Introduction to Theory of Computation

00:11:34
https://www.youtube.com/watch?v=58N2N7zJGrQ

摘要

TLDRThe video introduces the 'Theory of Computation' course, which is fundamental to computer science. This course doesn't directly aid in programming but offers insights into the theoretical aspects of computing. Key topics include what can be computed mechanically, the efficiency of such computations, and the limitations of machines. The lecturer uses examples, like designing a machine to accept specific binary strings or validate Java code, to explore these concepts. The course covers several important layers: finite state machines (FSM), context-free languages (CFL), Turing machines, and undecidable problems. This structure helps students understand the capabilities and limitations of computational systems. The course is essential for grasping the science behind computer operations and understanding what sorts of problems machines can solve.

心得

  • 📚 Introduction to the Theory of Computation
  • 🖥️ Discusses computability and mechanical computation
  • 🔍 Examples include accepting binary strings and Java code
  • 💡 Highlights limits of computation and undecidability
  • 🏗️ Key layers: FSM, CFL, Turing machines
  • 🔍 Examines what computers can or cannot solve
  • 🧠 Course covers core theoretical aspects of CS
  • 🌀 Discusses problems that lead to infinite loops
  • 🔬 A foundational course in computer science
  • 🔗 Connections to compiler design and problem-solving

时间轴

  • 00:00:00 - 00:05:00

    Welcome to the first lecture on Theory of Computation. This course is fundamental and abstract in computer science, aimed at understanding what can be computed, the speed at which it can be done, and the space it requires. The lecture introduces the concept of theory of computation as a foundational course that helps understand historical perspectives in computer science, despite not focusing on practical programming skills. It explores what can be computationally solved mechanically and the limitations of machines in solving problems, using examples like designing machines to accept binary strings or validating Java code.

  • 00:05:00 - 00:11:34

    The lecture further explores the capabilities and limitations of computation using examples. It discusses the impossibility of creating a machine that accepts all valid Java codes and avoids infinite loops, illustrating computational limits. The subject involves designing machines that accept or reject inputs based on rules. The curriculum includes studying finite state machines, context-free languages, Turing machines, and undecidable problems, laying a path from simple computational models with limited memory to complex systems capable of high-level calculations and undecidable computational challenges.

思维导图

Mind Map

常见问题

  • What is the course 'Theory of Computation' about?

    The course covers the foundational and abstract concepts of computer science, focusing on what can be computed mechanically, how fast, and how much space it takes. It explains the theoretical aspects of computers, including problems they cannot solve.

  • What are some examples used in this lecture?

    Examples include designing a machine to accept binary strings ending in zero and building a system to validate Java code without entering infinite loops.

  • What are the key layers in the Theory of Computation?

    The layers include finite state machines (FSM), context-free language (CFL), Turing machines, and undecidable problems.

  • Why is the Theory of Computation important?

    It helps understand the theoretical foundations of computer science, including what computers can and cannot do.

  • Can a machine always determine if a Java code will enter an infinite loop?

    No, there is no mechanical method to guarantee a machine never enters an infinite loop.

