2001L1 - 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 (http://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: should be available the previous day Office hours: Monday 4-5 pm, Wed 1-2 pm or by appointment at CSB3043 Textbook: 1/10/2006 Administrivia – contd. • Cheating will not be tolerated. Visit the webpage for more details on policies. • TA: grading and invigilation only • I will have some extra-credit quizzes. These will be announced beforehand. 1/10/2006 Course objectives • What problems can computers solve? • Different computation models – Finite Automata – Pushdown Automata – Turing Machines 1/10/2006 Today Ch. 0:Set notation and languages •Sets and sequences •Tuples •Functions and relations •Graphs •Boolean logic: ∨∧¬⇔⇒ Review of proof techniques •Construction, Contradiction, Induction Ch. 1: deterministic finite automata (DFA) 1/10/2006 Topics you should know: • Elementary set theory • Elementary logic • Functions • Graphs
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1/10/2006 Set Theory review • Definition: A = { x | x N , f(x)=0 } N = {1,2,3,…} • Union: A B • Intersection: A B • Complement: • Cartesian Product: A × B = { (x,y) | x A and y B} A 1/10/2006 Some Examples L <6 = { x | x N , x<6 } L prime = {x| x N , x is prime} L <6 L prime = {2,3,5} Σ = {0,1} Σ×Σ = {(0,0), (0,1), (1,0), (1,1)} Formal: A B = { x | x A and x B} 1/10/2006 Power set “Set of all subsets” Formal: P (A) = { S | S A} Example: A = {x,y} P (A) = { {} , {x} , {y} , {x,y} } Note the different sizes: for finite sets | P (A)| = 2 |A| |A × A| = |A| 2 1/10/2006 Graphs: review • Nodes, edges, weights • Undirected, directed • Cycles, trees, • Connected 1/10/2006 Logic: review Boolean logic: ∨∧¬ Quantifiers: , statement : Suppose x N, y N. Then x y y > x for any integer, there exists a larger integer : a b “is the same as” (is logically equivalent to) ¬ a b : a b is logically equivalent to (a b) (b a) 1/10/2006 Logic: review - 2 Contrapositive and converse: the converse of a b is b a the contrapositive of a b is ¬ b ⇒¬ a Negation of statements ¬ ( x y y > x) “=“
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2001L1 - CSE 2001: Introduction to Theory of Computation...

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