Module 18
NFA's
nondeterministic transition functions
computations are trees, not paths
L(M) and LNFA
LFSA subset of LNFA
1
Nondeterministic Finite State Automata
NFA's
2
Change: is a relation
For an FSA M, (q,a) results in one and only o
Module 7 Worksheet In Class Questions 1) (S3) Is the input a yes or no input instance to the halting problem?
2) (S3) Can you change the input x so that the input changes from yes to no or no to yes?
3) (S5) What is the earliest element of list L t
Module 8 Worksheet In Class Questions 1) (S5) A universal Turing machine is able to execute any program on any input. Which of the two following people is most like a universal Turing machine and why? Brilliant scientist Obedient soldier
Take home r
Module 12
Computation and Configurations
Formal Definition Examples
1
Definitions
Configuration
Functional Definition Given the original program and the current configuration of a computation, someone should be able to complete the computatio
Module 24 Worksheet In Class Questions 1) (S20) What does OUT1 in the given table mean? That is, what string is OUT of EQUAL?
2) (S20) What strings are in different equivalence classes defined by EQUAL as illustrated by this table?
3) (S21) What eq
Module 1: Course Overview
Course: CSE 460 Instructor: Dr. Eric Torng Grader/TA: Jignesh Patel
Physics
Science
Our material
Study of fundamental computational laws and phenomenon like undecidability and universal computers Study of fundamental
Module 1: Course Overview
Course: CSE 460 Instructor: Dr. Eric Torng Grader/TA: Jignesh Patel
1
What is this course?
Philosophy of computing course
We take a step back to think about computing in broader terms
Science of computing course
We
Module 31 Worksheet
Take home review questions
1) Apply the Kleene closure construction to the following grammar with start symbol S:
P: S → aTb  ab
T → aba  U
U→ab
2) Apply the set union construction to the above grammar and your answer to the above
q
Module 1: Course Overview
Course: CSE 460 Instructor: Dr. Eric Torng Grader/TA: Jignesh Patel
1
What is this course?
Philosophy of computing course
We take a step back to think about computing in broader terms
Science of computing course
We
Module 30 Worksheet
Take home review questions
1) What is the production rule used to generate the first derivation of the string aaababbb?
2) Describe how the string aaababbb can be decomposed into the appropriate form aubv.
That is, what are u and v?
Module 3 Worksheet In Class Questions 1) (S9) Which of the following two problems is a function problem? Problem 1 Problem 2 Input: Integer n Input: Integers m and n Output: An integer smaller than n Output: Answer to "Is m < n?" 2) (S9) Convert the
Module 32 Worksheet In Class Questions The running example will be to use the grammar G with the following productions: S AACD ED A aAb  C aC  a D aDa  bDb  E ADD
1) (S4) Nullable variables N0 = N1 = N2 = N3 = 2) (S5) Give the updat
Module 28 Worksheet In Class Questions 1) (S10) What is wrong with the following string derivation using the ABG grammar? S aSb aaSbb aaabbb
2) (S11) Does grammar ABG generate string aSb?
3) (S11) Is aSb
L(ABG)? Why or why not?
4) (S12) How do
Module 30
EQUAL language
Designing a CFG Thinking recursively
1
EQUAL language
Designing a CFG
2
EQUAL
EQUAL is the set of strings over {a,b} with an equal number of a's and b's Strings in EQUAL include
aabbab bbbaaa abba
Strings in {a,
Module 13 Worksheet
In Class Questions
1) (S5) Consider the following two problems. Define what a natural notion of size might
be for these problems.
Shortest path problem
Input: Graph G=(V,E)
2 nodes s and t
Task: Output the shortest path from
node s to
Module 13
Studying the internal structure of REC, the set of solvable problems
Complexity theory overview Automata theory preview
Motivating Problem
string searching
1
Studying REC
Complexity Theory Automata Theory
2
Current picture of all
CSE 460  Computability and Formal Language Theory Homework 7 Due: 3PM, Thursday, October 25, 2007 This homework is based on material from Modules 1417. 1. Describe the set of strings that end up in each state of the following FSA. Think binary. [2,
Module 11 Worksheet In Class Questions 1) (S7) The variable x is an input to what program (problem) and thus consists of what?
2) (S7) The variable PT(x) is an input to what program (problem) and thus consists of what?
3) (S9) What would happen if
Simulating 2 FSA's with 1 FSA
Why the algorithm works!
Purpose
This presentation attempts to give the reader some intuition as to why the algorithm which takes as input two FSA's and produces as output an FSA which "simulates" both input FSA's on a
Module 29 Worksheet
In Class Questions
1) (S5) What is wrong with the following parse tree for ( ) from BALG?
S

(S)

λ
2) (S8) Draw the corresponding parse tree (see slide 8).
3) (S8) Draw the corresponding rightmost derivation (see slide 8).
4) (S8) D
Module 20 Worksheet
In Class Questions
1) (S4) Draw the computation graph of the given NFAλ on the input string ab.
Take home review questions
1) What is the key difference between a “regular” NFA and an NFAλ?
2) Consider the following NFAλ.
I
λ
II
a,λ
Module 9
Closure Properties
Definition Language class definition
set of languages
Closure properties and firstorder logic statements
For all, there exists
1
Closure Properties
A set is closed under an operation if applying the operation to
Module 12
Computation and Configurations
Formal Definition Examples Configuration
Definitions
Functional Definition Given the original program and the current configuration of a computation, someone should be able to complete the computation
Module 15 Worksheet In Class Questions 1) (S7) How much of M = (Q, , q0, A, ) can you determine from a specification of ? For example, what components of M can you determine from {(1,a,2), (1,b,2), (2,a,1), (2,b,2)}?
2) (S12) What is the functional
Simulating 2 FSA's with 1 FSA
Purpose
This presentation presents an example execution of the algorithm which takes as input two FSA's and produces as output an FSA which "simulates" both input FSA's on any input string Algorithm Specification Inp
Module 34
Showing CFL's not closed under set intersection and set complement
1
Nonclosure Properties for CFL's
2
CFL's not closed under set intersection
How can we prove that CFL's are not closed under set intersection?
3
Counterexample
What
Module 26
Pumping Lemma
A technique for proving a language L is NOT regular What does the Pumping Lemma mean? Proof of Pumping Lemma
1
Pumping Lemma
How do we use it?
2
1
Pumping Condition
A language L satisfies the pumping condition if:
t
Simulating 2 FSA's with 1 FSA
Why the algorithm works!
Purpose
This presentation attempts to give the reader some intuition as to why the algorithm which takes as input two FSA's and produces as output an FSA which "simulates" both input FSA's on a
NFA to NFA conversion
Purpose
This presentation presents an example execution of the algorithm which takes as input an NFA with transitions and produces as output an equivalent NFA without transitions Algorithm Specification
Input: NFA M1 with