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Theory of Automata. By: Fasee Ullah MS(IT) from SZABIST~ Islamabad 4 International Publications. Background. Twentieth century has given the most incredible shocks and surprises e.g, The rise and fall of communism Nuclear war Television Moon walks Inherited engineering etc .

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theory of automata

Theory of Automata

By: Fasee Ullah

MS(IT) from SZABIST~ Islamabad

4 International Publications

background
Background
  • Twentieth century has given the most incredible shocks and surprises e.g,
  • The rise and fall of communism
  • Nuclear war
  • Television
  • Moon walks
  • Inherited engineering
  • etc
background1
Background
  • Due to these great novels
  • Our development moved towards calculating device(s)
  • In the 1930’s, A. Turing studied an “ abstract machine”
  • That had all the capabilities of today’s machines(computers)
background2
Background
  • His abstract machine to define the upper bound and lower bound,
  • What could do and what couldn’t
  • was beneficial for turning machine
  • Also his conclusion is for today’s real machines
  • In the 1940’s and 1950’s, a machine invented
background3
Background
  • Studied by a number of researchers
  • Currently called “Finite Automata”
  • Proposed to model the brain function
  • Also used for variety of other purposes
  • In late 1950’s, the Linguist N. Chomsky
  • Introduced new formal grammar
  • Not defined for machines at that time
background4
Background
  • Has close relationship to abstract automata
  • Also important in development of software components and compilers
  • In 1969’s, S. Cook extended the theory of Turing “what could solve and what couldn’t”
  • S. Cook separated the solvable problems from those that can in principle be solved
  • Latter class of problems called “intractable or NP-hard”
background5
Background
  • Moore’s Law
  • says that chip density doubles every eighteen months, This means that memory sizes, processor power increases,
  • Number of transistors on a chip will double every year
year of introduction transistors
Year of IntroductionTransistors
  • 4004 1971 2,250
  • 8008 1972 2,500
  • 8080 1974 5,000
  • 8086 1978 29,000
  • 286 1982 120,000
  • Intel386™ processor 1985 275,000
  • Intel486™ processor 1989 1,180,000
  • Intel® Pentium® processor 1993 3,100,000
  • Intel® Pentium® II processor 1997 7,500,000
  • Intel® Pentium® III processor 1999 24,000,000
  • Intel® Pentium® 4 processor 2000 42,000,000
  • Intel® Itanium® processor 2002 220,000,000
  • Intel® Itanium® 2 processor 2003 410,000,000
background6
Background
  • Due to theoretical approaches, what computer scientists do today, e.g
  • Finite Automata, formal grammars, turning machines etc
  • Helps in design and construction of different softwares and what we can expect from our softwares
what is theory
What is theory?
  • The word “theory” shows to study abstraction of computing system
  • In Abstraction, irrelevant complications dropped
  • In order to isolate important concepts
what does automata mean
What does automata mean?
  • It is the plural of automaton, and it means “something that works automatically”
  • Automata heavily used in compilers, text editors, circuits, AI etc
  • Shows how simple operations performed with help of set theoretic operations on language
automaton
Automaton
  • It accepts input, produces output, may have some temporary storage and can make decisions in transforming the input into the output
what is automata theory
What is Automata Theory?
  • Study of mathematical models that describe with varying degrees of accuracy, parts of computers, types of mathematical computers and similar machines
  • The term Automata Theory, therefore, is used to refer to the study of such ‘Machines’ whose boundaries of capabilities could be predefined.
a simple computer
A simple computer
  • input: switch
  • output: light bulb
  • actions: flip switch
  • states: on, off

SWITCH

BATTERY

a simple computer1

SWITCH

BATTERY

A simple “computer”
  • input: switch
  • output: light bulb
  • actions:f for “flip switch”
  • states: on, off

f

on

start

off

f

different kinds of automata
Different kinds of automata
  • This was only one example of a computational device, and there are others
  • We will look at different devices, and look at these kinds of questions:
    • What kinds of problems can a given type of device solve?
    • What things are impossible for this kind of device?
    • Is one type of device more powerful than another?
some devices
Some devices

finite automata Devices with a finite amount of memory.Used to model “small” computers.

push-down automata Devices with infinite memory that can be accessed in a restricted way.

Used to model parsers, etc.

Turing Machines Devices with infinite memory.

Used to model any computer.

time-bounded Turing Machines Infinite memory, but bounded running time.Used to model any computer program that runs in a “reasonable” amount of time.

introduction to languages
Introduction to languages

There are two types of languages

  • Formal Languages (Syntactic languages)
  • Informal Languages (Semantic languages)
formal language
Formal Language
  • It is an abstraction of the general characteristics of programming languages
  • It consists of a set of symbols and some rules of formation of sentences
  • Sentences are formed by grouping the symbols
formal language1
Formal Language
  • A formal language is the set of all strings permitted by the rules of formation
  • Study of formal languages is very useful in learning about the different programming languages
central concepts of automata theory
Central Concepts of Automata Theory
  • Three basic concepts
    • Alphabet --- a set of symbols
    • Strings --- a list of symbols from an alphabet
    • Language--- a set of strings from the same alphabet
central concepts of automata theory1
Central Concepts of Automata Theory
  • Alphabets
  • An ALPHABET is a nonempty set of symbols
  • It is denoted by S
  • Example:

S = {a,b}

where a and b are symbols

central concepts of automata theory2
Central Concepts of Automata Theory
  • Strings are constructed from the individual symbols
  • Strings are finite sequences of symbols from the alphabet
  • Example : aabba, ababaaa, abbbaaa, etc are the strings formed by t he symbols of the alphabet
central concepts of automata theory3
Central Concepts of Automata Theory

Assumptions

  • Lower case letters a,b,c,… are used for elements of the alphabet
  • Lower case letters u,v,w,… for string names eg w=aabbaba
  • This indicates that w is a string having specific value aabbaba
central concepts of automata theory4
Central Concepts of Automata Theory

Concatenation of the strings

  • Two strings are concatenated by appending the symbols of one string to the end of the other string
  • Example u=aaabbb

v=abbabba

Concatenated string uv=aaabbbabbabba

reverse of the string
Reverse of the string
  • The reverse of a string is obtained by writing the symbols in reverse order.
  • Example

wR = anan-1an-2……………a0

Where w=a0a1a2……………an

length of the string
Length of the string
  • The length of the string is the number of symbols in the string
  • |w| = 5 if w = aabaa
  • Empty String has no symbols and is denoted by l
  • |l| = 0
s and s
S+andS*
  • S is an alphabet
  • S* is the set of allstrings obtained by concatenating zero or more symbols fromS
  • S ={a,b,c}
  • S*={e, a,b,c,aa,ab,ac,ba,bb,bc,ca,cb,cc,aaa,…}
slide30
S+
  • S+ is the set of allstrings obtained by concatenating one or more symbols
  • S ={y}
  • S+ ={y,yy,yyy,yyyy,…}
language
Language
  • A set of strings of characters from alphabet

Grammar

  • Set of rules defining a language
  • Enable us to decide in a finite time
  • Given string of alphabet is or isn’t in the language.
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