof Techniques Alphabets, Strings, and Languages. Foundations of Computer Science Theory
Proof Techniques Alphabets, Strings, and Languages Foundations of Computer Science Theory Proof By Case Enumeration Sometimes the most straightforward way to prove that a property holds for all elements
More informationChapter Seven: Regular Expressions
Chapter Seven: Regular Expressions Regular Expressions We have seen that DFAs and NFAs have equal definitional power. It turns out that regular expressions also have exactly that same definitional power:
More informationImplementation of Lexical Analysis
Implementation of Lexical Analysis Lecture 4 (Modified by Professor Vijay Ganesh) Tips on Building Large Systems KISS (Keep It Simple, Stupid!) Don t optimize prematurely Design systems that can be tested
More informationFinite Automata Part Three
Finite Automata Part Three Friday Four Square! Today at 4:15PM, Outside Gates. Announcements Problem Set 4 due right now. Problem Set 5 out, due next Friday, November 2. Play around with finite automata
More informationMidterm I - Solution CS164, Spring 2014
164sp14 Midterm 1 - Solution Midterm I - Solution CS164, Spring 2014 March 3, 2014 Please read all instructions (including these) carefully. This is a closed-book exam. You are allowed a one-page handwritten
More informationAnswer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.
Code No: 134BD Set No. 1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech. II Year II Sem., I Mid-Term Examinations, February - 2018 FORMAL LANGUAGES AND AUTOMATA THEORY Objective Exam Name:
More informationCS103 Handout 13 Fall 2012 May 4, 2012 Problem Set 5
CS103 Handout 13 Fall 2012 May 4, 2012 Problem Set 5 This fifth problem set explores the regular languages, their properties, and their limits. This will be your first foray into computability theory,
More informationFinal Course Review. Reading: Chapters 1-9
Final Course Review Reading: Chapters 1-9 1 Objectives Introduce concepts in automata theory and theory of computation Identify different formal language classes and their relationships Design grammars
More informationNon-context-Free Languages. CS215, Lecture 5 c
Non-context-Free Languages CS215 Lecture 5 c 2007 1 The Pumping Lemma Theorem (Pumping Lemma) Let be context-free There exists a positive integer divided into five pieces Proof for for each and Let and
More informationCS6160 Theory of Computation Problem Set 2 Department of Computer Science, University of Virginia
CS6160 Theory of Computation Problem Set 2 Department of Computer Science, University of Virginia Gabriel Robins Please start solving these problems immediately, and work in study groups. Please prove
More informationRelational Database: The Relational Data Model; Operations on Database Relations
Relational Database: The Relational Data Model; Operations on Database Relations Greg Plaxton Theory in Programming Practice, Spring 2005 Department of Computer Science University of Texas at Austin Overview
More informationQUESTION BANK. Unit 1. Introduction to Finite Automata
QUESTION BANK Unit 1 Introduction to Finite Automata 1. Obtain DFAs to accept strings of a s and b s having exactly one a.(5m )(Jun-Jul 10) 2. Obtain a DFA to accept strings of a s and b s having even
More informationFinite Automata Theory and Formal Languages TMV027/DIT321 LP4 2016
Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2016 Lecture 15 Ana Bove May 23rd 2016 More on Turing machines; Summary of the course. Overview of today s lecture: Recap: PDA, TM Push-down
More informationLexical Analysis - 2
Lexical Analysis - 2 More regular expressions Finite Automata NFAs and DFAs Scanners JLex - a scanner generator 1 Regular Expressions in JLex Symbol - Meaning. Matches a single character (not newline)
More information1. [5 points each] True or False. If the question is currently open, write O or Open.
University of Nevada, Las Vegas Computer Science 456/656 Spring 2018 Practice for the Final on May 9, 2018 The entire examination is 775 points. The real final will be much shorter. Name: No books, notes,
More informationCS 361 Meeting 8 9/24/18
CS 36 Meeting 8 9/4/8 Announceents. Hoework 3 due Friday. Review. The closure properties of regular languages provide a way to describe regular languages by building the out of sipler regular languages
More information9.5 Equivalence Relations
9.5 Equivalence Relations You know from your early study of fractions that each fraction has many equivalent forms. For example, 2, 2 4, 3 6, 2, 3 6, 5 30,... are all different ways to represent the same
More informationCS314: FORMAL LANGUAGES AND AUTOMATA THEORY L. NADA ALZABEN. Lecture 1: Introduction
CS314: FORMAL LANGUAGES AND AUTOMATA THEORY L. NADA ALZABEN Lecture 1: Introduction Introduction to the course 2 Required Text Book: INTRODUCTION TO THE THEORY OF COMPUTATION, SECOND EDITION, BY MICHAEL
More informationQualifying Exam Theory
Theory This exam contains 8 problems, some with multiple parts. (including 2 blank pages). There are 11 pages to the exam Write your solutions in the space provided. If you need more space, write on the
More informationComputer Sciences Department
1 Reference Book: INTRODUCTION TO THE THEORY OF COMPUTATION, SECOND EDITION, by: MICHAEL SIPSER 3 D E C I D A B I L I T Y 4 Objectives 5 Objectives investigate the power of algorithms to solve problems.
