2001Lec2 - CSE 2001: Introduction to Theory of Computation...

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1/10/2006 CSE 2001: Introduction to Theory of Computation Winter 2006 Suprakash Datta datta@cs.yorku.ca Office: CSEB 3043 Phone: 416-736-2100 ext 77875 Course page: http://www.cs.yorku.ca/course/2001 Some of these slides are adapted from Wim van Dam’s slides ( www.cs.berkeley.edu/~vandam/CS172/ ) and from Nathaly Verwaal ( cpsc.ucalgary.ca/~verwaal/313/F2005 /) 1/10/2006 Administrivia Michael Sipser. Introduction to the Theory of Computation, Second Edition . Thomson Course Technology, 2005. Lectures: Tue 7:00-10:00 pm (SLH E) Exams: 2 tests (40%), final (45%) Homework (15%): equally divided between 3 assignments. Slides: usually available the previous day Office hours: Monday 4-5 pm, Wed 1-2 pm or by appointment at CSB3043 Textbook: 1/10/2006 Last class • Basic definitions – sets, strings, languages • Finite automata • Automata accepting strings and recognizing languages. • Review of proof techniques 1/10/2006 Concept to remember • Decision problems vs input/output problems – equivalent in a specific way. • We will deal with decision problems all through this course. • We will use properties of languages to reason about and classify models of computation. 1/10/2006 Today (Ch 1) •Review basics of finite automata (FA) •Designing FA •Regular languages (RL) •Properties of languages recognized by FA – regular operations •Non-deterministic finite automata (NFA) •Equivalence of NFA and DFA. •Regular expressions (RE) •RE = RL 1/10/2006 Finite Automata The most simple machine that is not just a finite list of words. “Read once”, “no write” procedure. Useful for describing algorithms as well.
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1/10/2006 A Simple Automaton (0) q 1 q 2 q 3 1 0 0,1 0 1 states transition rules starting state accepting state 1/10/2006 Finite Automaton (defn) • A deterministic finite automaton (DFA) M is defined by a 5-tuple M=(Q, Σ , δ ,q 0 ,F) – Q: finite set of states Σ : finite alphabet δ : transition function δ :Q ×Σ→ Q –q 0 Q: start state –F Q: set of accepting states 1/10/2006 M = (Q, Σ , δ ,q,F) states Q = {q 1 ,q 2 ,q 3 } alphabet Σ = {0,1} start state q 1 accept states F={q 2 } transition function δ : 2 2 3 2 3 2 2 1 1 q q q q q q q q q 1 0 q 1 q 2 q 3 1 0 0 1 0,1 1/10/2006 Recognizing Languages (defn) A finite automaton M = (Q, Σ , δ ,q,F) accepts a string/word w = w 1 …w n if and only if there is a sequence r 0 …r n of states in Q such that: 1) r 0 = q 0 2) δ (r i ,w i+1 ) = r i+1 for all i = 0,…,n–1 3) r n F 1/10/2006 Today (Ch 1) •Review basics of finite automata (FA) •Designing FA •Regular languages (RL) •Properties of languages recognized by FA – regular operations •Non-deterministic finite automata (NFA) •Equivalence of NFA and DFA. •Regular expressions (RE)
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2001Lec2 - CSE 2001: Introduction to Theory of Computation...

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