查看更多视频摘要

即时访问由人工智能支持的免费 YouTube 视频摘要！
字幕
en
自动滚动:
  • 00:00:05
    hello everyone welcome to the first
  • 00:00:07
    lecture in the course theory of
  • 00:00:09
    computation in this lecture I will be
  • 00:00:11
    giving you an introduction to the course
  • 00:00:13
    theory of computation where we shall see
  • 00:00:16
    what this course is all about what can
  • 00:00:19
    we study from this course and what this
  • 00:00:22
    course has to offer all right so let's
  • 00:00:24
    get started so what is theory of
  • 00:00:28
    computation this theory of comput ation
  • 00:00:30
    is one of the most fundamental courses
  • 00:00:32
    of computer science this course is one
  • 00:00:34
    of the most fundamental as well as
  • 00:00:36
    abstract courses of computer science
  • 00:00:39
    which every computer scientist and
  • 00:00:40
    Engineers must
  • 00:00:42
    know this course is not going to help
  • 00:00:44
    you write programs or build a computer
  • 00:00:46
    as such but it will help you understand
  • 00:00:50
    how people have thought about computer
  • 00:00:52
    science as a science in the past 50
  • 00:00:55
    years okay so what does this mean and
  • 00:00:58
    what is it really about
  • 00:01:00
    so this subject is mainly about what
  • 00:01:03
    kind of things can you really compute
  • 00:01:05
    mechanically how fast can you do it and
  • 00:01:08
    how much space does it take to do
  • 00:01:10
    so okay so we know that in computer
  • 00:01:13
    science there are certain kind of
  • 00:01:15
    problems that a computer or a machine
  • 00:01:17
    can solve and also there are certain
  • 00:01:19
    kind of problems or things that a
  • 00:01:21
    machine cannot do or certain kind of
  • 00:01:24
    things that a computer cannot solve so
  • 00:01:26
    we shall be seeing all these kind of
  • 00:01:28
    things in this subject okay so we talked
  • 00:01:30
    about how fast and how much space does
  • 00:01:33
    it take to do so so let us just leave
  • 00:01:35
    these two points for a while and let us
  • 00:01:38
    just focus on about what kind of things
  • 00:01:40
    can you really compute
  • 00:01:42
    mechanically so to make this point clear
  • 00:01:45
    let us take a simple example so let's
  • 00:01:48
    say I want to design a machine that
  • 00:01:51
    accepts all binary strings that end in
  • 00:01:54
    zero I want to design a machine that
  • 00:01:58
    accepts all
  • 00:02:02
    binary
  • 00:02:05
    strings that end in zero so my machine
  • 00:02:11
    that I designed should accept all binary
  • 00:02:13
    strings that end in zero and should
  • 00:02:16
    reject all other strings that does not
  • 00:02:18
    end in zero okay so let me take an
  • 00:02:20
    example string here let's say 11 1 0 1 0
  • 00:02:24
    1 1 0 so this is my example string that
  • 00:02:27
    I have
  • 00:02:28
    here okay now now what I want to do is I
  • 00:02:33
    should check whether this string is
  • 00:02:34
    accepted by my machine so as a human
  • 00:02:37
    being how would I perform this task as a
  • 00:02:40
    human being I would just look at the
  • 00:02:41
    last digit and if I see that it is zero
  • 00:02:43
    I say yes I accept it or if I find that
  • 00:02:46
    it is equal to one I say no I reject it
  • 00:02:49
    so how would a machine do this a machine
  • 00:02:51
    would scan the last digit and if it
  • 00:02:55
    finds that it is equal to Zer it says
  • 00:02:59
    yes it is accepted
  • 00:03:00
    or if it finds that it is equal to one
  • 00:03:02
    it says no and it rejects it why because
  • 00:03:05
    our machine is supposed to accept all
  • 00:03:08
    binary strings that end in
  • 00:03:11
    zero okay so that was fairly a very
  • 00:03:14
    simple example now let us take another
  • 00:03:17
    example in this example I want to design
  • 00:03:20
    a machine that accepts all valid Java
  • 00:03:25
    code it
  • 00:03:27
    accepts all
  • 00:03:33
    valid Java
  • 00:03:37
    codes okay so what should my machine do
  • 00:03:40
    my machine should check the binary
  • 00:03:43
    equivalent of my codes when I write a
  • 00:03:46
    code in Java it should check the binary
  • 00:03:50
    equivalent of this codes and from this
