30577507 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, Lecture 1, slide 2
Automata theory The word “Automata“ is the plural of “automaton"
which simply means any machine.
automata theory is the study of abstract machines and problems they are able to solve.
Automata theory is closely related to formal languagetheory as the automata are often classified by theclass of formal languages they are able to recognize.
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Automata Theory, Lecture 1, slide 3
Abstract Machine An abstract machine, also called an abstract computer,
is a theoretical model of a computer hardware or software
system used in Automata 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 experiments regarding computability or to analyze the complexity of algorithms
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What do we do here? We construct abstract models of computers and
computations
These models possess the important featuresthat are common to both hardware and software
These features are essential to many of the
special and complex constructs we encounterwhile working with computers
Automata Theory, Lecture 1, slide 4
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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.
Automata Theory, Lecture 1, slide 5
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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 0’s and 1’s on S = {0,1}) written on an input file.
A finite automaton has a set of states
Its control moves from state to state inresponse to external “inputs”
Automata Theory, Lecture 1, slide 6
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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 frame Automata 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
Automata Theory, Lecture 1, slide 8
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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 = f
final state
f = M,C,G,W
transition
Automata Theory, Lecture 1, slide 9
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Intermediate states
Class assignment
(M,C,G,W=f) =………..= (f =M,C,G,W)
Automata Theory, Lecture 1, slide 10
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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 forprocessing languages and language processors will be
proven. 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.
Automata Theory, Lecture 1, slide 11
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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?
Automata Theory, Lecture 1, slide 12
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Some devices we will see
finite automata Devices with a finite amount of memory. Used to
model “small” computers.
push-downautomata
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 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.
Automata Theory, Lecture 1, slide 13
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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 it cannot do Introduce simulation: the ability of one device to
“imitate” 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 Automata Theory, Lecture 1, slide 14
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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 that computers cannotdo:
Automata Theory, Lecture 1, slide 15
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Some highlights of the course
Time-bounded Turing Machines
Many problems are possible to solve on a
computer 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
Automata Theory, Lecture 1, slide 16