Here we show that the AMBIG_CFG problem is undecidable, which asks if a given context-free grammar is ambiguous. We reduce from the Post correspondence problem.
▶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=j_BDMeZI4kk
Here we show that if A and B are regular, then A/B is regular, where this is the set of all strings w such that wx is in A for some x in B. We show that this is regular by making a DFA for it by changing the final states of A. The new final states are going to be the ones where reading ANY string from B will result in an ORIGINAL final state of A. This is not a "constructive" method for a DFA, but this shows that the DFA exists, which is all that is needed.
#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem
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▶ADDITIONAL QUESTIONS◀
1. Can it be possible that A/B is equal to B/A (without using trivial examples of A, B)?
▶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 two different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=mtURMW_VSUA
Here we look at my Java code for processing an order for a hypothetical In-And-Out customer by building a menu for it. Let's just say that they shouldn't hire me.
Easy Theory Website: https://www.easytheory.org
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▶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=6nrfXo1hTzU
Here we prove that the language of all strings with more 1s than 0s is not regular. The trick here is to structure the string "well" (i.e., it's easy to add characters, so we want 0s first instead of 1s) and then apply the pumping lemma in the usual way.
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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=3CN6QCQYFpk
Here we celebrate getting 500 thousand views on the channel. We also do a pumping lemma problem example, and a cool result on the number of strings a DFA accepts of a certain length.
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
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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=HLox-pqUecU
Here we start a new series on complexity theory, which is asking the question about how efficiently we can solve various problems. We classify languages into sets based on certain properties (poly-time solvable, randomized, etc.) and see how the sets relate to each other.
Intro Theory of Computation: https://www.youtube.com/watch?v=xilR6Ky6JhU&list=PLylTVsqZiRXN3Q86XJV6OWOmIzvVZs75E
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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=r49Yqtrx1tU
Here we show that the language of all strings of the form 0^2n 1^n is not regular. The proof is very similar to the 0^n 1^n language.
Easy Theory Website: https://www.easytheory.org
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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=vV6goaEFxyQ
Here we look at a question from the GATE 2019 exam, about which of the four given languages is a context-free language. Instead of just giving the answer, we prove why the answer is what it is. For three of the languages, we are able to create a context-free grammar for each, and for the fourth, we appeal to the pumping lemma for context-free languages to prove that it is not a context-free language.
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▶ADDITIONAL QUESTIONS◀
1. Is there another way to prove that the language is not a CFL?
2. Are all of these languages decidable?
3. Which of these languages is regular?
▶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
a
...
https://www.youtube.com/watch?v=P08mxzF9pjM
Here we look back at one of the most amazing cheating stories in academia that I have ever witnessed (this time as a graduate student).
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◀
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=yYnRa7EJgOM
Here we show, with an example, that one can create a DFA directly from a regular expression using Brzozowski Derivatives. Therefore, no NFA is ever needed to do the conversion. We first set the start state to be the original regex, and its transitions correspond to taking partial derivatives of that regex with each of the input characters. If a new regex is formed that hasn't been seen before, then that transition goes to a new state. This is repeated until no new states are formed, and the final states are ones that can make the empty string (epsilon).
The original video is here: https://www.youtube.com/watch?v=s9EPoy9r-ok
#easytheory #gate #theory
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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=rcjR3--M7iM