  • 00:03:52
    binary equivalent it should tell whether
  • 00:03:55
    this came from
  • 00:03:57
    a valid piece of java code or it is
  • 00:04:02
    invalid okay so my question is is it
  • 00:04:05
    possible to design this kind of a
  • 00:04:07
    system the answer to this is absolutely
  • 00:04:10
    yes we can and the best example I can
  • 00:04:13
    give for this
  • 00:04:14
    is
  • 00:04:18
    compilers when we write a piece of code
  • 00:04:20
    into our compilers let's say that I'm
  • 00:04:22
    writing a piece of java code so I write
  • 00:04:25
    a piece of java code into my compiler
  • 00:04:27
    and when I compile that program if if I
  • 00:04:29
    have written that program correctly
  • 00:04:31
    without any mistakes the compiler
  • 00:04:33
    compiles that program and runs it
  • 00:04:35
    because it is valid on the other hand if
  • 00:04:40
    you have made some mistakes in that code
  • 00:04:42
    or if you have written something wrongly
  • 00:04:45
    then the compiler tells you that there
  • 00:04:46
    is an error and it does not run the
  • 00:04:48
    program because it is
  • 00:04:51
    invalid all right so we can we see that
  • 00:04:54
    it is very much possible to design this
  • 00:04:56
    kind of a system and from this example I
  • 00:04:59
    I think we got a slight hint that the
  • 00:05:02
    whole of compiler design it came from
  • 00:05:04
    this subject theory of
  • 00:05:07
    computation okay so I hope that was
  • 00:05:09
    clear now let's take another example now
  • 00:05:14
    in this example I want to design another
  • 00:05:17
    system
  • 00:05:18
    that that
  • 00:05:21
    accepts
  • 00:05:23
    all
  • 00:05:26
    valid Java
  • 00:05:28
    codes
  • 00:05:33
    and never
  • 00:05:36
    goes
  • 00:05:39
    into
  • 00:05:42
    Infinite loop I assume you know what is
  • 00:05:45
    the meaning of infinite Loop okay
  • 00:05:49
    so I want a machine that accepts all
  • 00:05:52
    valid Java codes and do not go into
  • 00:05:54
    Infinite Loop so is it possible to
  • 00:05:57
    design this kind of a system so from
  • 00:05:59
    this uh previous example we have found
  • 00:06:01
    that it is possible to design a system
  • 00:06:03
    that accepts all valid Java codes this
  • 00:06:06
    part is possible it's fine but we have
  • 00:06:08
    one more condition here and never goes
  • 00:06:10
    into Infinite Loop can I design a system
  • 00:06:14
    that never allows my code to go into an
  • 00:06:16
    infinite
  • 00:06:17
    Loop the answer to this is no I can
  • 00:06:21
    never design a system that
  • 00:06:23
    performs this
  • 00:06:26
    task okay so even if you design it you
  • 00:06:29
    would either get the wrong output or it
  • 00:06:32
    could run forever and give you no output
  • 00:06:34
    at all so this kind of a machine that
  • 00:06:38
    performs this kind of a task cannot be
  • 00:06:41
    designed okay so this third example has
  • 00:06:45
    given us an idea about what kind of
  • 00:06:47
    things can we not compute
  • 00:06:51
    mechanically okay I hope that was
  • 00:06:53
    clear so what is this subject all about
  • 00:06:57
    this Sub in this subject what we usually
  • 00:07:00
    do is that we have a we have a system or
  • 00:07:04
    a machine we design a machine and
  • 00:07:06
    suppose this is a machine and then we
  • 00:07:09
    send an input to this machine and then
  • 00:07:12
    the machine thinks about this input
  • 00:07:14
    based on some formula or based on some
  • 00:07:17
    rules and it either says yes and it
  • 00:07:20
    accepts the input or it rejects the
  • 00:07:22
    input so this is what we are going to
  • 00:07:25
    basically do in this subject we are
  • 00:07:28
    going to design systems or machines
  • 00:07:32
    which can take certain kind of inputs
  • 00:07:33
    and this machine will be based on some
  • 00:07:35
    rules and it should either accept the
  • 00:07:38
    input or reject the input so this will
  • 00:07:40
    be the thing that we'll be doing don't
  • 00:07:42
    worry even if it is a little unclear
  • 00:07:44
    right now when we take uh other examples
  • 00:07:46
    and when we start from the very Basics
  • 00:07:48
    from the following lectures it will all