More informationYet More CFLs; Turing Machines. CS154 Chris Pollett Mar 8, 2006.
Yet More CFLs; Turing Machines CS154 Chris Pollett Mar 8, 2006. Outline Algorithms for CFGs Pumping Lemma for CFLs Turing Machines Introduction to Cocke-Younger- Kasami (CYK) algorithm (1960) This is an
More informationFormal Languages and Automata
Mobile Computing and Software Engineering p. 1/3 Formal Languages and Automata Chapter 3 Regular languages and Regular Grammars Chuan-Ming Liu cmliu@csie.ntut.edu.tw Department of Computer Science and
More informationLexical Analysis. Lecture 2-4
Lexical Analysis Lecture 2-4 Notes by G. Necula, with additions by P. Hilfinger Prof. Hilfinger CS 164 Lecture 2 1 Administrivia Moving to 60 Evans on Wednesday HW1 available Pyth manual available on line.
More informationActually talking about Turing machines this time
Actually talking about Turing machines this time 10/25/17 (Using slides adapted from the book) Administrivia HW due now (Pumping lemma for context-free languages) HW due Friday (Building TMs) Exam 2 out
More informationOutline. Language Hierarchy
Outline Language Hierarchy Definition of Turing Machine TM Variants and Equivalence Decidability Reducibility Language Hierarchy Regular: finite memory CFG/PDA: infinite memory but in stack space TM: infinite
More informationTheory of Computation
Theory of Computation For Computer Science & Information Technology By www.thegateacademy.com Syllabus Syllabus for Theory of Computation Regular Expressions and Finite Automata, Context-Free Grammar s
More informationLearn Smart and Grow with world
Learn Smart and Grow with world All Department Smart Study Materials Available Smartkalvi.com TABLE OF CONTENTS S.No DATE TOPIC PAGE NO. UNIT-I FINITE AUTOMATA 1 Introduction 1 2 Basic Mathematical Notation
More informationName: Finite Automata
Unit No: I Name: Finite Automata What is TOC? In theoretical computer science, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation,
More informationTOPIC PAGE NO. UNIT-I FINITE AUTOMATA
TABLE OF CONTENTS SNo DATE TOPIC PAGE NO UNIT-I FINITE AUTOMATA 1 Introduction 1 2 Basic Mathematical Notation Techniques 3 3 Finite State systems 4 4 Basic Definitions 6 5 Finite Automaton 7 6 DFA NDFA
More informationSkyup's Media. PART-B 2) Construct a Mealy machine which is equivalent to the Moore machine given in table.
Code No: XXXXX JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD B.Tech II Year I Semester Examinations (Common to CSE and IT) Note: This question paper contains two parts A and B. Part A is compulsory
More information1. Which of the following regular expressions over {0, 1} denotes the set of all strings not containing 100 as a sub-string?
Multiple choice type questions. Which of the following regular expressions over {, } denotes the set of all strings not containing as a sub-string? 2. DFA has a) *(*)* b) ** c) ** d) *(+)* a) single final
More informationRegular Expression Constrained Sequence Alignment
Regular Expression Constrained Sequence Alignment By Abdullah N. Arslan Department of Computer science University of Vermont Presented by Tomer Heber & Raz Nissim otivation When comparing two proteins,
More informationLexical Analysis. Chapter 2
Lexical Analysis Chapter 2 1 Outline Informal sketch of lexical analysis Identifies tokens in input string Issues in lexical analysis Lookahead Ambiguities Specifying lexers Regular expressions Examples
More informationNon-deterministic Finite Automata (NFA)
Non-deterministic Finite Automata (NFA) CAN have transitions on the same input to different states Can include a ε or λ transition (i.e. move to new state without reading input) Often easier to design
More informationCS103 Handout 14 Winter February 8, 2013 Problem Set 5
CS103 Handout 14 Winter 2012-2013 February 8, 2013 Problem Set 5 This fifth problem set explores the regular languages, their properties, and their limits. This will be your first foray into computability
More informationCS154. Streaming Algorithms and Communication Complexity
CS154 Streaming Algorithms and Communication Complexity 1 Streaming Algorithms 2 Streaming Algorithms 01 42 3 L = {x x has more 1 s than 0 s} Initialize: C := 0 and B := 0 When the next symbol x is read,
More information