Does the NFA to DFA conversion always make more states?

Here we look at the question of whether the NFA to DFA conversion always makes more states or not. We show that sometimes the conversion can yield the same number of states, and sometimes even fewer states! The essential idea behind having more states is having "missing" transitions; the second for having the NFA already be a DFA; and the third exploiting epsilon closure.
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▶ADDITIONAL QUESTIONS◀
1. Can you do an example of (3) from the video without using epsilon transitions?
2. How large can the DFA be in relation to the NFA, in general?
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▶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.
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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
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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
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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
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(like whether it performs addition of 16-bit registers correctly).
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On the other hand, most problems that ask properties about Turing machines
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This CZcams 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,
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C program will halt on a particular input. To prove something is possible is, of course, challenging.
But to show something is impossible is rare in computer
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Next video! Is Do(L) or Sq(L) regular? czcams.com/video/UCr8Zh_DTas/video.html