Here we give two (hard) problems on the CYK algorithm. The main video is here: https://www.youtube.com/watch?v=N8d4kkfxM-s. For more information about CFGs and CNF, check out the following playlists:
▶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=ZGDqiCS4K1s
Here we show that determining if a Turing Machine state is "useless" is undecidable.
Easy Theory Website: https://www.easytheory.org
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Gold Supporters: Micah Wood
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▶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=PvdnxMmd2lA
Here we show off my real college grades.
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
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▶SEND ME THEORY QUESTIONS◀
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▶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=JP7ZvfQoRkA
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
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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
▶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
Thanks for supporting the channel and letting us hit 20k subscribers and over 2 million total views!
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=fjD0fJKt0Ok
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)?
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▶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 show that the "universality" problem for context-free grammars is undecidable. It is similar to the E_LBA video but we instead embed strings NOT encoding "reversed" accepting computation histories into the CFG.
What is a context-free grammar? It is a set of 4 items: a set of "variables," a set of "terminals," a "start variable," and a set of rules. Each rule must involve a single variable on its "left side", and any combination of variables and terminals on its right side. See https://www.youtube.com/watch?v=h1OSmLSacNA&ab_channel=EasyTheory for more details.
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
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Youtube Live Streaming (Sundays) - subscribe for when these occur.
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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=L9AKRVBSpYQ
Here we show that the conversion from multi-tape to single-tape Turing machines encounters (at most) a quadratic slowdown in the runtime.
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
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#easytheory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
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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=FgOtJVcYTfU
Here we show the problem of checking if a Turing Machine has regular language is undecidable (or CFL as its language), called Regular_TM. The idea is similar to showing E_TM undecidable in that we suppose it is decidable, then build a decider for A_TM.
What is a Turing Machine? It is a state machine that has a set of states, input, tape alphabet, a start state, exactly one accept state, and exactly one reject state. See https://www.youtube.com/watch?v=j0bIxPqlYLE&ab_channel=EasyTheory for more details.
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
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#easytheory
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=zo3kyFumkws
Here we show that the Path problem for graphs is in P, the problem of determining if a directed graph G has an s-t path (a way of picking vertices starting at s and ending at t).
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
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Patreon: https://www.patreon.com/easytheory
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#easytheory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
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▶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=sOXEiBWTBRU