Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Names are listed in alphabetical order by surname. Platinum: Micah Wood Silver: Dolev Abuhazira, Simone Glinz, Timmy Gy, Josh Hibschman, Patrik Keinonen, Travis Schnider, and Tao Su
▶SEND ME THEORY QUESTIONS◀ ryan.e.dougherty@icloud.com
▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes. ... https://www.youtube.com/watch?v=OC9UztB071E
Here we make an important video intended for a general audience about theoretical computer science, namely about what it even is, and giving several reasons for why it is important. We first give an introduction about the subject, by giving some definitions of "theory" and "computer science". Then I highlight the need for why precise writing and formalism are necessary. I then discuss the Collatz conjecture and give an example program to find counterexamples, highlighting that if we had a magical program to solve whether an arbitrary program halts, then we could in principle solve the conjecture.
Then I discuss the halting problem, and show that it is unsolvable by any computer by means of a proof by contradiction. Additionally, I give a brief sketch on why there are more real numbers than natural numbers, which implies that there are more problems to solve (corresponding to real numbers) than there are programs to solve them (corresponding to natural numbers). And finally I give four possible ways of "dealing" with unsolvable problems.
All music was created by and attributed to bensound: https://www.bensound.com/
Chapters:
0:00 - Chapter 1: Intro
2:19 - Chapter 2: What is Theory of Computer Science?
8:02 - Chapter 3: The Need for Formalism
10:20 - Chapter 4: Computer Program Setup
11:31 - Chapter 5: An Example Program
17:05 - Chapter 6: The Halting Problem
24:45 - Chapter 7: Natural and Real Numbers
27:43 - Chapter 8: How to Deal with Unsolvable Problems
30:53 - Chapter 9: Conclusion
Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below.
Dolev Abuhazira, Josh Hibschman, Micah Wood, Morgan Jones, Patrik Keinonen, Simone Glinz, Tao Su, Timothy Gorden, unit220, Valentine Eben
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
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If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=7GWP0oP4_Vc
Here we prove Rice's Theorem using the Recursion Theorem (https://www.youtube.com/watch?v=iXpp5X6WPkE&ab_channel=EasyTheory). The idea is very simple: have the machine obtain its own description, and then simulate itself based on whether or not it has the property, but with a "different" machine that has the opposite property. Specifically, if A has the property, and B does not, then if we find our own machine does have the property, we simulate B on the same input, not A (and simulate A if we do not have the property). This yields a contradiction about the property itself being decidable.
What is Rice's Theorem? It is a result that shows a lot of languages are undecidable using simple criteria, involving whether the language is nontrivial (not empty and not everything), and if the language involves Turing Machines and the criteria to be in the language is based on that of the TMs. See https://www.youtube.com/watch?v=kr7n_3LpWhc&ab_channel=EasyTheory for more details.
Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Names are listed in alphabetical order by surname.
Platinum: Micah Wood
Silver: Josh Hibschman, Timmy Gy, Patrik Keinonen, Travis Schnider, and Tao Su
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Youtube Live Streaming (Sundays) - subscribe for when these occur.
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=gZU4Vz4U-5o
Here we give an example of a language that cannot be shown to be non-regular using the "standard" pumping lemma, and then prove a more "generalized" version that works for this language.
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
#easytheory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
Social Media:
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Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
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If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=fyBtApg4SZ0
Here we show that the A_NFA language is decidable. Note that this language has all pairs M, w where M is an NFA and w is a string such that M accepts w. We cannot just simulate M on w since there are choices. We then convert M into an equivalent DFA, and ask the decider for A_DFA the same question.
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
#easytheory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
Social Media:
Facebook Page: https://www.facebook.com/easytheory/
Facebook group: https://www.facebook.com/groups/easytheory/
Twitter: https://twitter.com/EasyTheory
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
Gold Supporters: Micah Wood
Silver Supporters: Timmy Gy
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=0KPwNmIdqXk
Here we give some problems about dynamic programming.
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
#easytheory #gate #theory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
Social Media:
Facebook Page: https://www.facebook.com/easytheory/
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Merch:
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If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
Gold Supporters: Micah Wood
Silver Supporters: Timmy Gy
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=O-iWiiy18Sw
Here we make a context-free grammar (CFG) for the language of all strings of the form 0^n 1^n 2^m 3^m, where n, m are at least 0. Note that we have essentially the same problem twice, and both problems are adjacent to each other. Since m and n are independent of each other, we can just make a small CFG for each, and then put them together with concatenation.
