lec 1 (automata theory)

8/9/2019 Lec 1 (Automata Theory)

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Lecture One:

Automata Theory

Automata Theory, Lecture 1, slide 1

Amjad Ali


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Automata theory

The word Automata is the plural of automaton"which simply means any machine.

automata theory is the study ofabstract machinesand problems they are able to solve.

Automata theory is closely related to formal languagetheory as the automata are often classified by theclass offormal languages they are able to recognize.


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Abstract Machine

An abstract machine, also called an abstract computer,is a theoretical model of a computer hardware or software

system used inAutomata theory.

Abstraction of computing processes is used in both thecomputer science and computer engineering disciplines andusually assumes discrete time paradigm.

abstract machines are often used in thought experimentsregarding computability or to analyze the complexity ofalgorithms


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Models

The construction of models is one of the

essentials of any scientific discipline.

The usefulness of a discipline is often

dependent on the existence of simple,

yet powerful, theories and laws.



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Automaton An automaton is an abstract model of a digital

computer

It has a mechanism to read input (string over agiven alphabet, e.g. strings of 0s and 1s on 7= {0,1}) written on an input file.

A finite automaton has a set of states Its control moves from state to state in

response to external inputs



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Automaton With every automaton, a transition function is

associated which gives the next state in terms

of the current state An automaton can be represented by a graph in

which the vertices give the internal states andthe edges transitions

The labels on the edges show what happens (interms of input and output) during thetransitions

An automaton operates in discrete time frameAutomata Theory, Lecture 1, slide 7


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Components of an automaton Input file : Contains strings of input

symbols

Storage unit: consists of an unlimitednumber of cells, each capable of holdinga single symbol from an alphabet

Control unit: can be in any one of a finitenumber of internal states and can changestates in defined manner



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Transitions from start state to

end state

There are 4 objectsCabbage, Man, Wolf and

Goat on one bank and thereis a boat

All 4 have to cross the riverso that (C,G) or (W,G) arenot left at one place

Man rows the boat andtakes one at a time

Present state

M,C,G,W = J

final state

J= M,C,G,W

transition



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Intermediate states

Class assignment

(M,C,G,W=

J=..= (J=M,C,G,W

)



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Applications of Automata A variety of properties concerning the models,

grammars, and languages will be proven. The existence or non-existence of algorithms for

processing languages and language processors will beproven. These algorithms form the basis of tools for processing

languages, e.g., parsers, compilers, assemblers, etc. Other algorithms will form the basis of tools that

automatically construct language processors, e.g.,yacc, lex, etc. Note that our perspective will be similar to, yet different from

a compiler class.

Additionally, some things will be proven to be non-computable, e.g., the enhanced compiler.



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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 thesekinds of questions:

What kinds of problems can a given type of devicesolve?

What things are impossible for this kind of device?

Is one type of device more powerful than another?



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Some devices we will see

finite automata Devices with a finite amount of memory. Used tomodel small computers.

push-down

automata

Devices with infinite memory that can be accessedin a restricted way.

Used to model parsers, etc.

Turing Machines Devices with infinite memory. Used to model anycomputer.

time-bounded

Turing Machines

Infinite memory, but bounded running time.

Used to model any computer program that runs in a

reasonable amount of time.



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Some highlights of the course Finite automata

We will understand what kinds of things a device

with finite memory can do, and what itcannotdo Introduce simulation: the ability of one device toimitate another device

Introduce nondeterminism: the ability of a device to

make arbitrary choices Push-down automata

These devices are related to grammars, whichdescribe the structure of programming (and natural)languages



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Some highlights of the course

Turing Machines This is a general model of a computer, capturing

anything we could ever hope to compute

But there are many things thatcomputers cannotdo:



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Some highlights of the course Time-bounded Turing Machines

Many problems are possible to solve on acomputer in principle, but take too muchtime in practice

Traveling salesman: Given a list of cities,

find the shortest way to visit them andcome back home


lec 1 (automata theory)

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