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Erik Jonsson School of Engineering and Computer Science. CS 4384 – 5 01. Automata Theory. h ttp ://www.utdallas.edu/~ pervin and eLearning. Tuesday : Start Chapter 2 Look at Ullman’s Lectures 2 & 3. Thurs day 1-16-14. FEARLESS Engineering. www.utdallas.edu/~pervin.
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Erik Jonsson School of Engineering and Computer Science CS 4384– 501 Automata Theory http://www.utdallas.edu/~pervin and eLearning Tuesday: Start Chapter 2 Look at Ullman’s Lectures 2 & 3 Thursday 1-16-14 FEARLESS Engineering www.utdallas.edu/~pervin
SyllabusOfficialS2014.docx SYLLABUS
Hopcroft & Ullman, Intro. to Automata Theory, Languages, and Computation • Lewis & Papadimitriou, Elements of the Theory of Computation • Martin, Intro. to Languages and the Theory of Computation (B&N $174) • Sipser, Intro. to the Theory of Computation ($170 for newest edition) • Du & Ko, Problem Solving in Automata, Languages, and Complexity (e-book $160) RESERVE BOOK LIST
CHAPTER ONE 1.3 Proof Techniques 1.3.6 Proof by Induction Note: Pigeon Hole CS 3305
A palindrome can be defined as a string that reads the same backward and forward, or by the following definition: • 1) e is a palindrome. • 2) If a is any symbol, then the string a is a palindrome. • 3) If a is a symbol and x is a palindrome, then axa is a palindrome. • 4) Nothing else is a palindrome unless it follows from 1) through 3). Palindrome Note: We will prove later that no FA accepts palindrome.
CS 4384 14 January 2014 HOMEWORK 1Due: 21 JANUARY 2014 Written carefully on 8.5x11 white paper as for your boss!
A = {w : w is a binary string containing an odd number of 1s} • B = {w: w is a binary string containing 101 as a substring} • C = {we {0,1}* : w has a 1 in the third position from the right} M&S Examples 2.2.1 p.26; 2.2.2 p.28; 2.2.3 p.29
A = {w : w is a binary string containing an odd number of 1s} What’s wrong with: ….
C = {we {0,1}* : w has a 1 in the third position from the right}Just remember the last three symbols
Language • A language is a set of strings. For example, {0, 1}, {all English words}, {0, 0, 0, ...} are all languages. • The following are operations on sets and hence also on languages. Union: A U B Intersection: A ∩ B Difference: A \ B (A - B when B A) Complement: A = Σ* - A where Σ* is the set of all strings on alphabet Σ. 0 1 2 _ Du
Concatenation: • For example, {0, 1}{1, 2} = {01, 02, 11, 12}. • Especially, we denote A = A, A = AA, ..., and define A = {ε}. 2 1 0 Concatenation of Languages Du
The set of regular languages is closed under the union operation Theorem 2.3.1 M&S p. 32
The set of regular languages is closed under the intersection operation Theorem 2.3.1 Addendum M&S p. 32
The set of regular languages is closed under the complement operation Theorem 2.3.1 Addendum M&S p. 32
The set of regular languages is closed under the Kleene star and concatenation operations To be proved later: M&S p. 32
Binary expansion of positive integers congruent to zero mod 5
Binary expansion of positive integers congruent to zero mod 5
Binary expansion of non-negative integers congruent to 0 mod 5
Any number (including zero) of a’s followed by an equal number of b’s. Recursive Definition
Any number of a’s (including zero) followed by a less than or equal number of b’s. Another Recursive Definition