Easy Theory Website: https://www.easytheory.org
Discord: https://discord.gg/SD4U3hs
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about it. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
The views expressed in this video are not reflective of any of my current or former employers.
...
https://www.youtube.com/watch?v=Qp3fvwDNwZo
Here we give a (faulty) proof that all languages are regular. We use the basic notions and concepts related to regular languages to give a "proof" of this fact. Can you spot the error(s)?
Patreon: https://www.patreon.com/easytheory
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If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ADDITIONAL QUESTIONS◀
1. Can you prove something about the resulting NFA/DFA if you were to construct this using the product construction directly?
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.
▶ABOUT THIS CHANNEL◀
The theory of computation is perhaps the fundamental
theory of computer science. It sets out to define, mathematically, what
exactly computation is, what is feasible to solve using a computer,
and also what is not possible to solve using a computer.
The main objective is to define a computer mathematically, without the
reliance on real-world computers, hardware or software, or the plethora
of programming languages we have in use today. The notion of a Turing
machine serves this purpose and defines what we believe is the crux of
all computable functions.
This channel is also about weaker forms of computation, concentrating on
two classes: regular languages and context-free languages. These two
models help understand what we can do with restricted
means of computation, and offer a rich theory using which you can
hone your mathematical skills in reasoning with simple machines and
the languages they define.
However, they are not simply there as a weak form of computation--the most attractive aspect of them is that problems formulated on them
are tractable, i.e. we can build efficient algorithms to reason
with objects such as finite automata, context-free grammars and
pushdown automata. For example, we can model a piece of hardware (a circuit)
as a finite-state system and solve whether the circuit satisfies a property
(like whether it performs addition of 16-bit registers correctly).
We can model the syntax of a programming language using a grammar, and
build algorithms that check if a string parses according to this grammar.
On the other hand, most problems that ask properties about Turing machines
are undecidable.
This Youtube channel will help you see and prove that several tasks involving Turing machines are unsolvable---i.e., no computer, no software, can solve it. For example,
you will see that there is no software that can
...
https://www.youtube.com/watch?v=gPyBg6FN1pE
Here we look at two languages Do(L) vs. Sq(L), where Do(L) is the set of strings wx where w, x are in L, and Sq(L) is the set of ww where w in L. We show that indeed these two languages are not always the same. Further, we show that Do(L) is always regular whenever L is, and Sq(L) is not always regular, even when L is.
Patreon: https://www.patreon.com/easytheory
Facebook: https://www.facebook.com/easytheory/
Twitter: https://twitter.com/EasyTheory
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ADDITIONAL QUESTIONS◀
1. What if L is not regular? Is Do(L) always not regular? Sq(L)?
2. For what languages L is Do(L) = Sq(L)?
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.
▶ABOUT THIS CHANNEL◀
The theory of computation is perhaps the fundamental
theory of computer science. It sets out to define, mathematically, what
exactly computation is, what is feasible to solve using a computer,
and also what is not possible to solve using a computer.
The main objective is to define a computer mathematically, without the
reliance on real-world computers, hardware or software, or the plethora
of programming languages we have in use today. The notion of a Turing
machine serves this purpose and defines what we believe is the crux of
all computable functions.
This channel is also about weaker forms of computation, concentrating on
two classes: regular languages and context-free languages. These two
models help understand what we can do with restricted
means of computation, and offer a rich theory using which you can
hone your mathematical skills in reasoning with simple machines and
the languages they define.
However, they are not simply there as a weak form of computation--the most attractive aspect of them is that problems formulated on them
are tractable, i.e. we can build efficient algorithms to reason
with objects such as finite automata, context-free grammars and
pushdown automata. For example, we can model a piece of hardware (a circuit)
as a finite-state system and solve whether the circuit satisfies a property
(like whether it performs addition of 16-bit registers correctly).
We can model the syntax of a programming language using a grammar, and
build algorithms that check if a string parses according to this grammar.
On the other hand, most problems that ask properties about Turing machines
are undecidable.
This Youtube channel will help you see and prove that several tasks involving Turing machines are unsolv
...
https://www.youtube.com/watch?v=UCr8Zh_DTas
The channel is now sponsored by a single bohemian crystal! Prepare to see more advertisements about this crystal.
Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below.
Dolev Abuhazira, Josh Hibschman, Micah Wood, Morgan Jones, Patrik Keinonen, Simone Glinz, Tao Su, Timothy Gorden, unit220, Valentine Eben
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
The views expressed in this video are not reflective of any of my current or former employers.
...
https://www.youtube.com/watch?v=3KZuONwBCww