Strings that are not substrings but are subsequences...WHAT?!

Here we look at the language of all strings within a regular language L that, given a finite language L', (1) no string in L contains a substring that is a string in L', and (2) for each string in L', it is a subsequence of a string in L. The goal is to show the resulting language is regular.

Yes, I know it sounds complicated, but the idea is very simple. We just show that (1) and (2) are regular, and then the result is regular. For both we make regular expressions that allow us to conclude that each is regular. Because L' is finite, even though (2) seems more complicated, it is very easy to make a regular expression for it.

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▶ADDITIONAL QUESTIONS◀

1. What if L' were infinite?
2. What if we wanted the strings that are either in (1) or (2), but not both?

▶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 ... https://www.youtube.com/watch?v=Ms3zpTbqmBI