CS301-Automata Theory
Lecture # 04 Dening Languages & Kleen
Closures
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Review
Finite set of fundamental units out of which
we build structure
CS317-Automata Theory
Fall 2014
Humaira Ehsan
Introduction
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Phone #: 378
Email: humaira.ehsan@nu.edu.pk
Walk in Hours: Tuesday & Thursday 9:30-10:30
Course Lectures will be available on SLATE
CS 317 | L01-Introduction
Humaira Ehsan | Fall 2
CS301-Automata Theory
Lecture # 05 Recursive Deni?on
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Dening Languages Con?nued
Recursive Deni?on
The following three steps are used in
recursi
CS301-Automata Theory
Lecture # 12 Kleenes Theorem
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Unification
We have learned three separate ways to define a language:
by regular expression
by finite automaton
by transition grap
CS301-Automata Theory
Lecture # 03 Mathema8cal Preliminaries II
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Func8ons and Rela8ons (3)
In a simple form, a relaAon can be represented
as a
CS301-Automata Theory
Lecture # 06 Regular Expressions
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Dening Languages by Another
New Method
Language-Dening Symbols
We now introduce the use
CS301-Automata Theory
Lecture # 09 Finite Automata
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
FA and Languages
We will study FA from two dierent angles:
1. Given a language, can we
CS301-Automata Theory
Lecture # 10 Transi:on Graphs
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Review: FA
Each FA has the following properAes (among
others):
For each state x and e
CS301-Automata Theory
Lecture # 07 Regular Expressions
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Example
The following equivalences show that we should not treat
expressions as algebraic
CS301-Automata Theory
Lecture # 10 Transi:on Graphs
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Transi:on Graphs
Relaxing the RestricBon on Inputs
Looking at TGs
Generalized TransiBon G
CS301-Automata Theory
Lecture # 08 Finite Automata
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Deni=on
A nite automaton is a collec?on of three things:
1. A nite set of states, one o
CS301-Automata Theory
Lecture # 13 Kleenes Theorem
Fall 2014
Humaira Ehsan
Adapted from slides of NUCES Fall 2013 course
Kleenes Theorem
Thus, to prove Kleenes theorem, we need to prove 3 parts:
Part 1: Every
The main issue with the single point estimate is that that give a point estimate. So we can get that
the required estimate of the population parameter is that particular value. But in most of the real
life situations, as stated by my managers, its not pos
Managers are sometimes funny to me. When they ask when they can expect something to be done and you give them a
specific answer, they kind of look at you funny. They arent expecting something to take you 3 hours, they would rather hear
you say that it is
._ l.
7.28. In each case, the grammar with the given productions does not satisfy the
LL13) property. Find an equivalent LLtl) grammar by factoring and
eliminating left recursion. '.
C. S —l* 31$ 31 H)— S1Tltl't'? T —> GT'FJDIHI}
7.28. {0:}
8H51$ 51—5obX
Prove that the following languages are not regular using the pumping lemma.
:1. L = {Unlmﬂn | m,n 2 0}.
Answer.
To prove that L is not a regular language, we Will use a proof by contradiction. Assume
that L is regular. Then by the Pumping Lemma for Regula
EXERCISES
ﬁ.1. In each case, say what language is generated by the content-free grammar
with the indicated productions.
i1.
3 -> ra.5'ﬂ'_b.3bl!t
S->aSn|bSb|cr[b
SanSblenln
S—>a5cr!b3blmiblen
A+aﬂa|h.4blaiblh
{See Example 5.3.)
smsmsua
S—FSSIIJSIH
E—> SeSl
Write the Regular Expressions of following languages.
1. (a+b).(a+b) corresponds to the language cfw_aa, ab, ba, bb, that is the set of strings of
length 2 over the alphabet cfw_a, b.
2. (a+b)* corresponds to the set of all strings over the alphabet cfw_a
National University of Computer & Emerging Sciences
Assignment # 3
Probability and Statistics (CS)
Date of submission: 23, 24th Nov, 15
Question 1: A random sample of 100 automobile owners in the state of Virginia shows that an
automobile is driven on ave
National University of Computer & Emerging Sciences
Assignment # 2
Probability and Statistics (CS)
Date of submission: 26th October, 15
Question 1: The number of hardware failures, X, and the number of software failures, Y, on any
day in a small computer
National University of Computer & Emerging Sciences
Assignment # 1
Submission date: 10th September, 15
Probability and Statistics (CS)
Late submissions will not be accepted.
Question 1: The following performance scores out of 110 have been recorded for 25