Are there DFAs for Concatenation and Star?

Here we look at the question of whether there are DFAs for concatenation or star. We saw that concatenation and star are two regular operations, so it's natural to ask if A, B are regular, then AB is regular also (or A* also regular)? The question turns out to be difficult to answer, because one would need to magically "guess" where the split of the string is, as well as "jumping" to the other DFA to read the rest of the string without consuming a character.

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▶ADDITIONAL QUESTIONS◀

1. Can you find DFAs for concatenation and star?

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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.

▶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 ... https://www.youtube.com/watch?v=a_koKXDCHUw