WTF is a DFA Computation?

Here we go over the concept of a DFA computation, which can be a bit daunting. The idea is to record the states of the DFA one at a time as the string is being read. Instead of thinking about a set of states visited (which cannot distinguish what the string is), the sequence of states can actually tell us quite a bit about what the DFA did on the input string. I give some examples of computations on a given DFA, as well as some definitions that relate to strings.

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▶ADDITIONAL QUESTIONS◀

1. If the DFA has n states, what if the input string has length n?
2. Can you determine a necessary and sufficient condition for a DFA to accept an infinite number of strings?

▶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 ... https://www.youtube.com/watch?v=cOITFNI53ps