August 23

August 23 - CSCI 2670 Introduction to Theory of Computing...

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August 23, 2005 CSCI 2670 Introduction to Theory of Computing August 23, 2005
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August 23, 2005 2 August 23, 2005 Agenda • Last class – Reviewed syllabus – Reviewed material in Chapter 0 of Sipser – Assigned pages Chapter 0 of Sipser • Questions? •Th is c lass – Begin Chapter 1 • Goal for the week –Sect ion 1 .1 • Read Section 1.1 (pages 29 – 47) this week
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August 23, 2005 3 August 23, 2005 Announcements •Webs ite is up • Quiz tomorrow (8/24) – Material: Chapter 0 • Homework due next Tuesday (8/30) – Chapter 0 numbers 0.3 all, 0.7b, 0.12 – Chapter 1 numbers 1.3, 1.4c, 1.5f, 1.6(a, c, h) • Unregistered students Please give me your student id after class
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August 23, 2005 4 August 23, 2005 Relation on A • Function R:A×A×…×A { true, false } – Often described as a set of elements for which the relation is true •Examp le – A={1,2,3,4,5} –R :A×A×A { true, false } •R is true if the three-tuple is increasing – {(1,2,3),(1,2,4),(2,3,4),(3,4,5)} R – (1,1,5) R
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August 23, 2005 5 August 23, 2005 Graphical representation (binary relations only) • Directed arrow with edge (a,b) if (a,b) R • Example: A={a,b,c,d}, R=“earlier in alphabet” R={(a,b),(a,c),(a,d),(b,c),(b,d),(c,d)} a c b d
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August 23, 2005 6 August 23, 2005 Equivalence Relation •Symmet r ic – {(a,a) | a A} R • Reflexive –(a ,b) R (b,a) R • Transitive R (b,c) R (a,c) R •Examp les – Equality – “Has the same eye color”
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August 23 - CSCI 2670 Introduction to Theory of Computing...

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