  • 00:07:50
    become very
  • 00:07:51
    clear okay now now let us see what are
  • 00:07:55
    the layers or the levels in this subject
  • 00:07:57
    that we have to go through for that I
  • 00:08:00
    will show you a diagram over here so
  • 00:08:03
    here I have a small diagram showing the
  • 00:08:06
    layers or levels in this subject so in
  • 00:08:09
    the first layer we have
  • 00:08:12
    FSM so what is
  • 00:08:15
    FSM FSM stands for finite State
  • 00:08:20
    machine FSM stands
  • 00:08:24
    for
  • 00:08:27
    finite state
  • 00:08:31
    machine this FSM that is finite State
  • 00:08:34
    machine it is one of the simplest model
  • 00:08:38
    of computation it is the simplest model
  • 00:08:41
    of computation and it has a very very
  • 00:08:44
    limited amount of memory and it can
  • 00:08:47
    perform very lowlevel computations and
  • 00:08:50
    calculations okay this is the basic
  • 00:08:53
    building block of this subject this is
  • 00:08:54
    the first thing that we will be learning
  • 00:08:56
    so keep in mind FSM it will be starting
  • 00:08:59
    starting with it in the following
  • 00:09:00
    lectures from the very Basics so don't
  • 00:09:02
    worry even if you don't understand these
  • 00:09:03
    terms now we will make make it clear as
  • 00:09:06
    we go further and then the next layer we
  • 00:09:09
    have is
  • 00:09:11
    CFL CFL CFL stands
  • 00:09:15
    for
  • 00:09:17
    context
  • 00:09:20
    free
  • 00:09:22
    language context free language CFL
  • 00:09:25
    stands for context free language and CFL
  • 00:09:29
    is a little more powerful than FSM and
  • 00:09:33
    it can perform some more higher level of
  • 00:09:36
    computations as compared to finite State
  • 00:09:38
    machines okay uh and one thing to
  • 00:09:41
    remember here this language over here
  • 00:09:44
    this language here does not mean a
  • 00:09:45
    programming language okay when we in
  • 00:09:48
    computer science when we come across the
  • 00:09:50
    term language we often think oh this
  • 00:09:52
    means a programming language but no in
  • 00:09:54
    this subject here in this context free
  • 00:09:57
    language this language actually mean
  • 00:09:59
    means
  • 00:10:00
    a set of
  • 00:10:04
    strings a set of strings is what is
  • 00:10:06
    known as language it'll become clear
  • 00:10:08
    when we uh explain it further in the
  • 00:10:10
    following lectures so don't worry about
  • 00:10:11
    it and in the next layer we have
  • 00:10:14
    something known as touring machine
  • 00:10:16
    touring machine is a uh machine that can
  • 00:10:19
    perform high level computations and
  • 00:10:21
    calculations it was designed by alen
  • 00:10:23
    touring in 1940 and it is much much more
  • 00:10:26
    powerful as compared to context free
  • 00:10:28
    language and final State
  • 00:10:31
    machines okay and in the next layer we
  • 00:10:35
    have this undecidable this is labeled as
  • 00:10:37
    undecidable and why is that it is
  • 00:10:40
    because the problems that cannot be
  • 00:10:43
    solved mechanically those kind of
  • 00:10:46
    problems it falls under this undecidable
  • 00:10:48
    layer like for example above uh some
  • 00:10:51
    time back we saw an example about a
  • 00:10:53
    problem that could not be solved
  • 00:10:55
    mechanically so those kind of problems
  • 00:10:58
    that fall they fall under this
  • 00:11:00
    undecidable layer okay so these are the
  • 00:11:03
    layers that we have to go through and we
  • 00:11:05
    will be starting with finite seit
  • 00:11:06
    machines FSM in the next uh following
  • 00:11:10
    lectures so we'll be start with the very
  • 00:11:11
    Basics so don't worry even if you don't
  • 00:11:14
    understand this terms that we used here
  • 00:11:16
    it will become very clear as we start
  • 00:11:18
    from the very Basics from the next
  • 00:11:20
    lecture onwards so thank you for
  • 00:11:26
    [Music]
  • 00:11:28
    watching
  • 00:11:30
    [Music]
标签
  • Theory of Computation
  • Computer Science
  • Finite State Machines
  • Context-Free Languages
  • Turing Machines
  • Computability
  • Mechanics
  • Java Code
  • Binary Strings
  • Undecidability