CSE 311: Foundations of Computing
announcements
Fall 2013
Hand in Homework 9 now
Lecture 29: Wrap up
Pick up all old homework and exams now
Review session
Sunday, 3pm, EEB 125
List of Final Exam Topics and sampling of some
typical kinds of exam quest
CSE 311: Foundations of Computing
highlights
Fall 2013
DFAs Regular Expressions
Lecture 26: Pattern matching, cardinality
No need to know details of
NFAsRegExpressions
Method for proving no DFAs for languages
e.g.
how to show language L has no DFA
Fi
CSE 311: Foundations of Computing
Fall 2013
Lecture 27: Turing machines and decidability
highlights
Cardinality
A set S is countable iff we can write it as
S=cfw_s1, s2, s3, . indexed by
1/1 1/2 1/3 1/4 1/5
Set of rationals is countable 2/1 2/2 2/3 2/
CSE 311: Foundations of Computing
highlights
Fall 2013
NFAs from Regular Expressions
Lecture 25: Non-regularity and limits of FSMs
(01 1)*0
0
1
highlights
1
1 in third position from end
Subset construction: NFA to DFA
1
1
0
1
1
c
0
b
0,1
D
C
0,1
a
c
0,1
B
CSE 311: Foundations of Computing
highlights
Turing machine = Finite control + Recording Medium + Focus of attention
Fall 2013
Lecture 28: Undecidability
Recording Medium
input x
Finite Control:
program P
_
_
0
s1
(1,s3)
(1,s2)
(0,s2)
s2
(H,s3)
(R,s1)
(H,
CSE 311: Foundations of Computing
announcements
Fall 2013
Reading assignments
7th Edition, 9.1 and pp. 594-601
6th Edition, 8.1 and pp. 541-548
Lecture 21: Relations and directed graphs
relations
Let A and B be sets,
A binary relation from A to B is a
CSE 311: Foundations of Computing
FSM highlights
Finite state machines
States, transitions, start state, final states
Languages recognized by FSMs
Fall 2013
Lecture 23: Finite state machines and minimization
R
0
0
s0
1
0
s1
1
1
s2
s3
0
0,1
s0
0,1
s1
s2
CSE 311: Foundations of Computing
Fall 2013
highlights: directed graphs
G = (V, E)
Lecture 22: Finite state machines (aka DFAs)
V vertices
E edges, order pairs of vertices
Path: v0, v1, , vk, with (vi, vi+1) in E
Simple Path
Cycle
Simple Cycle
highlights:
CSE 311: Foundations of Computing
Fall 2013
Lecture 16: Recursively defined sets and structural
induction
announcements
Reading assignment
Induction
5.3, 7th edition
4.3, 6th edition
Homework 5 due today. No new homework now.
Midterm
Monday, November 4th,
CSE 311: Foundations of Computing
announcements
Fall 2013
Reading assignments
7th Edition, pp. 851-855
6th Edition, pp. 789-793
Today and Friday
7th Edition, Section 9.1 and pp. 594-601
6th Edition, Section 8.1 and pp. 541-548
Lecture 20: Context-fr
CSE 311: Foundations of Computing
Fall 2013
Lecture 18: Structural induction, regular expressions
announcements
Reading assignment
7th Edition, pp. 878-880 and pp. 851-855
6th Edition, pp. 817-819 and pp. 789-793
Midterm back today
Average 73%
Graded Home
CSE 311: Foundations of Computing
announcements
Fall 2013
Reading assignments
7th Edition, pp. 878-880 and pp. 851-855
6th Edition, pp. 817-819 and pp. 789-793
Today and Wednesday
7th Edition, Section 9.1 and pp. 594-601
6th Edition, Section 8.1 and