2 turing machine (formal definition) mp4

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Hello, everyone.
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Welcome to the next lecture.
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In the course and theory of Atom meta.
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In this lecture we will discuss about the
formal definition of a Turing machine.
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In the previous lecture we studied about
the the introduction of a Turing machine,
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and now we will see how can we
formally define a Turing machine?
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All right.
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So Turing machine can be defined
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as set of seven tuples, which are Q,
Sigma, Tau, Delta, Q, Naught, B, and F.
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Now let us see what these tuples are.
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The first one is Q, which is
the known empty set of stats.
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So you already know that also in finite
state machine and pushdown Automata,
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this Q tuple is used to represent
the non empty set of States.
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And then we have Sigma and Sigma.
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Also, just like in other machines, it
represents the non empty set of symbols.
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Or we can say it is the set of input
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symbols that we have
in our Turing machine.
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Then we have Tau.
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Now Tau is something different from finite
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state machine and pushdown Automata, and
it is the nonimplice set of tape symbols.
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When we studied the introduction of Turing
machine, we saw that Turing machine has
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something known as tape,
and what is a tape?
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It is an infinite sequence of symbols.
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So these symbols are the tape symbols.
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They are represented by this tuple Tau.
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So it is non empty set of tape symbols.
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And then we have Delta,
which is the transition function.
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And we know that transition functions are
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also there in finite Automata and push
down Automata, and they are defined
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in different ways according
to how the machine works.
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So in case of Turing machine,
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the transition function is defined as Q
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cross Sigma, two Tau, cross R, R cross Q.


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Now let us see what this actually means.
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We know that in Turing machine we have
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States and we have input symbols,

and then we also have the tape symbols.
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So here this transition function means
that if we are in a particular state
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and we get a particular input symbol,
then we write something into the tape
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sequence and we move either
right or left on the tape.
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And then we go to the next step.
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So this is what we mean by the transition
function Delta in a Turing machine.
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This will be more clear to you when we
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will take our examples
in the next lecture,
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and then we have Q naught,
which is the initial state.
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Also, we have B, which is a plank symbol.
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So in introduction to Turing machine,
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I told you that in the tab we have
a special symbol card blank symbol,

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which is used to fill the empty
cells of a Turing machine.
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Also, this empty symbol does not belong
to the set of symbols Sigma,


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and then we have F,
which is the set of final States.
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So also in introduction,
I told you that there are two kinds
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of final States in Turing machine
that is accepted and reject state.
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So these are the seven tuples that are
used to define a Turing machine.
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Now let us discuss
the production rule of a Turing machine.
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Thus, the production rule of Turing
machine will be written as
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the input argument,
which have two arguments Q naught and A,
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and then the output have three
arguments Q one, Y and R.
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So what does this mean?
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This means that if we are in the initial
state Q naught, and if we get input symbol
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A, then we go to another state Q one,
and we write the input symbol Y onto our
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tab and we move to the right
or left on our table.
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Here it shows that we move to the right.
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So it was all about the formal
definition of a Turing machine.
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In the next lecture,


we will take two examples
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where we will construct Turing machines
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for languages which we will
discuss in the example.
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So thank you for watching

and see you in the next lecture.